From b412e24b47281e66a263f64fb46dd2f896fc04a9 Mon Sep 17 00:00:00 2001 From: Yimin Zhong Date: Tue, 30 Jul 2024 06:37:48 +0000 Subject: [PATCH] Update Awards --- .../Awards-Algebra-and-Number-Theory-2024.csv | 43 ++++++++++--------- Analysis/Awards-Analysis-2024.csv | 20 +++++---- Combinatorics/Awards-Combinatorics-2024.csv | 9 ++-- Probability/Awards-Probability-2024.csv | 7 +-- Statistics/Awards-Statistics-2024.csv | 29 +++++++------ 5 files changed, 57 insertions(+), 51 deletions(-) diff --git a/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv b/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv index 1fd626b..cd6677f 100644 --- a/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv +++ b/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv @@ -1,20 +1,33 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2417981","Conference: New Trends in Geometry, Combinatorics and Mathematical Physics","DMS","ALGEBRA,NUMBER THEORY,AND COM, Combinatorics","08/01/2024","07/26/2024","Natalia Rojkovskaia","KS","Kansas State University","Standard Grant","James Matthew Douglass","07/31/2025","$17,500.00","","rozhkovs@math.ksu.edu","1601 VATTIER STREET","MANHATTAN","KS","665062504","7855326804","MPS","126400, 797000","7556, 9150","$0.00","The project supports travel of the US-based mathematicians to the international conference New Trends in Geometry, Combinatorics and Mathematical Physics, that will be take place October 21-25, 2024 at the CNRS center la Vieille Perrotine - Oleron, France. The goal of the project is to provide opportunities for early-career, US-based researchers and to boost the visibility and impact of US-based research. Early-career participants will benefit by acquiring new scientific knowledge from international experts and building long-term professional connections. Ultimately, participation of US-based researchers in the conference will have a positive impact on research projects conducted in the United States.

The scientific foci of the conference are differential geometry and algebraic combinatorics, with applications to mathematical physics. More specifically, applications of cluster algebras in integrable systems and mathematical physics. These applications will be a main topic of the conference, along with interactions between cluster algebras and complex geometry. Further applications of cluster algebras in physics will also be highlighted. Participants from a wide variety of backgrounds will serve to boost the exchange of methods, applications and new ideas, and will form foundations for continuing collaborations. This project is jointly funded by the Algebra and Number Theory and the Combinatorics programs. The conference website is https://indico.math.cnrs.fr/event/11259/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401358","Studies in Moduli Theory and Birational Geometry","DMS","OFFICE OF MULTIDISCIPLINARY AC, ALGEBRA,NUMBER THEORY,AND COM","08/01/2024","07/24/2024","Dan Abramovich","RI","Brown University","Standard Grant","James Matthew Douglass","07/31/2027","$250,000.00","","dan_abramovich@brown.edu","1 PROSPECT ST","PROVIDENCE","RI","029129100","4018632777","MPS","125300, 126400","9150","$0.00","The area of study of this project lies within algebraic geometry, the branch of mathematics devoted to geometric shapes called algebraic varieties, defined by polynomial equations. Algebraic geometry has significant applications in in coding, industrial control, computation, and in theoretical physics, where physicists consider algebraic varieties as a piece of the fine structure of our universe. One focus of this project is moduli theory, which studies a remarkable phenomenon in which the collection of all algebraic varieties of the same type is often manifested as an algebraic variety, called a moduli space, in its own right. Thus in algebraic geometry, the metaphor of thinking about a community of ""organisms"" as itself being an ""organism"" is not just a metaphor but a rigorous and quite useful fact. A second focus in this project is birational geometry, focusing here on resolution of singularities. Resolution of singularities is a fundamental procedure where ""bad"" points of an algebraic variety are removed and replaced by ""good"" points; it is the most powerful tool in the hands of a binational geometer. The project will provide research training opportunities for graduate students.

In more detail, regarding moduli spaces the PI will study the enumerative geometry of certain moduli spaces of surfaces, a decades-old challenge. In an area where birational geometry and moduli spaces overlap, the PI will continue to study the birational geometry of stack theoretic weighted blowups, a transformation that occurs frequently on moduli spaces that has proven instrumental in describing their geometry. Regarding resolutions of singularities, new algorithms will be developed for logarithmic resolution that are remarkably simpler than earlier ones, an algorithm for resolution in the presence of a nested family of foliations will be developed, and singularity invariants in positive characteristic will be studied that will lead to new insights into the formidable challenges of resolution in positive characteristic. These efforts will serve as platforms to directly mentor PhD students and young researchers, and for lectures and training programs reaching broader audiences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2402637","Conference: Connecticut Summer School in Number Theory 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/03/2024","Alvaro Lozano-Robledo","CT","University of Connecticut","Standard Grant","Adriana Salerno","03/31/2025","$29,967.00","Keith Conrad, Jennifer Balakrishnan, Christelle Vincent","alvaro.lozano-robledo@uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","126400","7556","$0.00","The Connecticut Summer School in Number Theory (CTNT 2024) is a conference for advanced undergraduate and beginning graduate students, to be followed by a research conference, taking place at at the University of Connecticut, Storrs campus, from June 10 through June 16, 2024. Even though the northeast of the United States is a hotspot for number theory research, there is no instructional school in number theory that occurs in this region. Undergraduate and beginning graduate students who are interested in number theory may only have had an elementary number theory course during college. The CTNT summer school will achieve several outcomes: expose undergraduate and beginning graduate students to accessible topics that are fundamental to contemporary number theory; provide an environment where students interested in number theory can meet each other and network with students, postdocs, and faculty from institutions where number theory is a strong research area; train a diverse group of students on topics of current importance in number theory; allow advanced undergraduates and beginning graduate students to attend a research conference in number theory; videotape the lectures and post them online at a dedicated website to reach as wide of an audience as possible later: https://ctnt-summer.math.uconn.edu/

CTNT 2024 will consist of a 4.5-day summer school followed by a 2-day conference. The summer school will have six mini-courses on topics important to contemporary number theory that are not available in a typical college curriculum, such as elliptic curves, reciprocity, adeles and ideles, and class field theory. The courses will be complemented with course projects, daily invited talks, evening problem sessions, and discussion panels about aspects of graduate school (both for those already in graduate school and those thinking of applying). The conference will consist of several sessions with research talks in number theory, arithmetic geometry, and related topics, and it will be an opportunity for young researchers to present their work.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401375","Collaborative Research: Small quantum groups, their categorifications and topological applications","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/15/2024","07/16/2024","Joshua Sussan","NY","CUNY Medgar Evers College","Standard Grant","Tim Hodges","06/30/2027","$201,860.00","","joshuasussan@gmail.com","1650 BEDFORD AVE","BROOKLYN","NY","112252017","7182706107","MPS","126400, 126700","","$0.00","This award funds research in an area of abstract algebra. Throughout history, mathematics and physics have had profound influences on each other. In the late 20th century, physicists discovered a deep connection between quantum physics and three-dimensional shapes, leading to the concept of topological quantum field theory (TQFT). While these 3D theories cannot fully describe our 4D universe, condensed matter physicists have found surprising applications of them in the field of quantum computing. In an effort to bridge the gap between these three-dimensional theories and our actual universe, Crane and Frenkel introduced a program called ""categorification"" in the late 1990s. This program aims to lift three-dimensional TQFTs to four dimensions, making it a more direct reflection of our physical reality. The PIs will involve students and postdocs in this research, with particular focus on students from underrepresented minorities.

The first significant development in categorification was the discovery of Khovanov homology. This is a powerful invariant of links whose graded Euler characteristic is the Jones polynomial. The investigators plan to use the technical machinery of hopfological algebra to extend a dual version of Khovanov homology to a homological invariant of three-dimensional manifolds whose graded Euler characteristic is the Witten-Reshetikhin-Turaev invariant. Ideally, this construction will be fully functorial, giving rise to an invariant of four-dimensional manifolds, while remaining computationally accessible. These invariants are expected be sensitive to smooth structures and should give insights into smooth topology not provided by gauge theoretic invariants like Donaldson and Seiberg-Witten invariants. This direction will build upon the investigators' previous work on categorified quantum groups and their representations at roots of unity. It is an open question of how to incorporate hopfological structures into Khovanov homology. This should lead to new homotopic notions. The investigators also plan on continuing to develop non-semisimple versions of three-dimensional topological quantum field theories with an eye toward applications to quantum computation. These non-semisimple invariants have certain topological advantages over their more classical semisimple counterparts. This line of research will also build upon their work on the centers of small quantum groups which has recently been an active area of research in geometric representation theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2414451","Collaborative Research: Conference: Special Trimester on Post-Quantum Algebraic Cryptography","DMS","ALGEBRA,NUMBER THEORY,AND COM, Secure &Trustworthy Cyberspace","09/01/2024","07/02/2024","Vladimir Shpilrain","NY","CUNY City College","Standard Grant","Tim Hodges","08/31/2025","$10,000.00","","shpilrain@yahoo.com","160 CONVENT AVE","NEW YORK","NY","100319101","2126505418","MPS","126400, 806000","025Z, 7556","$0.00","This award funds participation by US-based researchers in a special trimester on Post-quantum algebraic cryptography, to be held at the The Henri Poincare Institute, Paris, France, September 9 - December 13, 2024. In recent years, there has been a substantial amount of research on quantum computers -- machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. The thematic trimester program will bring together researchers and practitioners from academia, industry, and government institutions with diverse backgrounds to discuss quantum algorithms, quantum-safe cryptography, as well as deployment issues, from different angles.

This thematic trimester program will address various proposed cryptographic primitives that are currently considered to be quantum-safe. This includes lattice-based, multivariate, code-based, hash-based, group-based, and other primitives some of which were considered by NIST during their post-quantum standardization process. Our program will also address various functionalities of cryptographic constructions that are in high demand in real life. This includes fully homomorphic encryption that provides for private search on encrypted database and machine learning on encrypted data. Another functionality that is getting increasingly popular is outsourcing (a.k.a. delegating) computation of algebraic functions including group exponentiation, product of group exponentiations, etc., from a computationally limited client holding an input and a description of a function, to a computationally stronger entity holding a description of the same function. Further information can be found at the program website:
https://www.ihp.fr/en/events/post-quantum-algebraic-cryptography-paris

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401104","Combinatorics of Complex Curves and Surfaces","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/15/2024","01/24/2024","Philip Engel","IL","University of Illinois at Chicago","Standard Grant","James Matthew Douglass","07/31/2025","$67,057.00","","pengel@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126400","","$0.00","Two-dimensional tilings lie at a fulcrum connecting many areas of mathematics and physics. Easy to visualize and appealing in their simplicity, tilings have fascinated mathematicians at all levels, artists, architects, and the general public. This goals of this project are (1) to study tilings in the context of recent mathematical developments about algebraic curves and surfaces, exploring their connections to algebra, geometry, and representation theory, (2) to disseminate mathematical ideas to a wide audience and increase aesthetic and intellectual appreciation of mathematics in the general public, and (3) to develop an active and diverse community of young researchers, postdocs, and PhD students focusing on this circle of ideas.

One primary area of research will be modular toroidal compactifications of spaces of K3 surfaces. This project, joint with V. Alexeev, seeks to build extensions of the universal family of polarized K3 surfaces to the boundary of a toroidal compactification, extending previous work on degree 2 and elliptic K3 surfaces. The approach employs tilings of integral-affine structures on the sphere. The second primary research topic is moduli spaces of higher differentials. This project aims to study strata of higher differentials, their volumes, and the connection with enumeration of tilings. Joint work with P. Smillie explores decompositions of flat surfaces into Penrose-like tiles. The approach is novel, requiring a generalization of Hurwitz theory to one complex-dimensional leaf spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2404973","Conference: Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","05/29/2024","Aaron Lauda","CA","University of Southern California","Standard Grant","James Matthew Douglass","05/31/2026","$50,000.00","Milen Yakimov","lauda@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","90033","2137407762","MPS","126400","7556","$0.00","The award will provide funding for the sixth and seventh meetings of the Canada-Mexico-USA Conference Series in Representation Theory, Noncommutative Algebra, and Categorification. These meetings will take place at the Universidad Nacional Autónoma de México in Mexico City in June 2024 and at the University of Southern California in Los Angeles in August 2025. Representation theory is a branch of mathematics that studies symmetries of physical theories and mathematical objects. Often, the main objects in representation theory are only the shadows of richer structures that are recovered through deeper study. Noncommutative algebra is a related branch of mathematics that studies deformations of commutative objects found in quantum theories, representation theory, and geometry. The foci of the conferences will be on recent advances at the interface of representation theory, categorification, and noncommutative algebra; on fostering an environment for the establishment of international collaborations between Canada, Mexico, and the USA in these research areas; and on exposing graduate students, post-docs, and early-career faculty in the three countries to current developments in the field. A poster session will run through the full meeting where early-career attendees will present their research.

The main scientific topics for the sixth meeting in Mexico City will be geometric, algebraic, and homological methods in representation theory, representation theoretic and homological properties of noncommutative algebras, and the investigation of those problems using categorical methods. The talks will cover some of the most recent trends, including the following: cluster algebras, monoidal and additive categorifications, quantum symmetries, finite tensor categories, representations of quantized affine Kac-Moody algebras, Calabi-Yau algebras and triangulated categories, Hopfological algebra, web approaches to modular representation theory, and representation theoretic aspects of Heegaard-Floer homology. The website for the 2024 conference is https://sites.google.com/im.unam.mx/canadausmexico-2024/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401383","Non-Abelian Hodge Theory and Transcendence","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/01/2024","04/16/2024","Benjamin Bakker","IL","University of Illinois at Chicago","Standard Grant","James Matthew Douglass","07/31/2027","$330,000.00","","bakker@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126400","","$0.00","Hodge theory is concerned with the integrals of algebraic forms along topological cycles. The study of these invariants traces its roots to the work of Jacobi, Abel, and Riemann in the nineteenth century; the modern theory ties together the algebraic, topological, complex analytic, and arithmetic facets of the geometry of an algebraic variety, and has many applications. Pioneering work of Simpson in the 1990s developed a non-abelian version of this theory where the space of representations of the fundamental group plays the role of the group of topological cycles. The resulting non-abelian Hodge theory touches equally many fields of mathematics, but many aspects of it remain mysterious. In this project, the PI will extend recent progress in classical Hodge theory and transcendence theory via o-minimal methods to the non-abelian setting. The project will specifically be geared towards fostering the involvement of students and early-career mathematicians.

In more detail, the PI will apply o-minimal techniques to address a number of open questions related to the geometry of local systems on algebraic varieties, and its connection to complex analysis, arithmetic, and transcendence theory. This includes the transcendence theory of the Riemann?Hilbert correspondence, the classification of tri-algebraic subvarieties, as well as the algebraicity and arithmeticity of non-abelian Hodge loci. These techniques will also be brought to bear on related geometric questions, including the construction of Shafarevich maps, transcendence theory of p-adic period maps, and the geometry of Lagrangian fibrations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401321","Euler Systems, Iwasawa Theory, and the Arithmetic of Elliptic Curves","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/05/2024","Francesc Castella","CA","University of California-Santa Barbara","Continuing Grant","Adriana Salerno","06/30/2027","$74,832.00","","castella@ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126400","","$0.00","Elliptic curves are a class of polynomial equations (of degree three in two variables) that have been studied for centuries, yet for which many basic questions remain open. For instance, at present there is no proven algorithm to decide whether or not a given elliptic curve has finite or infinitely many rational solutions. Over the past century, mathematicians conjectured that an answer to these questions could be extracted from certain functions of a complex variable, namely the L-function of the elliptic curve. Euler systems and Iwasawa theory are two of the most powerful tools available to date for the study of these and related conjectured links between arithmetic and analysis. This award will advance our understanding of the arithmetic of elliptic curves by developing new results and techniques in Euler systems and Iwasawa theory. The award will also support several mentoring, training, dissemination, and outreach activities.

More specifically, the research to be pursued by the PI and his collaborators will largely focus on problems whose solutions will significantly advance our understanding of issues at the core of the Birch and Swinnerton-Dyer conjecture and related questions in situations of analytic rank 1, and shed new light on the much more mysterious cases of analytic rank 2 and higher. In rank 1, they will prove the first p-converse to the celebrated theorem of Gross-Zagier and Kolyvagin in the case of elliptic curves defined over totally real fields. In rank 2, they will continue their investigations of the generalized Kato classes introduced a few years ago by Darmon-Rotger, establishing new nonvanishing results in the supersingular case. They will also study a systematic p-adic construction of Selmer bases for elliptic curves over Q of rank 2 in connection with the sign conjecture of Mazur-Rubin. For elliptic curves of arbitrary rank, they will establish various non-triviality results of associated Euler systems and Kolyvagin systems, as first conjectured by Kolyvagin and Mazur-Tate.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2400006","Conference: Underrepresented Students in Algebra and Topology Research Symposium (USTARS)","DMS","INFRASTRUCTURE PROGRAM, ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","03/15/2024","03/12/2024","Ryan Moruzzi","CA","California State University, East Bay Foundation, Inc.","Standard Grant","Adriana Salerno","02/28/2025","$36,000.00","Christopher ONeill, Robyn Brooks","ryan.moruzzi@csueastbay.edu","25800 CARLOS BEE BLVD","HAYWARD","CA","945423000","5108854212","MPS","126000, 126400, 126700","7556","$0.00","This award will support the Underrepresented Students in Topology and Algebra Research Symposium (USTARS). A goal of this conference is to highlight research being conducted by underrepresented students in the areas of algebra and topology. At this unique meeting, attendees are exposed to a greater variety of current research, ideas, and results in their areas of study and beyond. Participants are also given the opportunity to meet and network with underrepresented professors and students who may later become collaborators and colleagues. This is particularly important for students with great academic potential who do not attend top-tier research institutions; students that are often overlooked, despite a strong faculty and graduate student population. Furthermore, USTARS promotes diversity in the mathematical sciences by encouraging women and minorities to attend and give talks. Participants of USTARS continue to influence the next generation of students in positive ways by serving as much needed mentors and encouraging students in the mathematical sciences to advance themselves and participate in research and conference events. USTARS exposes all participants to the research and activities of underrepresented mathematicians, encouraging a more collaborative mathematics community.

The Underrepresented Students in Topology and Algebra Research Symposium (USTARS) is a project proposed by a group of underrepresented young mathematicians. The conference organizing committee is diverse in gender, ethnicity, and educational background, and is well-positioned to actively encourage participation by women and minorities. The symposium includes networking sessions along with research presentations. Speakers will give 30-minute parallel research talks. Graduate students will give at least 75% of these presentations. Two distinguished graduate students and one invited faculty member are chosen to give 1-hour presentations and a poster session featuring invited undergraduates is also planned. Additionally, a discussion panel and creative math session will provide networking, guidance, and mentorship opportunities from past USTARS participants that have transitioned to full-time faculty positions. The conference website is https://www.ustars.org/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401662","Conference: Southern Regional Algebra Conference 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/15/2024","01/18/2024","Jean Nganou","TX","University of Houston - Downtown","Standard Grant","Tim Hodges","02/28/2025","$14,990.00","","nganouj@uhd.edu","1 MAIN ST","HOUSTON","TX","770021014","7132218005","MPS","126400","7556","$0.00","This award supports participation in the Southern Regional Algebra Conference (SRAC). The SRAC is a yearly weekend conference that has been in existence since 1988. Its first edition was held at the University of Southern Mississippi in the Spring of 1988. This spring the SRAC will be held at the University of Houston-Downtown, March 22-24, 2024. The SRAC brings together mathematicians that carry out research in the area of algebra and closely related areas for a full weekend of lectures, short presentations and discussions. The conference attracts researchers from many undergraduate institutions in the Gulf Coast Region that usually do not have sufficient funding to support their research activities, especially long-distance meetings. It is also an important platform for graduate students and early career mathematicians to present their research in algebra and be exposed to a community of algebraists outside their respective home institutions.

The main themes of the conference are Lie/Leibniz Algebras and their representation theory; and the theory of nearrings and other generalizations of rings. On Friday March 22, there will be a single session on topics in algebra that lie either at the intersection of two themes of the conference or outside of their union. On Saturday March 23, the conference will begin with an hour-long plenary session on Leibniz algebras and the rest of the day will be split into two parallel sessions of 25-min talks, with each session focusing on one of the main themes. On Sunday March 24, the conference will start with an hour-long plenary session on the near-rings theory, and the rest of the morning will be split into two parallel sessions of 25-min talks, with each session focusing on one of the main themes. There will be plenty of opportunity for informal follow-up discussions. Further information is available at the conference website:
https://www.uhd.edu/academics/sciences/mathematics-statistics/southern-regional-algebra-conference.aspx

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2426080","Conference: Motivic homotopy, K-theory, and Modular Representations","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/15/2024","07/08/2024","Aravind Asok","CA","University of Southern California","Standard Grant","Swatee Naik","06/30/2025","$31,500.00","Paul Sobaje, Julia Pevtsova, Christopher Bendel","asok@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","90033","2137407762","MPS","126400, 126700","7556","$0.00","This award provides partial support for the participation of early career US-based mathematicians to attend the conference ""Motivic homotopy, K-theory, and Modular Representations"" to be held August 9-11, at the University of Southern California in Los Angeles, California. While recent events have often focused on specific aspects within these domains, this conference aims to unite mathematicians from diverse yet interconnected areas. The core purpose of the project is to support the attendance and career development of emerging scholars from the United States, and support from this award will benefit scholars from a broad selection of U.S. universities and diverse backgrounds; the intent is to maximize the effect on workforce development.

The conference will convene at the intersection of homotopy theory, algebraic geometry, and representation theory, focusing on areas that have experienced significant growth over the past three decades. Furthermore, it will explore applications of these fields to neighboring disciplines such as mathematical physics. All these fields have seen major advances and changes in the last five years, and this conference with international scope aims to synthesize major recent developments. More information about the conferences can be found at the website: https://sites.google.com/view/efriedlander80.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401444","Conference: Workshop on Automorphic Forms and Related Topics","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/01/2024","02/27/2024","Melissa Emory","OK","Oklahoma State University","Standard Grant","Andrew Pollington","02/28/2025","$24,800.00","Kimberly Logan, Liyang Yang, Jonathan Cohen","melissa.emory@okstate.edu","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","126400","7556, 9150","$0.00","The 36th Annual Workshop on Automorphic Forms and Related Topics (AFW) will take place May 20-24, 2024, at Oklahoma State University in Stillwater, OK. The AFW is an internationally recognized, well-respected conference on topics related to automorphic forms, which have played a key role in many recent breakthroughs in mathematics. The AFW will bring together a geographically diverse group of participants at a wide range of career stages, from graduate students to senior professors. Typically, about half of the attendees at the AFW are at early stages of their careers, and about one quarter to one third of participants are women. The AFW will continue to provide a supportive and encouraging environment for giving talks, exchanging ideas, and beginning new collaborations. This is the first time the AFW will meet in Oklahoma where many experts on automorphic forms and closely related topics are nearby. Thus, in addition to attracting speakers who participate annually, the workshop is likely to draw a mix of new attendees who will contribute new perspectives and energy and benefit from the workshop. The workshop is known for its inclusive, encouraging atmosphere, particularly to early career researchers and to those from underrepresented groups in the number theory community. The workshop has traditionally been a fruitful place for these researchers to connect with potential collaborators and mentors at other institutions, working on related topics. To help achieve this goal, the 2024 AFW will feature five expository talks on various fundamental topics in the theory of automorphic forms, aimed at the graduate student level. There will also be two panel discussions focused on mathematical career questions.

Automorphic forms play a central role in number theory, being integral to the proofs of many groundbreaking theorems, including Fermat's Last Theorem (by Andrew Wiles), the Sato-Tate Conjecture (by Thomas Barnet-Lamb, David Geraghty, Michael Harris, and Richard Taylor), Serre's Conjecture (by Chandrashekhar Khare, Mark Kisin, and Jean-Pierre Wintenberger), the Sato-Tate Conjecture (by Thomas Barnet-Lamb, David Geraghty, Michael Harris, and Richard Taylor), Serre's Uniformity Conjecture (by Yuri Bilu and Pierre Parent), and the Fundamental Lemma (for which Ngo Bau Chau was awarded the Fields Medal). Automorphic forms are the subject of many important ongoing conjectures, among them the Langlands program, connections to random matrix theory, and the generalized Riemann hypothesis. They also appear in many areas of mathematics outside number theory, most notably in mathematical physics. The topics covered in this year's workshop are likely to include elliptic, Siegel, Hilbert, and Bianchi modular forms, elliptic curves and abelian varieties, special values of L-functions, p-adic aspects of L-functions and automorphic forms, connections with representation theory, mock modular forms, quadratic forms, connections with mathematical physics, monstrous moonshine, and additional related areas of research.


Additional information can be found on the conference website: http://automorphicformsworkshop.org/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2337451","CAREER: Higgs bundles and Anosov representations","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS","07/01/2024","02/02/2024","Brian Collier","CA","University of California-Riverside","Continuing Grant","Swatee Naik","06/30/2029","$79,647.00","","brian.collier@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","126400, 126500","1045","$0.00","This project focuses on the mathematical study of curved surfaces by connecting algebraic objects to them and thereby generalizing the scope of their application. One of the main notions used is that of a surface group representation, a concept which connects surfaces to generalizations of classical geometries such as Euclidean and hyperbolic geometry. The study of surfaces has surprising applications throughout many fields of mathematics and physics. Consequently, the project lies at the intersection of multiple disciplines. In addition to cutting edge mathematical research, the project will promote the progress of science and mathematics through different workshops aimed at graduate students as well as community outreach events. The educational component will also focus on creating an engaging and inclusive place for mathematical interactions for students and early career researchers.

In the past decades, both the theories of Higgs bundles and Anosov dynamics have led to significant advancements in our understanding of the geometry of surface groups. Recent breakthroughs linking these approaches are indirect and mostly involve higher rank generalizations of hyperbolic geometry known as higher rank Teichmuller spaces. The broad aim of this project is to go beyond higher rank Teichmuller spaces by using Higgs bundles to identify subvarieties of surface group representations which generalize the Fuchsian locus in quasi-Fuchsian space. The cornerstone for the approach is the role of Slodowy slices for Higgs bundles. Specifically, the PI aims to establish Anosov properties of surface group representations associated to Slodowy slices in the Higgs bundle moduli space. This approach will significantly extend applications of Higgs bundles to both Anosov representations and (G,X) geometries. It will complete the component count for moduli of surface group representations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2349244","Conference: Texas Algebraic Geometry Symposium (TAGS) 2024-2026","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","01/19/2024","Frank Sottile","TX","Texas A&M University","Continuing Grant","James Matthew Douglass","03/31/2027","$15,000.00","","sottile@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126400","","$0.00","The Texas Algebraic Geometry Symposium (TAGS) will be held at Texas A&M University April 5,6, and 7, 2024, and in Spring 2025 and Spring 2026. TAGS is an annual regional conference which is jointly organized by faculty at Rice University, Texas A&M University, and the University of Texas at Austin. The conference series began in 2005, and serves to enhance the educational and research environment in Texas and the surrounding states, providing an important opportunity for interaction and sharing of ideas for students and researchers in this region.

TAGS serves to ensure that members of the algebraic geometry community in the Texas region stay in regular contact and brings distinguished mathematicians and rising stars to an area with no other comparable regular gatherings in algebraic geometry. The 2024 TAGS will have nine lectures delivered by a diverse group of speakers, and will include accessible lectures for graduate students and a juried poster session for students and junior researchers. It will be held in conjunction with the annual Maxson lectures at Texas A&M the week before and delivered by Prof. David Eisenbud. The TAGS website is https://franksottile.github.io/conferences/TAGS24/index.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2414452","Collaborative Research: Conference: Special Trimester on Post-Quantum Algebraic Cryptography","DMS","ALGEBRA,NUMBER THEORY,AND COM, Secure &Trustworthy Cyberspace","09/01/2024","07/02/2024","Delaram Kahrobaei","NY","CUNY Queens College","Standard Grant","Tim Hodges","08/31/2025","$10,000.00","","dkahrobaei@gc.cuny.edu","6530 KISSENA BLVD","FLUSHING","NY","113671575","7189975400","MPS","126400, 806000","025Z, 7556","$0.00","This award funds participation by US-based researchers in a special trimester on Post-quantum algebraic cryptography, to be held at the The Henri Poincare Institute, Paris, France, September 9 - December 13, 2024. In recent years, there has been a substantial amount of research on quantum computers -- machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. The thematic trimester program will bring together researchers and practitioners from academia, industry, and government institutions with diverse backgrounds to discuss quantum algorithms, quantum-safe cryptography, as well as deployment issues, from different angles.

This thematic trimester program will address various proposed cryptographic primitives that are currently considered to be quantum-safe. This includes lattice-based, multivariate, code-based, hash-based, group-based, and other primitives some of which were considered by NIST during their post-quantum standardization process. Our program will also address various functionalities of cryptographic constructions that are in high demand in real life. This includes fully homomorphic encryption that provides for private search on encrypted database and machine learning on encrypted data. Another functionality that is getting increasingly popular is outsourcing (a.k.a. delegating) computation of algebraic functions including group exponentiation, product of group exponentiations, etc., from a computationally limited client holding an input and a description of a function, to a computationally stronger entity holding a description of the same function. Further information can be found at the program website:
https://www.ihp.fr/en/events/post-quantum-algebraic-cryptography-paris

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2412921","Conference: CAAGTUS (Commutative Algebra and Algebraic Geometry in TUcSon)","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","02/14/2024","Debaditya Raychaudhury","AZ","University of Arizona","Standard Grant","Tim Hodges","04/30/2025","$15,000.00","Arvind Suresh, Zhengning Hu","draychaudhury@math.arizona.edu","845 N PARK AVE RM 538","TUCSON","AZ","85721","5206266000","MPS","126400","7556","$0.00","This award will support participation in a weekend conference to be held at the University of Arizona, Tucson on May 4 - 5. The aim of the conference is to establish a solid basis for contacts and collaborations among researchers in Commutative Algebra and Algebraic Geometry located in Arizona and its neighboring states. Its main purposes are to stimulate new directions of research, to provide opportunities to junior researchers to share their work, and to provide a venue for networking and collaboration in the southwest. Its other aim is to expand the network of algebraic and arithmetic geometers by providing an algebro-geometric complement of the Arizona Winter School.

The conference plans to host four leading researchers from Arizona and its neighboring states working in Commutative Algebra and Algebraic Geometry, who will give colloquium-style one-hour lectures on their respective areas of expertise. These hour-long lectures are expected to provide surveys of the current state of the research in these areas, and to provide suggestions for new avenues of research. There will be five or six 30-minute talks given by young researchers, as well as six to eight contributed short 20-minute talks and a poster session. Priority for these contributed talks and posters will be given to recent PhD recipients and members of groups underrepresented in mathematics. Further information is available at the conference website: https://sites.google.com/math.arizona.edu/caagtus/home

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2346615","Conference: Zassenhaus Groups and Friends Conference 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","11/08/2023","Yong Yang","TX","Texas State University - San Marcos","Standard Grant","Tim Hodges","12/31/2024","$18,000.00","Thomas Keller","yy10@txstate.edu","601 UNIVERSITY DR","SAN MARCOS","TX","786664684","5122452314","MPS","126400","7556","$0.00","This award supports participation in the 2024 Zassenhaus Groups and Friends Conference which will be held at Texas State University in San Marcos, TX. It will take place on the campus of the university from noon of Friday, May 31, 2024, to the early afternoon on Sunday, June 2, 2024. It is expected that about 40 researchers will attend the conference, many of whom will give a talk.

The Zassenhaus Groups and Friends Conference, formerly known as Zassenhaus Group Theory Conference, is a series of yearly conferences that has served the mathematical community since its inception in the 1960s. The speakers are expected to come from all over the country and will cover a broad spectrum of topics related to the study of groups, such as representations of solvable groups, representations of simple groups, character theory, classes of groups, groups and combinatorics, recognizing simple groups from group invariants, p-groups, and fusion systems.

The conference will provide group theory researchers in the US a forum to disseminate their own research as well as to learn about new and significant results in the area. The conference will provide a particularly inviting environment to young mathematicians and will inspire future cooperation and collaborations among the participants. It is expected that it will have great impacts on the group theory research community. The organizers will make great effort to attract a demographically diverse group of participants including women and racial and ethnic minorities. More information can be found at the conference website, https://zassenhausgroupsandfriends.wp.txstate.edu/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349836","Local and Global Problems in the Relative Langlands Program","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/01/2024","07/24/2024","Chen Wan","NJ","Rutgers University Newark","Standard Grant","Andrew Pollington","07/31/2027","$174,000.00","","chen.wan@rutgers.edu","123 WASHINGTON ST","NEWARK","NJ","071023026","9739720283","MPS","126400","","$0.00","This award concerns mathematical objects called reductive groups which are special kinds of topological groups characterized by abundant symmetries. These symmetries serve as key insights into understanding the intrinsic structures of objects in our universe. The study of reductive groups dates back to the late 19th century. Two crucial areas of this field are the representation theory of reductive groups and automorphic forms on reductive groups, which are specialized functions with additional symmetry on reductive groups. These two areas also have many connections to various other disciplines, including physics and computer science. This project aims to explore the restriction of representations of reductive groups to a spherical subgroup and to investigate the period integrals of automorphic forms. In the meantime, the PI will continue advising his current undergraduate and graduate students, as well as any potential students interested in studying the Langlands program. He will hold weekly meetings with them and assign suitable thesis problems. He will also continue organizing seminars and conferences in this area. Additionally, he will maintain his outreach efforts in K-12 education by mentoring high school students and coaching local kids in the Newark area for math competitions, among other activities.

To be specific, the primary objective in the local theory is to use the trace formula method to study the multiplicity problem for spherical varieties. In recent years, the PI and his collaborators have examined the local multiplicity for some spherical varieties and have proposed a conjectural multiplicity formula for all spherical varieties. Additionally, they have formulated an epsilon dichotomy conjecture for all strongly tempered spherical varieties. The PI intends to prove these conjectures and investigate further structures and properties related to multiplicity. Additionally, the PI plans to study the multiplicity for varieties that are not necessarily spherical, as well as the relations between distribution characters and orbital integrals. In the global theory, the PI intends to use the relative trace formula method and some beyond endoscopic type comparison method to study various relations between period integrals and automorphic L-functions (in particular proving the Ichino-Ikeda type formula for period integrals in some cases). Moreover, Ben-Zvi?Sakellaridis?Venkatesh have recently developed a beautiful theory of relative Langlangs duality. The PI intends to use this theory to explain all the existing automorphic integrals and to explore some new integrals. The PI also hopes to extend the theory of relative Langlands duality beyond the current spherical setting.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2337942","CAREER: Arithmetic Dynamical Systems on Projective Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","01/22/2024","Nicole Looper","IL","University of Illinois at Chicago","Continuing Grant","Tim Hodges","08/31/2029","$36,742.00","","nrlooper@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126400","1045","$0.00","This project centers on problems in a recent new area of mathematics called arithmetic dynamics. This subject synthesizes problems and techniques from the previously disparate areas of number theory and dynamical systems. Motivations for further study of this subject include the power of dynamical techniques in approaching problems in arithmetic geometry and the richness of dynamics as a source of compelling problems in arithmetic. The funding for this project will support the training of graduate students and early career researchers in arithmetic dynamics through activities such as courses and workshops, as well as collaboration between the PI and researchers in adjacent fields.

The project?s first area of focus is the setting of abelian varieties, where the PI plans to tackle various conjectures surrounding the fields of definition and S-integrality of points of small canonical height. One important component of this study is the development of quantitative lower bounds on average values of generalized Arakelov-Green?s functions, which extend prior results in the dimension one case. The PI intends to develop such results for arbitrary polarized dynamical systems, opening an avenue for a wide variety of arithmetic applications. A second area of focus concerns the relationship between Arakelov invariants on curves over number fields and one-dimensional function fields, and arithmetic on their Jacobian varieties. Here the project aims to relate the self-intersection of Zhang?s admissible relative dualizing sheaf to the arithmetic of small points on Jacobians, as well as to other salient Arakelov invariants such as the delta invariant. The third goal is to study canonical heights of subvarieties, especially in the case of divisors. A main focus here is the relationship between various measurements of the complexity of the dynamical system and the heights of certain subvarieties. The final component of the project aims to relate the aforementioned generalized Arakelov-Green?s functions to
pluripotential theory, both complex and non-archimedean.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2339274","CAREER: New directions in the study of zeros and moments of L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","02/12/2024","Alexandra Florea","CA","University of California-Irvine","Continuing Grant","Tim Hodges","06/30/2029","$87,350.00","","alexandra.m.florea@gmail.com","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126400","1045","$0.00","This project focuses on questions in analytic number theory, and concerns properties of the Riemann zeta-function and of more general L-functions. L-functions are functions on the complex plane that often encode interesting information about arithmetic objects, such as prime numbers, class numbers, or ranks of elliptic curves. For example, the Riemann zeta-function (which is one example of an L-function) is closely connected to the question of counting the number of primes less than a large number. Understanding the analytic properties of L-functions, such as the location of their zeros or their rate of growth, often provides insight into arithmetic questions of interest. The main goal of the project is to advance the knowledge of the properties of some families of L-functions and to obtain arithmetic applications. The educational component of the project involves groups of students at different stages, ranging from high school students to beginning researchers. Among the educational activities, the PI will organize a summer school in analytic number theory focusing on young mathematicians, and will run a yearly summer camp at UCI for talented high school students.

At a more technical level, the project will investigate zeros of L-functions by studying their ratios and moments. While positive moments of L?functions are relatively well-understood, much less is known about negative moments and ratios, which have applications to many difficult questions in the field. The planned research will use insights from random matrix theory, geometry, sieve theory and analysis. The main goals fall under two themes. The first theme is developing a general framework to study negative moments of L-functions, formulating full conjectures and proving partial results about negative moments. The second theme involves proving new non-vanishing results about L-functions at special points. Values of L-functions at special points often carry important arithmetic information; the PI plans to show that wide classes of L-functions do not vanish at the central point (i.e., the center of the critical strip, where all the non-trivial zeros are conjectured to be), as well as to study correlations between the values of different L-functions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2347096","Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","12/19/2023","Lea Beneish","TX","University of North Texas","Standard Grant","Andrew Pollington","12/31/2026","$20,000.00","Anne Shepler, Olav Richter","lea.beneish@unt.edu","1112 DALLAS DR STE 4000","DENTON","TX","762051132","9405653940","MPS","126400","7556","$0.00","This award supports the TORA mathematics conference series. This series consists of annual meetings hosted by the University of North Texas, Oklahoma State University, and the University of Oklahoma on a rotating basis. This award provides support for three weekend conferences, one at the University of North Texas in Spring 2024 (TORA XIII), one at Oklahoma State University in Spring 2025 (TORA XIV), and another at the University of Oklahoma in Spring 2026 (TORA XV). Each conference will feature three prominent guest speakers from outside the Texas-Oklahoma region, in addition to other participants including students, post-doctoral researchers, and junior faculty. Regional graduate students and researchers will also give talks describing their work. These conferences will facilitate collaborations and interactions among the students and researchers in the region who work in the areas of Automorphic Forms, Representation Theory, and Number Theory.

Over the last century, the theories of automorphic forms and representations have grown enormously. Important applications impact various fields of research, ranging from number theory, coding theory, algebraic geometry, and topology to Kac-Moody algebras and quantum field theory. The interplay of automorphic forms and representation theory has been especially fruitful, and many surprising and deep results have emerged. The TORA conference series will emphasize the interplay between automorphic forms and representations, both in the classical and adelic languages, and related topics like analytic number theory and harmonic analysis.



The conference Texas-Oklahoma Representations and Automorphic forms XIII will take place on April 12-14, 2024, at the University of North Texas. Additional information can be found on the conference website: https://www.math.unt.edu/~richter/TORA/TORA13.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2402637","Conference: Connecticut Summer School in Number Theory 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/03/2024","Alvaro Lozano-Robledo","CT","University of Connecticut","Standard Grant","Adriana Salerno","03/31/2025","$29,967.00","Keith Conrad, Jennifer Balakrishnan, Christelle Vincent","alvaro.lozano-robledo@uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","126400","7556","$0.00","The Connecticut Summer School in Number Theory (CTNT 2024) is a conference for advanced undergraduate and beginning graduate students, to be followed by a research conference, taking place at at the University of Connecticut, Storrs campus, from June 10 through June 16, 2024. Even though the northeast of the United States is a hotspot for number theory research, there is no instructional school in number theory that occurs in this region. Undergraduate and beginning graduate students who are interested in number theory may only have had an elementary number theory course during college. The CTNT summer school will achieve several outcomes: expose undergraduate and beginning graduate students to accessible topics that are fundamental to contemporary number theory; provide an environment where students interested in number theory can meet each other and network with students, postdocs, and faculty from institutions where number theory is a strong research area; train a diverse group of students on topics of current importance in number theory; allow advanced undergraduates and beginning graduate students to attend a research conference in number theory; videotape the lectures and post them online at a dedicated website to reach as wide of an audience as possible later: https://ctnt-summer.math.uconn.edu/

CTNT 2024 will consist of a 4.5-day summer school followed by a 2-day conference. The summer school will have six mini-courses on topics important to contemporary number theory that are not available in a typical college curriculum, such as elliptic curves, reciprocity, adeles and ideles, and class field theory. The courses will be complemented with course projects, daily invited talks, evening problem sessions, and discussion panels about aspects of graduate school (both for those already in graduate school and those thinking of applying). The conference will consist of several sessions with research talks in number theory, arithmetic geometry, and related topics, and it will be an opportunity for young researchers to present their work.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401495","Theory of Atoms","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/01/2024","07/18/2024","Ludmil Katzarkov","FL","University of Miami","Standard Grant","Adriana Salerno","07/31/2027","$215,000.00","","lkatzarkov@gmail.com","1320 SOUTH DIXIE HIGHWAY STE 650","CORAL GABLES","FL","331462919","3052843924","MPS","126400","","$0.00","Algebraic varieties are shapes defined by solution sets of systems of polynomial equations. A fundamental problem in geometry is the classification of algebraic varieties, as it helps us gain a better understanding of the structures and relations between them. The first step in classification is called birational classification, i.e. two algebraic varieties are called birational if they are equal outside some lower-dimensional loci. In this proposal, the PI will investigate new birational invariants, atoms, based on foundations coming from theoretical physics. The theory of atoms has its origin in conformal field theory and homological mirror symmetry. This project will also support training of early-career mathematicians and dissemination events through the Institute of Mathematical Sciences of Americas in the University of Miami.

More specifically, the PI?s approach in birational geometry is based on developing a new singularity theory of Landau-Ginzburg models and a non-commutative refinement of the notion of an eigenspectrum of quantum multiplication operators. These new non-commutative spectra provide natural obstructions to rationality and equivariant rationality of Fano varieties. This could lead to even stronger birational invariants as well as to new unexpected bridges, including: a new connection between Steenbrink spectra of the LG models and asymptotics of quantum differential equations; new birational applications of atoms to the cases of singular varieties and the case of varieties over algebraically non closed fields; and a new relation between non-Kahler manifolds, their Homological Mirror Symmetry (HMS) and their atoms.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401375","Collaborative Research: Small quantum groups, their categorifications and topological applications","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/15/2024","07/16/2024","Joshua Sussan","NY","CUNY Medgar Evers College","Standard Grant","Tim Hodges","06/30/2027","$201,860.00","","joshuasussan@gmail.com","1650 BEDFORD AVE","BROOKLYN","NY","112252017","7182706107","MPS","126400, 126700","","$0.00","This award funds research in an area of abstract algebra. Throughout history, mathematics and physics have had profound influences on each other. In the late 20th century, physicists discovered a deep connection between quantum physics and three-dimensional shapes, leading to the concept of topological quantum field theory (TQFT). While these 3D theories cannot fully describe our 4D universe, condensed matter physicists have found surprising applications of them in the field of quantum computing. In an effort to bridge the gap between these three-dimensional theories and our actual universe, Crane and Frenkel introduced a program called ""categorification"" in the late 1990s. This program aims to lift three-dimensional TQFTs to four dimensions, making it a more direct reflection of our physical reality. The PIs will involve students and postdocs in this research, with particular focus on students from underrepresented minorities.

The first significant development in categorification was the discovery of Khovanov homology. This is a powerful invariant of links whose graded Euler characteristic is the Jones polynomial. The investigators plan to use the technical machinery of hopfological algebra to extend a dual version of Khovanov homology to a homological invariant of three-dimensional manifolds whose graded Euler characteristic is the Witten-Reshetikhin-Turaev invariant. Ideally, this construction will be fully functorial, giving rise to an invariant of four-dimensional manifolds, while remaining computationally accessible. These invariants are expected be sensitive to smooth structures and should give insights into smooth topology not provided by gauge theoretic invariants like Donaldson and Seiberg-Witten invariants. This direction will build upon the investigators' previous work on categorified quantum groups and their representations at roots of unity. It is an open question of how to incorporate hopfological structures into Khovanov homology. This should lead to new homotopic notions. The investigators also plan on continuing to develop non-semisimple versions of three-dimensional topological quantum field theories with an eye toward applications to quantum computation. These non-semisimple invariants have certain topological advantages over their more classical semisimple counterparts. This line of research will also build upon their work on the centers of small quantum groups which has recently been an active area of research in geometric representation theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2429145","Conference: Binghamton University Graduate Combinatorics, Algebra, and Topology Conference (BUGCAT Conference) 2024,2025,2026","DMS","ALGEBRA,NUMBER THEORY,AND COM, Combinatorics","09/15/2024","07/16/2024","Alexander Borisov","NY","SUNY at Binghamton","Continuing Grant","Andrew Pollington","08/31/2027","$28,000.00","","borisov@math.binghamton.edu","4400 VESTAL PKWY E","BINGHAMTON","NY","139024400","6077776136","MPS","126400, 797000","7556","$0.00","This award supports the BUGCAT Conference (Binghamton University Graduate Combinatorics, Algebra, and Topology Conference) 2024 which will take place at the Binghamton University campus on October 26-27, 2024 and also tosupport the conference in the fall of 2025 and 2026. This conference has been running since 2008, with support from NSF in many years, including the last three in-person conferences, in 2019, 2022, and 2023. Continuing NSF support will allow to keep the conference at a current level of more than 100 registered participants, three hour-long keynote presentations, and 40-45 contributed talks of 20-25 minutes in length. The three keynote speakers are professional mathematicians, while most of the other participants are graduate students, with some postdocs and undergraduates.

The conference is run by a rotating committee of graduate students, with general oversight and guidance from the P.I. and some other faculty members. This helps to maintain a friendly and inclusive atmosphere, to facilitate free scientific interactions at the level appropriate for the beginning researchers at various stages of their mathematical development. This also gives the graduate student organizers experience in running a larger conference, and helps them appreciate what is involved in this, when they go give talks at conferences elsewhere. The organizers make efforts to encourage diversity, both by virtue of the varied backgrounds of the organizing committee members, and by the selection of the keynote speakers, without sacrificing the scientific level of the conference. The permanent conference website with the 2023 information, and some previous years' documents, can be found here: https://seminars.math.binghamton.edu/BUGCAT/index.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401376","Collaborative Research: Small quantum groups, their categorifications and topological applications","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/15/2024","07/16/2024","You Qi","VA","University of Virginia Main Campus","Standard Grant","Tim Hodges","06/30/2027","$172,247.00","","yq2dw@virginia.edu","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126400, 126700","","$0.00","This award funds research in an area of abstract algebra. Throughout history, mathematics and physics have had profound influences on each other. In the late 20th century, physicists discovered a deep connection between quantum physics and three-dimensional shapes, leading to the concept of topological quantum field theory (TQFT). While these 3D theories cannot fully describe our 4D universe, condensed matter physicists have found surprising applications of them in the field of quantum computing. In an effort to bridge the gap between these three-dimensional theories and our actual universe, Crane and Frenkel introduced a program called ""categorification"" in the late 1990s. This program aims to lift three-dimensional TQFTs to four dimensions, making it a more direct reflection of our physical reality. The PIs will involve students and postdocs in this research, with particular focus on students from underrepresented minorities.

The first significant development in categorification was the discovery of Khovanov homology. This is a powerful invariant of links whose graded Euler characteristic is the Jones polynomial. The investigators plan to use the technical machinery of hopfological algebra to extend a dual version of Khovanov homology to a homological invariant of three-dimensional manifolds whose graded Euler characteristic is the Witten-Reshetikhin-Turaev invariant. Ideally, this construction will be fully functorial, giving rise to an invariant of four-dimensional manifolds, while remaining computationally accessible. These invariants are expected be sensitive to smooth structures and should give insights into smooth topology not provided by gauge theoretic invariants like Donaldson and Seiberg-Witten invariants. This direction will build upon the investigators' previous work on categorified quantum groups and their representations at roots of unity. It is an open question of how to incorporate hopfological structures into Khovanov homology. This should lead to new homotopic notions. The investigators also plan on continuing to develop non-semisimple versions of three-dimensional topological quantum field theories with an eye toward applications to quantum computation. These non-semisimple invariants have certain topological advantages over their more classical semisimple counterparts. This line of research will also build upon their work on the centers of small quantum groups which has recently been an active area of research in geometric representation theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401462","Commutative Algebra methods for Hilbert schemes and beyond","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/15/2024","07/15/2024","Ritvik Ramkumar","NY","Cornell University","Standard Grant","Tim Hodges","06/30/2027","$175,000.00","","rr675@cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","126400","","$0.00","Polynomial equations are ubiquitous in science, describing important physical principles and serving as mathematical models for complex natural phenomena. Algebraic geometry studies geometric structures arising from solutions to systems of polynomial equations. To gain a better understanding of these structures, it is useful to study how they change when the corresponding equations are slightly perturbed. This is achieved by studying a ?parameter space? for these structures. The overarching goal of this project is to use techniques from commutative algebra to tackle longstanding questions related to the Hilbert scheme, a parameter space for polynomials with fixed properties. The project?s broader impacts include developing new packages for the open-source computer algebra system Macaulay2, organizing local seminars, and organizing mathematical conferences.

The investigator will focus on three areas of commutative algebra and algebraic geometry: 1) Singularities of the Hilbert scheme of points on a threefold: The main goal is to understand the singularities of the Hilbert scheme of points on a smooth threefold. In particular, the investigator will focus on determining the smooth points and explaining some of the patterns appearing in the structure of the singularities. 2) Exploring multigraded Hilbert schemes and other moduli spaces: The investigator will study the space of branch varieties, a close analogue of the Hilbert scheme, and focus on studying the projectivity of this moduli space. 3) Varieties in weighted projective spaces: The investigator will focus on developing a set of tools to extend classical theorems in projective space, such as Macaulay?s theorem on the existence of Hilbert functions and the del Pezzo-Bertini classification of varieties of minimal degree, to weighted projective spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2426080","Conference: Motivic homotopy, K-theory, and Modular Representations","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/15/2024","07/08/2024","Aravind Asok","CA","University of Southern California","Standard Grant","Swatee Naik","06/30/2025","$31,500.00","Christopher Bendel, Julia Pevtsova, Paul Sobaje","asok@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","900890701","2137407762","MPS","126400, 126700","7556","$0.00","This award provides partial support for the participation of early career US-based mathematicians to attend the conference ""Motivic homotopy, K-theory, and Modular Representations"" to be held August 9-11, at the University of Southern California in Los Angeles, California. While recent events have often focused on specific aspects within these domains, this conference aims to unite mathematicians from diverse yet interconnected areas. The core purpose of the project is to support the attendance and career development of emerging scholars from the United States, and support from this award will benefit scholars from a broad selection of U.S. universities and diverse backgrounds; the intent is to maximize the effect on workforce development.

The conference will convene at the intersection of homotopy theory, algebraic geometry, and representation theory, focusing on areas that have experienced significant growth over the past three decades. Furthermore, it will explore applications of these fields to neighboring disciplines such as mathematical physics. All these fields have seen major advances and changes in the last five years, and this conference with international scope aims to synthesize major recent developments. More information about the conferences can be found at the website: https://sites.google.com/view/efriedlander80.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2414451","Collaborative Research: Conference: Special Trimester on Post-Quantum Algebraic Cryptography","DMS","ALGEBRA,NUMBER THEORY,AND COM, Secure &Trustworthy Cyberspace","09/01/2024","07/02/2024","Vladimir Shpilrain","NY","CUNY City College","Standard Grant","Tim Hodges","08/31/2025","$10,000.00","","shpilrain@yahoo.com","160 CONVENT AVE","NEW YORK","NY","100319101","2126505418","MPS","126400, 806000","025Z, 7556","$0.00","This award funds participation by US-based researchers in a special trimester on Post-quantum algebraic cryptography, to be held at the The Henri Poincare Institute, Paris, France, September 9 - December 13, 2024. In recent years, there has been a substantial amount of research on quantum computers -- machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. The thematic trimester program will bring together researchers and practitioners from academia, industry, and government institutions with diverse backgrounds to discuss quantum algorithms, quantum-safe cryptography, as well as deployment issues, from different angles.

This thematic trimester program will address various proposed cryptographic primitives that are currently considered to be quantum-safe. This includes lattice-based, multivariate, code-based, hash-based, group-based, and other primitives some of which were considered by NIST during their post-quantum standardization process. Our program will also address various functionalities of cryptographic constructions that are in high demand in real life. This includes fully homomorphic encryption that provides for private search on encrypted database and machine learning on encrypted data. Another functionality that is getting increasingly popular is outsourcing (a.k.a. delegating) computation of algebraic functions including group exponentiation, product of group exponentiations, etc., from a computationally limited client holding an input and a description of a function, to a computationally stronger entity holding a description of the same function. Further information can be found at the program website:
https://www.ihp.fr/en/events/post-quantum-algebraic-cryptography-paris

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2416129","Local Geometric Langlands Correspondence and Representation Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","01/12/2024","Sam Raskin","CT","Yale University","Standard Grant","James Matthew Douglass","06/30/2024","$47,858.00","","sam.raskin@yale.edu","150 MUNSON ST","NEW HAVEN","CT","065113572","2037854689","MPS","126400","","$0.00","Representation theory studies the realization of groups as linear symmetries. There are two typical stages: 1) finding the general structure of representations of a given group (e.g., classifying irreducible representations), and 2) applying this to representations of particular interest (e.g., functions on a homogeneous space). This project aims to study higher representation theory, which studies the realization of groups as categorical symmetries. The emphasis of the proposal focuses on loop groups, where the theory remarkably mirrors classical harmonic analysis for p-adic groups. In particular, one finds Langlands-style decompositions here. This project focuses on understanding some key categories of interest in this framework. The investigator will study 3d mirror symmetry conjectures, representations of affine Lie algebras, and moduli spaces of bundles arising in the global geometric Langlands program. This project provides training opportunities for graduate students.

In more detail, 3d mirror symmetry, representations of (reductive) affine Lie algebras, and the geometric Langlands program are the three primary ways actions of loop groups of reductive groups on categories arise. A large class of 3d mirror symmetry conjectures concerns the categorical Plancherel formula for loop group actions on categories of sheaves on loop spaces of particular varieties with group actions. The PI will establish first cases of 3d mirror symmetry and apply the results to give coherent descriptions of some categories of primary interest in geometric representation theory. Representations of Lie algebras concern the action of a group on its category of Lie algebra representations. The PI will extend previous work on critical level localization theory and develop a substitute for Soergel modules that will apply to poorly understood categories in the local geometric Langlands program. The applications to global geometric Langlands concern actions of loop groups of reductive groups on moduli spaces of a global nature, namely bundles with a level structure. The PI will extend the Satake theorem and apply the result to study Eisenstein series in the global geometric Langlands program.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2414452","Collaborative Research: Conference: Special Trimester on Post-Quantum Algebraic Cryptography","DMS","ALGEBRA,NUMBER THEORY,AND COM, Secure &Trustworthy Cyberspace","09/01/2024","07/02/2024","Delaram Kahrobaei","NY","CUNY Queens College","Standard Grant","Tim Hodges","08/31/2025","$10,000.00","","dkahrobaei@gc.cuny.edu","6530 KISSENA BLVD","FLUSHING","NY","113671575","7189975400","MPS","126400, 806000","025Z, 7556","$0.00","This award funds participation by US-based researchers in a special trimester on Post-quantum algebraic cryptography, to be held at the The Henri Poincare Institute, Paris, France, September 9 - December 13, 2024. In recent years, there has been a substantial amount of research on quantum computers -- machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. The thematic trimester program will bring together researchers and practitioners from academia, industry, and government institutions with diverse backgrounds to discuss quantum algorithms, quantum-safe cryptography, as well as deployment issues, from different angles.

This thematic trimester program will address various proposed cryptographic primitives that are currently considered to be quantum-safe. This includes lattice-based, multivariate, code-based, hash-based, group-based, and other primitives some of which were considered by NIST during their post-quantum standardization process. Our program will also address various functionalities of cryptographic constructions that are in high demand in real life. This includes fully homomorphic encryption that provides for private search on encrypted database and machine learning on encrypted data. Another functionality that is getting increasingly popular is outsourcing (a.k.a. delegating) computation of algebraic functions including group exponentiation, product of group exponentiations, etc., from a computationally limited client holding an input and a description of a function, to a computationally stronger entity holding a description of the same function. Further information can be found at the program website:
https://www.ihp.fr/en/events/post-quantum-algebraic-cryptography-paris

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401327","Algebraic Points on Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","07/02/2024","Bianca Viray","WA","University of Washington","Standard Grant","Adriana Salerno","08/31/2027","$260,000.00","","bviray@uw.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","126400","","$0.00","This project centers on understanding the arithmetic of solutions to systems of polynomial equations, i.e., varieties. A key tool in the project is to use the limiting geometric structure of solutions of large complexity, thereby allowing the PI to study solutions of increasing complexity in a uniform manner. Understanding the arithmetic of varieties has many applications including to cryptography and to coding theory. This project also funds mentoring and training of early career mathematicians, particularly those from groups who have been historically excluded from mathematics. In addition to training Ph.D. students at their own institution, the PI also co-organizes the Roots of Unity workshop series and the Women in Numbers conference series.

More specifically, the main research focus of the proposal is to organize and, in the case of a rank 0 curve, even describe all algebraic points on a curve. This includes characterizing the local splitting behavior of the residue fields of points that appear in a fixed linear system. In addition, the PI will use the Abel-Jacobi map to package all algebraic points on a curve with rank 0 Jacobian in terms of a finite set of complete linear systems. This project builds on the PI's prior work on isolated and parameterized points and on degree sets over Henselian fields. The proposal also includes complementary projects that explore the behavior of algebraic points on surfaces. These complementary projects focus on particular classes of surfaces of negative Kodaira dimension and surfaces of Kodaira dimension 0 with a view to understanding the different phenomena that can arise for higher dimensional varieties.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2428995","Conference: Betti Numbers in Commutative Algebra and Equivariant Homotopy Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","08/01/2024","06/17/2024","Claudia Miller","NY","Syracuse University","Standard Grant","Tim Hodges","07/31/2025","$15,000.00","","clamille@syr.edu","900 S CROUSE AVE","SYRACUSE","NY","13244","3154432807","MPS","126400, 126700","7556","$0.00","This award provides travel funding for US-based participants in the week-long workshop ?Betti numbers in commutative algebra and equivariant homotopy theory? to be held September 23?27, 2024, at Bielefeld University, in Bielefeld, Germany. The workshop centers on a series of long-standing conjectures that appear in parallel in two major fields of mathematics. The goal of the workshop is to bring together researchers from these two fields to discuss recent advances on these conjectures. Another goal is to train more researchers to work on these important problems and help them build connections between the two fields. The overarching goal of this award would be to increase US participation in this highly active area of research, and to foster collaborations between US mathematicians and those from other countries. The funding is aimed especially at postdoctoral fellows and graduate students, as well as participants who do not have independent funding, to attend this workshop, and it will also be used to encourage participation by individuals from underrepresented groups in mathematics. A recent workshop held in Banff, Canada in 2022 initiated this goal, and funding for this event would cement the connections already made and build new ones for younger participants. The bridges we are building will not only connect researchers located in different countries but also between those working in different areas of mathematics.

Algebra and topology are thriving branches of mathematics that are well represented in most math departments. Commutative algebra, as the algebraic underpinnings of algebraic geometry, and algebraic topology, with its strong focus on homology and homotopy, have occasional significant overlap in both methods and aims. The goal is to create a strong working alliance between the groups working on these conjectures and related problems, and also to get younger researchers involved in these problems. In fact, total Betti numbers appear in related, decades-old rank conjectures in commutative algebra and equivariant topology. On the topological side, Halperin and Carlsson conjectured that the total Betti number of a compact space with a free torus action or p-torus action of rank r is bounded below by 2r, which has inspired much research on the topological side of spaces with a group action. On the algebraic side, Avramov conjectured a similar lower bound for the total Betti number of finite length modules over a local ring. Recent work of Walker and VandeBogert-Walker resolves this conjecture positively for rings of prime characteristic, whereas counterexamples to a stronger conjecture show the subtlety of the questions. The web site for the workshop is at https://www.math.uni-bielefeld.de/birep/meetings/betti2024/index.php and includes a full speaker list.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401104","Combinatorics of Complex Curves and Surfaces","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/15/2024","01/24/2024","Philip Engel","IL","University of Illinois at Chicago","Standard Grant","James Matthew Douglass","07/31/2025","$67,057.00","","pengel@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126400","","$0.00","Two-dimensional tilings lie at a fulcrum connecting many areas of mathematics and physics. Easy to visualize and appealing in their simplicity, tilings have fascinated mathematicians at all levels, artists, architects, and the general public. This goals of this project are (1) to study tilings in the context of recent mathematical developments about algebraic curves and surfaces, exploring their connections to algebra, geometry, and representation theory, (2) to disseminate mathematical ideas to a wide audience and increase aesthetic and intellectual appreciation of mathematics in the general public, and (3) to develop an active and diverse community of young researchers, postdocs, and PhD students focusing on this circle of ideas.

One primary area of research will be modular toroidal compactifications of spaces of K3 surfaces. This project, joint with V. Alexeev, seeks to build extensions of the universal family of polarized K3 surfaces to the boundary of a toroidal compactification, extending previous work on degree 2 and elliptic K3 surfaces. The approach employs tilings of integral-affine structures on the sphere. The second primary research topic is moduli spaces of higher differentials. This project aims to study strata of higher differentials, their volumes, and the connection with enumeration of tilings. Joint work with P. Smillie explores decompositions of flat surfaces into Penrose-like tiles. The approach is novel, requiring a generalization of Hurwitz theory to one complex-dimensional leaf spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401356","Modular forms and L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","10/01/2024","06/14/2024","Olivia Beckwith","LA","Tulane University","Standard Grant","Andrew Pollington","09/30/2027","$182,101.00","","obeckwith@tulane.edu","6823 SAINT CHARLES AVE","NEW ORLEANS","LA","701185665","5048654000","MPS","126400, 915000","9150","$0.00","The research in this project is in the area of analytic number theory, a field that uses analytic functions to study arithmetic structure. The main objects of study in this project are modular forms, complex analytic functions that encode a wide variety of arithmetic information in various ways and play a major role in modern number theory, with connections to combinatorics, algebraic geometry, representation theory, topology, and mathematical physics. While the most classical modular forms are holomorphic, real-analytic modular forms have also been studied for decades and become essential tools in analytic number theory. More recently, harmonic Maass forms have appeared in many applications, for example, to indefinite theta functions, combinatorics, and elliptic curves. This project will explore the arithmetic information encoded by the harmonic Maass forms and their closely related generalizations, and ways of extending classical methods from analytic number theory to study them. The PI will also use the grant to support the dissemination of the research ideas by the PI and her PhD students at conferences and to organize number theory seminars.

The PI plans to explore the connections between real-analytic modular forms and L-functions. This project will elucidate connections between values of L-functions and harmonic and polyharmonic Maass forms, and will use these connections to develop new methods of constructing modular forms and summation formulas for mock modular forms. The methods will utilize differential operators on modular forms, the spectral theory of automorphic forms, and techniques from the analytic theory of L-functions such as converse theorems. Applications to the study of Hurwitz class numbers and quadratic number fields will also be explored.

This project is jointly funded by Algebra and Number Theory program, and the Established Program to Stimulate Competitive Research (EPSCoR).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2435243","Analytic Number Theory over Function Fields","DMS","ALGEBRA,NUMBER THEORY,AND COM","02/15/2024","06/12/2024","Will Sawin","NJ","Princeton University","Continuing Grant","Andrew Pollington","06/30/2024","$24,864.00","","sawin@math.columbia.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","126400","","$0.00","Number theory is an area of mathematics that centers on the ordinary counting numbers and their behavior when we add and multiply them. While problems in this area are often simple to state, they can be fiendishly difficult to solve. The subfield of function field number theory aims to obtain insight on these problems by considering a kind of model or parallel universe where numbers behave differently. We consider what happens when we add or multiply numbers as normal but, except, instead of carrying digits, we simply drop the excess. Certainly arithmetic is a little easier with this modified rule, but more surprisingly, some of the most important problems in number theory become easier as well, with even some of the most difficult ones becoming solvable. (Technically, we should work in binary, or any prime base, rather than our usual base 10, for this.) Alternately, we can describe this variant arithmetic as the addition or multiplication of polynomial functions in a single variable. In this setting, we can connect number-theoretic questions to geometry, by viewing the graph of the polynomial as a geometric object. In this award the PI's research uses geometric tools to solve new problems in this area.

The PI's research has resolved function field analogues of classical problems in number theory, including the twin primes conjecture and Chowla's conjecture (both joint with Shusterman), cases of the Ramanujan conjecture (joint with Templier), and conjectures about moments of L-functions. In this award the PI will continue along these lines, proving additional results about the distribution of prime numbers, L-function moments, and automorphic forms, and work in further directions such as non-abelian Cohen-Lenstra heuristics. These works are all based on etale cohomology theory, where the foundational result, Deligne's Riemann Hypothesis, allows many different analytic problems (problems about proving some inequality) to be reduced to cohomology problems (problems about calculating some of the cohomology groups of a variety or sheaf). The relevant varieties are high-dimensional, and calculating the necessary cohomology groups requires techniques like vanishing cycles theory and the characteristic cycle.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2342252","RTG: Geometry and Topology","DMS","ALGEBRA,NUMBER THEORY,AND COM, WORKFORCE IN THE MATHEMAT SCI","06/15/2024","06/12/2024","David Gay","GA","University of Georgia","Continuing Grant","Swatee Naik","05/31/2029","$899,466.00","Gordana Matic, Akram Alishahi, Pierrick Bousseau, Nuromur Arguz","dgay@uga.edu","623 BOYD GRADUATE RESEARCH CTR","ATHENS","GA","306020001","7065425939","MPS","126400, 733500","7301, 9251","$0.00","This award supports the research training of postdoctoral researchers, PhD students and undergraduates in the mathematics department at the University of Georgia working in three closely related geometric areas: algebraic geometry, symplectic geometry and low-dimensional topology. These fields deal with both foundational questions at the heart of pure mathematics, such as understanding the possible shapes of spaces and their descriptions in terms of equations, and questions related to mathematical physics, computation and new ideas for analysis of large data. The training includes collaborative seminars, outreach and visualization projects, summer schools, visiting speakers, and research working groups.

This RTG award supports students and postdocs working under the supervision of eight topologists, algebraic geometers and symplectic geometers at the University of Georgia (UGA). The topologists all work on problems that have strong connections with symplectic and contact topology, the algebraic geometers study moduli spaces that have fascinating topology and can be studied using symplectic techniques, with connections to mirror symmetry and mathematical physics, while the symplectic geometry work extends all the way to connections with topological data analysis. In addition to special seminars, workshops, RTG bridge-building topics courses, research working groups, and computational working groups, this project supports several innovative outreach and recruitment-oriented activities. These include the Geometry Research, Outreach and Visualization Initiative, in collaboration with Moon Jang, UGA associate professor of graphic design, and with interdisciplinary project management provided by the UGA Arts Collaborative, which involves participants from multiple levels working together on visual communication projects directly related to this RTG?s research activities.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -31,13 +44,11 @@ "2348653","Bessel functions on higher-rank groups","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","06/15/2024","06/03/2024","Jack Buttcane","ME","University of Maine","Standard Grant","Andrew Pollington","05/31/2027","$300,000.00","","jack.buttcane@maine.edu","5717 CORBETT HALL","ORONO","ME","044695717","2075811484","MPS","126400, 915000","9150","$0.00","Classical Bessel functions arise as solutions to certain differential equations and appear throughout mathematics and the sciences. There are numerous books on their properties and behaviors and descriptions as integrals, series, and so on. They appear in number theory through formulas of Voronoi, Petersson and Kuznetsov. In particular, the formula of Kuznetsov, also known as a relative trace formula, gives connections between interesting objects in analysis and algebra/geometry. This research studies the generalizations of Kuznetsov's formula and the generalized Bessel functions that appear in such formulas, with the goal of building a body of knowledge similar to what is known about the classical Bessel functions. This will allow analytic number theorists to explore the applications of these new Kuznetsov-type formulas. Part of the funding for the project will be used to support undergraduate and master's-level research in analytic number theory.

While the Kuznetsov formula for SL(2) has been the subject of intense research for the past 40 years, much less is known about its generalizations to reductive groups. These generalizations relate the exponential sums occurring in the Fourier coefficients of Poincare series to the Fourier coefficients of automorphic forms and the integral transforms in these generalized Kuznetsov formulas can, conjecturally, be expressed as kernel integral transforms; the kernels are generalized Bessel functions. This research aims to extend the study of Bessel functions to groups such as GL(n) and GSp(n). The immediate goals are to study their differential equations, integral representations and give basic asymptotics of their integral transforms in low-rank groups such as GL(4) and GSp(4). Long-term goals for the project include extending these results to arbitrary rank and applications such as the arithmetically-weighted Weyl law. Smaller, associated projects on GL(3) include studying the Poincare series occurring in the GL(3) Fourier expansion, application of the Kuznetsov formula to the supremum norm problem as well as the relationship between vector sup norms and scalar sup norms for Maass forms with weight.

This project is jointly funded by Algebra and Number Theory program, and the Established Program to Stimulate Competitive Research (EPSCoR).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401483","Moduli Spaces and Invariants in Algebraic Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","05/29/2024","Dori Bejleri","MD","University of Maryland, College Park","Standard Grant","James Matthew Douglass","06/30/2027","$225,000.00","","dbejleri@umd.edu","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","126400","","$0.00","Algebraic geometry deals with the study of algebraic varieties: higher-dimensional geometric shapes defined by systems of polynomial equations. Solving such systems directly often proves to be intractable. A fundamental theme in algebraic geometry is the interplay between the qualitative geometry of algebraic varieties and the quantitative analysis of solutions to polynomial equations. Central to this is the question of classifying algebraic varieties. The answer to the classification question often comes in the form of a so-called moduli space, which is a parameter space for the algebraic varieties of interest. Each point of a moduli space represents a variety, and the geometry of the moduli space reflects the ways these varieties change and deform as the parameters vary. The classification question, then, is tantamount to understanding the geometry of the corresponding moduli space. This project will develop new tools in moduli theory and use them to advance the classification of algebraic varieties. In addition, the project will provide research training opportunities for both undergraduate and graduate students.

In more detail, the Deligne-Mumford compactification of the space of pointed curves by pointed stable curves has been the gold standard in moduli theory. In higher dimensions, the stable pair, or KSBA, compactification serves the same role. However, its construction and geometry are considerably more intricate, and few general reults about its local and global geometry are known. This project will develop and refine techniques in the deformation theory of stable pairs and wall-crossing phenomena for higher-dimensional moduli, thereby offering a path toward developing higher-dimensional enumerative geometry. A second focus is to explore the log Calabi-Yau wall. The theory of stable pairs applies to varieties of log general type, and the theory of K-stability applies to log Fano varieties. This project will develop a moduli theory for log Calabi-Yau pairs that will bridge the gap between KSBA- and K-moduli. Finally, the project aims to use the previously developed moduli theoretic techniques to answer questions in arithmetic geometry and arithmetic statistics, namely on counting rational points of bounded height on stacks.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401554","Functoriality for Relative Trace Formulas","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","05/30/2024","Ioannis Sakellaridis","MD","Johns Hopkins University","Continuing Grant","Andrew Pollington","06/30/2027","$106,185.00","","sakellar@jhu.edu","3400 N CHARLES ST","BALTIMORE","MD","212182608","4439971898","MPS","126400","","$0.00","The Langlands functoriality conjecture, that ""different arithmetic drums share some common eigenfrequencies,"" has immense applications in number theory, among others to the century-old conjectures due to Ramanujan and others about the size of coefficients of special functions called automorphic forms. The PI and his collaborators have broadened this conjecture to the so-called ""relative"" setting, which includes methods of studying special values of L-functions (also called zeta functions), such as in the prominent, and more recent, conjectures of Gan, Gross, and Prasad. The main tool for proving important instances of functoriality so far has been the trace formula, but in its current form it has nearly reached its limits. This project will examine ways to prove these conjectures by use of the idea of quantization, whose origins lie in mathematical physics. This idea will be used to construct novel ways of comparing (relative) trace formulas, drastically expanding their potential reach and applicability. The broader impacts of the project include conference organization and mentoring of graduate students.

The PI has already shown, in prior work, that in some low-rank cases one can establish relative functoriality via some novel ""transfer operators"" between relative trace formulas. Such non-standard comparisons of trace formulas were envisioned in Langlands's ""Beyond Endoscopy"" proposal; the ""relative"" setting allows for more flexibility, and more potential applications, for the exploration of such comparisons. Prior work was focused mostly on the case when the L-groups associated to the relative trace formulas are of rank one. The main goal of this project will be to examine ways to generalize the construction of transfer operators to higher rank. The main idea is to view a trace formula as the quantization of its cotangent stack, which in turn is largely controlled by the L-group. Using natural correspondences between such cotangent stacks, the project aims to construct transfer operators between their quantizations. On a separate track, the project will continue work on the duality of Hamiltonian spaces conjectured in the PI's recent work with Ben-Zvi and Venkatesh, with the aim of extending this duality beyond the hyperspherical setting, and exploring applications for the representation theory of p-adic groups.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2404973","Conference: Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","05/29/2024","Aaron Lauda","CA","University of Southern California","Standard Grant","James Matthew Douglass","05/31/2026","$50,000.00","Milen Yakimov","lauda@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","900890701","2137407762","MPS","126400","7556","$0.00","The award will provide funding for the sixth and seventh meetings of the Canada-Mexico-USA Conference Series in Representation Theory, Noncommutative Algebra, and Categorification. These meetings will take place at the Universidad Nacional Autónoma de México in Mexico City in June 2024 and at the University of Southern California in Los Angeles in August 2025. Representation theory is a branch of mathematics that studies symmetries of physical theories and mathematical objects. Often, the main objects in representation theory are only the shadows of richer structures that are recovered through deeper study. Noncommutative algebra is a related branch of mathematics that studies deformations of commutative objects found in quantum theories, representation theory, and geometry. The foci of the conferences will be on recent advances at the interface of representation theory, categorification, and noncommutative algebra; on fostering an environment for the establishment of international collaborations between Canada, Mexico, and the USA in these research areas; and on exposing graduate students, post-docs, and early-career faculty in the three countries to current developments in the field. A poster session will run through the full meeting where early-career attendees will present their research.

The main scientific topics for the sixth meeting in Mexico City will be geometric, algebraic, and homological methods in representation theory, representation theoretic and homological properties of noncommutative algebras, and the investigation of those problems using categorical methods. The talks will cover some of the most recent trends, including the following: cluster algebras, monoidal and additive categorifications, quantum symmetries, finite tensor categories, representations of quantized affine Kac-Moody algebras, Calabi-Yau algebras and triangulated categories, Hopfological algebra, web approaches to modular representation theory, and representation theoretic aspects of Heegaard-Floer homology. The website for the 2024 conference is https://sites.google.com/im.unam.mx/canadausmexico-2024/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404896","Geometry of Moduli Spaces and Metaplectic Representations","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","05/30/2024","Nicola Tarasca","VA","Virginia Commonwealth University","Continuing Grant","Swatee Naik","06/30/2027","$100,000.00","","tarascan@vcu.edu","910 WEST FRANKLIN ST","RICHMOND","VA","232849005","8048286772","MPS","126400","","$0.00","Conformal field theories, rooted in theoretical physics, offer a powerful framework for geometers to study algebraic curves. While traditionally focused on curves, recent advancements in the geometric manifestations of infinite-dimensional algebras suggest the emergence of a rich theory applicable to higher-dimensional varieties as well. Motivated by promising preliminary findings, the PI will lead an exploration of conformal field theories extending beyond curves, probing fundamental questions concerning the geometry of higher-dimensional varieties. Similarly, the PI will investigate invariants for knots and 3-manifolds. This project will fuel the integration of ideas from several fields of mathematics, such as representation theory, algebraic geometry, and quantum topology. It will also feature experiential learning initiatives tailored for middle school students, alongside research training opportunities designed for undergraduate and graduate students. Furthermore, the project aims to foster interdisciplinary collaborations and enhance mathematical literacy within the general public through a series of public lectures and events.

More specifically, the PI will build upon recent work on coinvariants of vertex algebras to explore geometric realizations of metaplectic modules on abelian varieties and their moduli spaces. These investigations will offer a novel perspective on the theory of theta functions and vector bundles equipped with a projectively flat connection on families of abelian varieties. Furthermore, the PI will investigate the factorization properties of spaces of coinvariants on decomposable abelian varieties, followed by an assessment of the persistence of these properties at boundary points across various compactifications. Finally, the PI will explore various refinements of the theory of homological blocks for knots and 3-manifolds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2346767","Conference: The Legacy of Ramanujan","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","05/29/2024","Amita Malik","PA","Pennsylvania State Univ University Park","Standard Grant","Adriana Salerno","05/31/2025","$34,955.00","Ae Ja Yee","azm7010@psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","126400","7556","$0.00","This award supports the conference ?The Legacy of Ramanujan?, to be held at The Pennsylvania State University, University Park, June 6?9, 2024. Ramanujan?s remarkable discoveries made a powerful impact on various branches of mathematics in the 20th century, and the broad scope of his pioneering work is represented in the wide range of topics that will be discussed. This conference aims to highlight recent discoveries and open problems from number theory to combinatorics, special functions, symbolic computations, and other related areas focusing on the topics influenced by the mathematics of Ramanujan. In addition, the conference will honor the work of George Andrews and Bruce Berndt, who have both done much to honor, advertise, and explain the work of Ramanujan. The broader impacts of this conference include: disseminating new achievements, research trends, and problems in this area, encouraging significant collaboration among mathematicians, and providing early-career mathematicians, including graduate students, with an opportunity to present their research.

The conference will host between 125 and 150 participants, and will feature thirteen invited plenary 50-minute talks and about twenty five 20-minute talks covering topics such as: Mock theta functions, partition theory and q-series, and Rogers-Ramanujan identities. There will be two poster-sessions presented by early-career researchers, including graduate students. After the conference, refereed proceedings papers will be disseminated through special issues of the Ramanujan Journal. More details can be found on the conference web-page: https://sites.psu.edu/ramanujan/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2419363","Conference: Workshop on Computational and Applied Enumerative Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/15/2024","05/14/2024","Luis Garcia Puente","CO","Colorado College","Standard Grant","James Matthew Douglass","04/30/2025","$22,500.00","Nickolas Hein, Taylor Brysiewicz","lgarciapuente@coloradocollege.edu","14 E CACHE LA POUDRE ST","COLORADO SPRINGS","CO","809033243","7193896318","MPS","126400","7556","$0.00","The ""Workshop on Computational and Applied Enumerative Geometry"" will be held June 3 to June 7, 2024 at the Fields Institute in Toronto, ON, Canada. Enumerative geometry is the study of a particular class of mathematical problems, called enumerative problems, which are fundamental to STEM fields including mathematics, particle physics, robotics, and computer vision. The main goal of this workshop is to unite experts working on problems related to enumerative geometry to increase dialogue between theory and application. There will be several talks on state-of-the-art research in computational and applied enumerative geometry, software demonstrations, and time to discuss open problems. The exchange of ideas will inform experts as they continue devising computational investigations of enumerative problems going forward. The grant supports the participation of fifteen US-based participants in the workshops.

Classically, an enumerative problem asks how many geometric objects have a prescribed position with respect to other fixed geometric objects. Famous examples include the problems of (a) 2 lines meeting four lines, (b) 27 lines on a cubic surface, and (c) 3264 conics tangent to five conics in the plane. A modern definition of an enumerative problem is a system of polynomial equations in variables and parameters with finitely many solutions given fixed generic parameters. Counting solutions to such a problem is the tip of the iceberg. Beyond enumeration lie questions of symmetries, solvability, real behavior, and computation. Techniques from a broad range of disciplines lend themselves to the creation of algorithms and software designed to answer these questions. ""Computational Enumerative Geometry"" refers to this approach of using computers to solve, experiment with, and prove theorems about, enumerative problems. The workshop website is http://www.fields.utoronto.ca/activities/23-24/enumerative-geometry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408914","Conference: Quantum Algebras and Representation Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/01/2024","05/16/2024","Naihuan Jing","NC","North Carolina State University","Standard Grant","James Matthew Douglass","07/31/2025","$39,999.00","Vyjayanthi Chari","jing@math.ncsu.edu","2601 WOLF VILLAGE WAY","RALEIGH","NC","276950001","9195152444","MPS","126400","7556","$0.00","This project supports participation in the conference ""Quantum Groups and Representation Theory"" to be held on October 12-15, 2024 at North Carolina State University. Quantum groups, which are generalizations of Lie groups and Lie algebras, are mathematical notions that describe symmetry in mathematics and physics. The conference aims to stimulate research collaboration in the representation theory of quantum groups and related topics. The conference will feature expository talks by leading researchers and provide a forum for experts to survey the current developments in the area. The conference will provide opportunities for graduate students and early-career researchers to enhance their research programs.

The conference will focus on several aspects of the representation theory of quantum groups and related algebraic structures, specifically, quantized enveloping algebras, quantum function algebras, Yangian algebras, Kac--Moody Lie algebras, Hecke algebras, canonical and crystal bases, vertex algebras, Hall algebras, cluster algebras, Hopf algebras, and Khovanov-Lauda-Rouquier algebras or quiver Hecke algebras. The conference website is https://sites.google.com/ncsu.edu/conf-quantum-groups-rep2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401461","Zeros of L-functions and Arithmetic","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","07/01/2024","05/15/2024","Micah Milinovich","MS","University of Mississippi","Standard Grant","Andrew Pollington","06/30/2027","$252,360.00","","mbmilino@olemiss.edu","113 FALKNER","UNIVERSITY","MS","386779704","6629157482","MPS","126400, 915000","9150","$0.00","This award concerns research in number theory which is a very active area of mathematics, and the theory of L-functions, which were first introduced into the subject by Dirichlet in the 19-th century to study the distribution of prime numbers, has played a central role in its modern development. The tools used to study L-functions draw from many fields including analysis, algebra, algebraic geometry, automorphic forms, representation theory, probability and random matrices, and mathematical physics. Many of the projects in this proposal concern the connection between problems in number theory and the distribution of zeros of L-functions. This connection is central to two of the seven Millennium Prize Problems, the Riemann hypothesis and the Birch and Swinnerton-Dyer conjecture. This award aims to use tools from the theory of L-functions to make new progress on some classical problems in number theory as well as establish new connections between the theory of L-functions to fields such as additive combinatorics. The PI will continue training and mentoring graduate students on topics related to this research, and this project will provide research training opportunities for them.

One goal of this project aims to use tools from Fourier analysis, along with input from zeros of L-functions, to study classical problems in number theory such as bounding the least quadratic non-residue modulo a prime, the least prime in an arithmetic progression, and the maximum size of modulus and argument of an L-functions on the critical line. Each of these problems requires using explicit formulae (connecting zeros of L-functions to the primes) to create a novel Fourier optimization framework and then to solve the resulting problem in analysis. This project also aims to study a number of problems concerning the L-functions associated to classical holomorphic modular forms, including studying simultaneous non-vanishing of L-functions at the central point, using sieve methods to studying non-vanishing of central values of L-functions in certain sparse (but arithmetically interesting) families, and to study the proportion of the non-trivial zeros of a modular form L-function that are simple. Using known partial progress toward the Birch and Swinnerton-Dyer conjecture, some of these proposed problems have applications to studying algebraic ranks of elliptic curves. Another goal of this project is to use tools from the theory of L-functions in a novel way to investigate problems in additive combinatorics such as studying sums of dilates in certain arithmetically interesting groups.


This project is jointly funded by Algebra and Number Theory program, and the Established Program to Stimulate Competitive Research (EPSCoR).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2339274","CAREER: New directions in the study of zeros and moments of L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","02/12/2024","Alexandra Florea","CA","University of California-Irvine","Continuing Grant","Tim Hodges","06/30/2029","$87,350.00","","alexandra.m.florea@gmail.com","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126400","1045","$0.00","This project focuses on questions in analytic number theory, and concerns properties of the Riemann zeta-function and of more general L-functions. L-functions are functions on the complex plane that often encode interesting information about arithmetic objects, such as prime numbers, class numbers, or ranks of elliptic curves. For example, the Riemann zeta-function (which is one example of an L-function) is closely connected to the question of counting the number of primes less than a large number. Understanding the analytic properties of L-functions, such as the location of their zeros or their rate of growth, often provides insight into arithmetic questions of interest. The main goal of the project is to advance the knowledge of the properties of some families of L-functions and to obtain arithmetic applications. The educational component of the project involves groups of students at different stages, ranging from high school students to beginning researchers. Among the educational activities, the PI will organize a summer school in analytic number theory focusing on young mathematicians, and will run a yearly summer camp at UCI for talented high school students.

At a more technical level, the project will investigate zeros of L-functions by studying their ratios and moments. While positive moments of L?functions are relatively well-understood, much less is known about negative moments and ratios, which have applications to many difficult questions in the field. The planned research will use insights from random matrix theory, geometry, sieve theory and analysis. The main goals fall under two themes. The first theme is developing a general framework to study negative moments of L-functions, formulating full conjectures and proving partial results about negative moments. The second theme involves proving new non-vanishing results about L-functions at special points. Values of L-functions at special points often carry important arithmetic information; the PI plans to show that wide classes of L-functions do not vanish at the central point (i.e., the center of the critical strip, where all the non-trivial zeros are conjectured to be), as well as to study correlations between the values of different L-functions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347095","Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","12/19/2023","Kimball Martin","OK","University of Oklahoma Norman Campus","Standard Grant","Andrew Pollington","12/31/2026","$20,000.00","Ameya Pitale","kmartin@math.ou.edu","660 PARRINGTON OVAL RM 301","NORMAN","OK","730193003","4053254757","MPS","126400","7556, 9150","$0.00","This award supports the TORA mathematics conference series. This series consists of annual meetings hosted by the University of North Texas, Oklahoma State University, and the University of Oklahoma on a rotating basis. This award provides support for three weekend conferences, one at the University of North Texas in Spring 2024 (TORA XIII), one at Oklahoma State University in Spring 2025 (TORA XIV), and another at the University of Oklahoma in Spring 2026 (TORA XV). Each conference will feature three prominent guest speakers from outside the Texas-Oklahoma region, in addition to other participants including students, post-doctoral researchers, and junior faculty. Regional graduate students and researchers will also give talks describing their work. These conferences will facilitate collaborations and interactions among the students and researchers in the region who work in the areas of Automorphic Forms, Representation Theory, and Number Theory.

Over the last century, the theories of automorphic forms and representations have grown enormously. Important applications impact various fields of research, ranging from number theory, coding theory, algebraic geometry, and topology to Kac-Moody algebras and quantum field theory. The interplay of automorphic forms and representation theory has been especially fruitful, and many surprising and deep results have emerged. The TORA conference series will emphasize the interplay between automorphic forms and representations, both in the classical and adelic languages, and related topics like analytic number theory and harmonic analysis.



The conference Texas-Oklahoma Representations and Automorphic forms XIII will take place on April 12-14, 2024, at the University of North Texas. Additional information can be found on the conference website: https://www.math.unt.edu/~richter/TORA/TORA13.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401184","Representation Theory and Geometry in Monoidal Categories","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","04/04/2024","Daniel Nakano","GA","University of Georgia Research Foundation Inc","Continuing Grant","Tim Hodges","08/31/2027","$88,519.00","","nakano@math.uga.edu","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126400","","$0.00","The Principal Investigator (PI) will investigate the representation theory of various algebraic objects. A representation of an abstract algebraic object is a realization of the object via matrices of numbers. Often times, it is advantageous to view the entire collection of representations of an algebraic object as a structure known as a tensor category. Tensor categories consist of objects with additive and multiplicative operations like the integers or square matrices. Using the multiplicative operation, one can introduce the spectrum of the tensor category which is a geometric object (like a cone, sphere or torus). The PI will utilize the important connections between the algebraic and geometric properties of tensor categories to make advances in representation theory. The PI will continue to involve undergraduate and graduate students in these projects. He will continue to be an active member of the mathematical community by serving on national committees for the American Mathematical Society (AMS), and as an editor of a major mathematical journal.

The PI will develop new methods to study monoidal triangular geometry. Several central problems will utilize the construction of homological primes in the general monoidal setting and the introduction of a representation theory for MTCs. This representation theory promises to yield new information about the Balmer spectrum of the MTC. In particular, the general MTC theory will be applied to study representations of Lie superalgebras. The PI will also explore new ideas to study representations of classical simple Lie superalgebras. This involves systematically studying various versions of Category O and the rational representations for the associated quasi-reductive supergroups. One of the main ideas entails the use of the detecting and BBW parabolic subgroups/subalgebras. Furthermore, the PI will study the orbit structure of the nilpotent cone and will construct resolutions of singularities for the orbit closures. The PI will study important questions involving representations of reductive algebraic groups. Key questions will focus on the understanding the structures of induced representations, and whether these modules admit p-filtrations. These questions are interrelated with the 30-year-old problem of realizing projective modules for the Frobenius kernels via tilting modules for the reductive algebraic group, and the structure of extensions between simple modules for the first Frobenius kernel.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401526","Geometric Langlands and Automorphic Functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/29/2024","Sam Raskin","CT","Yale University","Continuing Grant","James Matthew Douglass","06/30/2027","$118,501.00","","sam.raskin@yale.edu","150 MUNSON ST","NEW HAVEN","CT","065113572","2037854689","MPS","126400","","$0.00","The modern, connected world is built on mathematical duality. Signals have two equivalent mathematical representations: one containing the data we care about, and a second, Fourier dual representation, as a formal mathematical sum of functions like sines and cosines. Mathematically, one can formally convert between the two pictures, but the differences between the two points of view matter in mathematics, physics, and engineering. For example, in order to ?simplify? an image, one might naively cut it in half; a better idea is to use the Fourier transform, forget some of the information, and then apply an inverse Fourier transform; this is the basis of image compression. This project will study an incarnation of duality in a setting that involves geometry and arithmetic. The project will provide research training opportunities for graduate students.

In more detail, in the 1960?s, Robert Langlands proposed settings in number theory where similar ideas about mathematical duality could be considered. He conjectured that automorphic functions would replace signals and representations of a dual group would replace the periodicity types of sine and cosine functions. These conjectures have been the starting point for a great deal of interesting mathematics since; they contain profound arithmetic meaning in a non-abelian Fourier package. A geometric variant of Langlands' conjectures was later proposed by Beilinson and Drinfeld. This project will prove the latter conjectures for general groups and obtain applications to the classical (arithmetic) Langlands conjectures. The results will be the first global theorems of their type for general reductive groups.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -53,24 +64,19 @@ "2401515","Constructing and Classifying Pre-Tannakian Categories","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/09/2024","Nate Harman","GA","University of Georgia Research Foundation Inc","Standard Grant","Tim Hodges","05/31/2027","$155,000.00","","nharman@uga.edu","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126400","","$0.00","This award funds research related to the representation theory of groups, which is the study of symmetry and the different ways symmetry can manifest itself and influence mathematical objects. It is an area of classical interest which has numerous applications to number theory, mathematical physics, algebraic geometry, topology, functional analysis, and many more areas of math. Classically, it is about representing collections of symmetries via matrices, but as a modern subject, it involves a number of more sophisticated algebraic structures. Broader impacts of this project include research training opportunities for undergraduate and graduate students, as well as the PI?s continued involvement in mathematical enrichment programs aimed at middle and high school students.

The specific algebraic structures this project aims to study are Tannakian and Pre-Tannakian categories, which are axiomatizations and generalizations of what is meant by ?the representation theory of a group.? Recently, the PI and his collaborator, Andrew Snowden, found a new connection between pre-Tannakian categories and model theory, a branch of mathematical logic. They were able to associate a pre-Tannakian category to an oligomorphic group, along with some additional numerical data known as a measure. This construction has since led to a slew of new examples as well as new insights into previously known examples. Moreover, they have shown that, in fact, these oligomorphic groups are, in a sense, unavoidable when trying to study and classify pre-Tannakian categories and need to be a part of any classification story. This project aims to continue these investigations to construct new and interesting examples of pre-Tannakian categories with exotic properties, to develop a theory for pre-Tannakian categories associated with a wider class of linear-oligomorphic groups, and to develop tools that are better suited for constructing positive characteristic versions of the categories previously constructed. All of these should be considered steps toward a long-term eventual goal of constructing and classifying all pre-Tannakian categories.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401238","Free Resolutions","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/03/2024","Irena Peeva","NY","Cornell University","Continuing Grant","Tim Hodges","05/31/2028","$83,779.00","","irena@math.cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","126400","","$0.00","This project concerns research in Commutative Algebra. A core goal in the subject deals with understanding the solutions of a system of polynomial equations, possibly in a large number of variables and with a large number of equations. Closely related to this is the concept of a free resolution. Constructing such a resolution amounts to repeatedly solving systems of polynomial equations. For many years, minimal free resolutions have been both central objects and fruitful tools in Commutative Algebra. The idea of constructing free resolutions was introduced by Hilbert in a famous paper in 1890. The study of these objects flourished in the second half of the twentieth century and has seen spectacular progress recently. The field is very broad, with strong connections and applications to other mathematical areas. The broader impacts of the project include the writing of an expository paper, organization of professional development workshops for undergraduate students, and organization of mathematical conferences.

The main research goal in this project is to make significant progress in understanding the structure of minimal free resolutions and their numerical invariants. In particular, the PI will: work jointly with M. Mastroeni and J. McCullough on Koszul Algebras; continue work on minimal free resolutions of binomial edge ideals; study the asymptotic structure of minimal free resolutions over exterior algebras.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2402367","Rational GAGA and Applications to Field Invariants","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/16/2024","Julia Hartmann","PA","University of Pennsylvania","Continuing Grant","Adriana Salerno","06/30/2027","$162,076.00","David Harbater","hartmann@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","126400","","$0.00","Geometric spaces arise in many contexts, and studying their behavior can lead to the solution of real world problems. The study of these spaces has used methods both from algebra and from calculus (also called analysis). Decades ago, a linkage between the algebraic and analytic approaches to geometry was established, which then led to important progress on geometric problems. The PIs will extend this linkage to situations in which information is given only on a piece of a geometric space, rather than on the entire space. This will make it possible to solve open problems concerning the computation of currently mysterious numerical data that relate to the behavior of geometric spaces. The approach will involve studying spaces locally in order to gain a greater insight into their overall behavior. The PIs will also engage in activities that have broader impacts. These include mentoring, widening the pipeline into mathematical research for people from groups traditionally underrepresented in mathematics, and communicating mathematics to a broader audience. In addition, graduate students supported by the award will receive training to contribute toward this research as well as to engage in further mathematical research in the future.

More precisely, the PIs will study an analog of Serre's GAGA theorem in the context of function fields of varieties, rather than for the varieties themselves. This will involve a structure sheaf that contains both holomorphic functions and rational functions. A key goal will then be to use this result to compute the conjectured period-index bound for rational function fields over the complex numbers in three or more variables. The PIs also aim to prove related results over more arithmetic ground fields, by bringing in ideas from the theory of formal schemes and building on their prior work in lower dimensions. In addition, the PIs will work to understand the structure of the absolute differential Galois group of real rational function fields. This work is motivated by results that they previously achieved in differential Galois theory over the complex numbers and in classical Galois theory over real function fields. The methods used will include local-global principles and patching, as well as the structure theory of linear algebraic groups, Galois cohomology, and other techniques.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401383","Non-Abelian Hodge Theory and Transcendence","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/01/2024","04/16/2024","Benjamin Bakker","IL","University of Illinois at Chicago","Standard Grant","James Matthew Douglass","07/31/2027","$330,000.00","","bakker@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126400","","$0.00","Hodge theory is concerned with the integrals of algebraic forms along topological cycles. The study of these invariants traces its roots to the work of Jacobi, Abel, and Riemann in the nineteenth century; the modern theory ties together the algebraic, topological, complex analytic, and arithmetic facets of the geometry of an algebraic variety, and has many applications. Pioneering work of Simpson in the 1990s developed a non-abelian version of this theory where the space of representations of the fundamental group plays the role of the group of topological cycles. The resulting non-abelian Hodge theory touches equally many fields of mathematics, but many aspects of it remain mysterious. In this project, the PI will extend recent progress in classical Hodge theory and transcendence theory via o-minimal methods to the non-abelian setting. The project will specifically be geared towards fostering the involvement of students and early-career mathematicians.

In more detail, the PI will apply o-minimal techniques to address a number of open questions related to the geometry of local systems on algebraic varieties, and its connection to complex analysis, arithmetic, and transcendence theory. This includes the transcendence theory of the Riemann?Hilbert correspondence, the classification of tri-algebraic subvarieties, as well as the algebraicity and arithmeticity of non-abelian Hodge loci. These techniques will also be brought to bear on related geometric questions, including the construction of Shafarevich maps, transcendence theory of p-adic period maps, and the geometry of Lagrangian fibrations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2422557","Conference: Resolution of Singularities, Valuation Theory and Related Topics","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/01/2024","04/03/2024","Steven Cutkosky","MO","University of Missouri-Columbia","Standard Grant","Tim Hodges","01/31/2025","$17,520.00","","cutkoskys@missouri.edu","121 UNIVERSITY HALL","COLUMBIA","MO","652113020","5738827560","MPS","126400","7556","$0.00","This award supports US-based participants in a conference on ``Resolution of Singularities, Valuation Theory and Related Topics'' which will be held from August 5 - 9, 2024 in Morelia, Mexico. The conference will be held at Centro de Ciencias Matematicas, UNAM, Morelia. NSF will provide significant travel and lodging support for 12 U.S. participants to the conference. The funding will be for students, postdoctoral scholars and other U.S. participants who do not have other federal support. A particular emphasis will be on supporting a diversity of participants, especially from under-represented groups.

The focus of the conference is on applications of valuation theory to resolution of singularities in positive characteristic and to other areas of algebraic geometry, commutative algebra and singularity theory. Recently, there have been significant advances in this area, and this conference will cover this progress in talks by the authors of this work. The proposed gathering will provide an opportunity for researchers from diverse fields to interact and establish research connections with each other; in particular, the participants will benefit from this interaction and from seeing recent developments in the field and its relationships with other areas. The conference webpage is
https://sites.google.com/view/spivakovsky60thbirthday/home/authuser=0

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401662","Conference: Southern Regional Algebra Conference 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/15/2024","01/18/2024","Jean Nganou","TX","University of Houston - Downtown","Standard Grant","Tim Hodges","02/28/2025","$14,990.00","","nganouj@uhd.edu","1 MAIN ST","HOUSTON","TX","770021014","7132218005","MPS","126400","7556","$0.00","This award supports participation in the Southern Regional Algebra Conference (SRAC). The SRAC is a yearly weekend conference that has been in existence since 1988. Its first edition was held at the University of Southern Mississippi in the Spring of 1988. This spring the SRAC will be held at the University of Houston-Downtown, March 22-24, 2024. The SRAC brings together mathematicians that carry out research in the area of algebra and closely related areas for a full weekend of lectures, short presentations and discussions. The conference attracts researchers from many undergraduate institutions in the Gulf Coast Region that usually do not have sufficient funding to support their research activities, especially long-distance meetings. It is also an important platform for graduate students and early career mathematicians to present their research in algebra and be exposed to a community of algebraists outside their respective home institutions.

The main themes of the conference are Lie/Leibniz Algebras and their representation theory; and the theory of nearrings and other generalizations of rings. On Friday March 22, there will be a single session on topics in algebra that lie either at the intersection of two themes of the conference or outside of their union. On Saturday March 23, the conference will begin with an hour-long plenary session on Leibniz algebras and the rest of the day will be split into two parallel sessions of 25-min talks, with each session focusing on one of the main themes. On Sunday March 24, the conference will start with an hour-long plenary session on the near-rings theory, and the rest of the morning will be split into two parallel sessions of 25-min talks, with each session focusing on one of the main themes. There will be plenty of opportunity for informal follow-up discussions. Further information is available at the conference website:
https://www.uhd.edu/academics/sciences/mathematics-statistics/southern-regional-algebra-conference.aspx

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347850","Structure theory for measure-preserving systems, additive combinatorics, and correlations of multiplicative functions","DMS","ALGEBRA,NUMBER THEORY,AND COM, ANALYSIS PROGRAM","07/01/2024","04/02/2024","Terence Tao","CA","University of California-Los Angeles","Continuing Grant","Wing Suet Li","06/30/2027","$244,222.00","","tao@math.ucla.edu","10889 WILSHIRE BLVD STE 700","LOS ANGELES","CA","900244200","3107940102","MPS","126400, 128100","","$0.00","Consider a stream of digital data - a sequence of zeroes and ones. This sequence could be highly structured - for instance, it could alternate periodically between 0 and 1. Or it could be completely random, with the value of each member of the sequence having no relation whatsoever to the next. It could also be ""pseudorandom"" - described by a deterministic algorithm, but yet statistically indistinguishable from a genuinely random sequence. Or it could be some complex mixture of structure and (pseudo)randomness. Can one define precisely what structure and randomness mean and describe arbitrary data as combinations of these two different components? Such questions are of importance in cryptography, computer science, combinatorics, dynamics, and number theory, as they allow one to mathematically determine whether certain patterns in arbitrary streams of data are guaranteed to occur or not. For instance, in 2004, Ben Green and the PI were able to settle a long-standing conjecture in number theory that the prime numbers contained arbitrarily long arithmetic progressions, with the key idea being to break up the prime numbers into structured and random components and study the contribution of each component. In computer science, this theory has led, for instance, to efficient ways to generate pseudorandom bits for several types of applications. In the subsequent twenty years, much progress has been made in quantifying more precisely what structure and randomness mean, particularly in the area of mathematics now known as higher-order Fourier analysis. More understanding has been gained on the precise way in which number-theoretic structures, such as the primes, exhibit (pseudo-)random behavior at both large and small scales. There has been steady progress in this direction in recent years, in which the scale on which one is able to definitively demonstrate various types of pseudorandomness has narrowed over time, and further work will be carried out in this project, in particular, it is tantalizingly near to resolve (a version) of a well-known conjecture in number theory - the Chowla conjecture - which could be in turn a stepping stone to even more famous conjectures such as the twin prime conjecture. This project provides research training opportunities for graduate students.


In this project, the PI (in conjunction with collaborators) plans to work on two related projects. Firstly, the PI will continue recent work on developing general inverse theorems for the Gowers uniformity norms in additive combinatorics on one hand and the Host--Kra uniformity seminorms in ergodic theory on the other. Secondly, the PI will continue building upon recent breakthroughs in the understanding of multiplicative functions, to make further progress towards the (logarithmically averaged) Chowla and Elliott conjectures for such functions, and to apply these results to related problems in analytic number theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349623","Invariant Rings, Frobenius, and Differential Operators","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/03/2024","Anurag Singh","UT","University of Utah","Continuing Grant","Tim Hodges","05/31/2027","$82,544.00","","singh@math.utah.edu","201 PRESIDENTS CIR","SALT LAKE CITY","UT","841129049","8015816903","MPS","126400","","$0.00","This project will investigate several questions in commutative algebra, a field that studies solution sets of polynomial equations. The research will yield concrete information about the properties of solution sets of such equations. Polynomial equations arise in a wide number of applications; one fruitful approach to their study is via studying polynomial functions on their solution sets, that form what is known as a commutative ring. This offers an enormous amount of flexibility in studying solutions sets in various settings, and indeed commutative algebra continues to develop a fascinating interaction with several fields, becoming an increasingly valuable tool in science and engineering. A key component of this project is the training of graduate students in topics connected with the research program.


The focus of the research is on questions related to local cohomology, differential operators, and the property of having finite Frobenius representation type. Local cohomology often provides the best answers to fundamental questions such as the least number of polynomial equations needed to define a solution set; this will be investigated for solution sets related to certain rings of invariants. The differential operators that one encounters in calculus make sense in good generality on solution sets of polynomial equations and are proving to be an increasingly fruitful object of study. Similarly, finite Frobenius representation type, first introduced for the study of differential operators, is proving to be a very powerful property with several applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2337942","CAREER: Arithmetic Dynamical Systems on Projective Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","01/22/2024","Nicole Looper","IL","University of Illinois at Chicago","Continuing Grant","Tim Hodges","08/31/2029","$36,742.00","","nrlooper@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126400","1045","$0.00","This project centers on problems in a recent new area of mathematics called arithmetic dynamics. This subject synthesizes problems and techniques from the previously disparate areas of number theory and dynamical systems. Motivations for further study of this subject include the power of dynamical techniques in approaching problems in arithmetic geometry and the richness of dynamics as a source of compelling problems in arithmetic. The funding for this project will support the training of graduate students and early career researchers in arithmetic dynamics through activities such as courses and workshops, as well as collaboration between the PI and researchers in adjacent fields.

The project?s first area of focus is the setting of abelian varieties, where the PI plans to tackle various conjectures surrounding the fields of definition and S-integrality of points of small canonical height. One important component of this study is the development of quantitative lower bounds on average values of generalized Arakelov-Green?s functions, which extend prior results in the dimension one case. The PI intends to develop such results for arbitrary polarized dynamical systems, opening an avenue for a wide variety of arithmetic applications. A second area of focus concerns the relationship between Arakelov invariants on curves over number fields and one-dimensional function fields, and arithmetic on their Jacobian varieties. Here the project aims to relate the self-intersection of Zhang?s admissible relative dualizing sheaf to the arithmetic of small points on Jacobians, as well as to other salient Arakelov invariants such as the delta invariant. The third goal is to study canonical heights of subvarieties, especially in the case of divisors. A main focus here is the relationship between various measurements of the complexity of the dynamical system and the heights of certain subvarieties. The final component of the project aims to relate the aforementioned generalized Arakelov-Green?s functions to
pluripotential theory, both complex and non-archimedean.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2346615","Conference: Zassenhaus Groups and Friends Conference 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","11/08/2023","Yong Yang","TX","Texas State University - San Marcos","Standard Grant","Tim Hodges","12/31/2024","$18,000.00","Thomas Keller","yy10@txstate.edu","601 UNIVERSITY DR","SAN MARCOS","TX","786664684","5122452314","MPS","126400","7556","$0.00","This award supports participation in the 2024 Zassenhaus Groups and Friends Conference which will be held at Texas State University in San Marcos, TX. It will take place on the campus of the university from noon of Friday, May 31, 2024, to the early afternoon on Sunday, June 2, 2024. It is expected that about 40 researchers will attend the conference, many of whom will give a talk.

The Zassenhaus Groups and Friends Conference, formerly known as Zassenhaus Group Theory Conference, is a series of yearly conferences that has served the mathematical community since its inception in the 1960s. The speakers are expected to come from all over the country and will cover a broad spectrum of topics related to the study of groups, such as representations of solvable groups, representations of simple groups, character theory, classes of groups, groups and combinatorics, recognizing simple groups from group invariants, p-groups, and fusion systems.

The conference will provide group theory researchers in the US a forum to disseminate their own research as well as to learn about new and significant results in the area. The conference will provide a particularly inviting environment to young mathematicians and will inspire future cooperation and collaborations among the participants. It is expected that it will have great impacts on the group theory research community. The organizers will make great effort to attract a demographically diverse group of participants including women and racial and ethnic minorities. More information can be found at the conference website, https://zassenhausgroupsandfriends.wp.txstate.edu/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400089","Higher Representation Theory and Subfactors","DMS","ALGEBRA,NUMBER THEORY,AND COM, ANALYSIS PROGRAM, EPSCoR Co-Funding","07/01/2024","04/10/2024","Cain Edie-Michell","NH","University of New Hampshire","Standard Grant","Tim Hodges","06/30/2027","$172,165.00","","cain.edie-michell@unh.edu","51 COLLEGE RD","DURHAM","NH","038242620","6038622172","MPS","126400, 128100, 915000","9150","$0.00","This project will involve research into quantum symmetry. The notion of symmetry is fundamental in classical physics. A famed result of Emmy Noether shows that for each symmetry of the laws of nature, there is a resulting conserved physical quantity. For example, the time invariance of the laws of physics results in the law of conservation of energy. In the setting of quantum physics, the more general notion of quantum symmetries is required to understand the behavior of the system. This project concerns the study of how quantum symmetries act on certain systems, with the end goal being to fully understand and classify these actions. We refer to these actions of quantum symmetries as `higher representation theory?. Particular emphasis will be placed on the examples which are relevant to topological quantum computation. This project will involve research opportunities for undergraduate students at the University of New Hampshire.

More technically, the notion of quantum symmetry is characterized mathematically by a tensor category, and the actions of quantum symmetries are characterized by module categories over these tensor categories. This project will study fundamental problems on the construction and classification of module categories. The following research problems will be addressed: 1) construct and classify the module categories over the tensor categories coming from the Wess-Zumino-Witten conformal field theories, 2) construct new continuous families of tensor categories which interpolate between the categories coming from conformal field theories, 3) use Jones?s graph planar algebra techniques to study Izumi?s near-group tensor categories, and 4) investigate the higher categorical objects related to the module categories in 1).

This project is jointly funded by the Algebra and Number Theory program and the Established Program to Stimulate Competitive Research (EPSCoR).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2402553","Torsors under Reductive Groups and Dualities for Hitchin Systems","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Roman Fedorov","PA","University of Pittsburgh","Standard Grant","Tim Hodges","06/30/2027","$250,000.00","","fedorov@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126400","","$0.00","The study of torsors (also known as principal bundles) began in the early 20th century by physicists as a formalism to describe electromagnetism. Later, this was extended to encompass strong and weak interactions, so that torsors became a basis for the so-called Standard Model - a physical theory describing all fundamental forces except for gravitation. The standard model predicted the existence of various particles, the last of which, called the Higgs boson, was found in a Large Hadron Collider experiment in 2012. In 1950's Fields medalist Jean-Pierre Serre recognized the importance of torsors in algebraic geometry. In his 1958 seminal paper he gave the first modern definition of a torsor and formulated a certain deep conjecture. The first part of this project is aimed at proving this conjecture, which is among the oldest unsolved foundational questions in mathematics. The second part of the project is related to the so-called Higgs bundles, which can be thought of as mathematical incarnations of the Higgs bosons. More precisely, the PI proposes to prove a certain duality for the spaces parameterizing Higgs bundles. This duality is a vast generalization of the fact that the Maxwell equations describing electromagnetic fields are symmetric with respect to interchanging electrical and magnetic fields. The duality is a part of the famous Langlands program unifying number theory, algebraic geometry, harmonic analysis, and mathematical physics. This award will support continuing research in these areas. Advising students and giving talks at conferences will also be part of the proposed activity.

In more detail, a conjecture of Grothendieck and Serre predicts that a torsor under a reductive group scheme over a regular scheme is trivial locally in the Zariski topology if it is rationally trivial. This conjecture was settled by Ivan Panin and the PI in the equal characteristic case. The conjecture is still far from resolution in the mixed characteristic case, though there are important results in this direction. The PI proposes to resolve the conjecture in the unramified case; that is, for regular local rings whose fibers over the ring of integers are regular. A more ambitious goal is to prove the purity conjecture for torsors, which is, in a sense, the next step after the Grothendieck?Serre conjecture. The second project is devoted to Langlands duality for Hitchin systems, predicting that moduli stacks of Higgs bundles for Langlands dual groups are derived equivalent. This conjecture may be viewed as the classical limit of the geometric Langlands duality. By analogy with the usual global categorical Langlands duality, the PI formulates a local version of the conjecture and the basic compatibility between the local and the global conjecture. The PI will attempt to give a proof of the local conjecture based on the geometric Satake equivalence for Hodge modules constructed by the PI.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408333","Conference: GAeL XXXI (Geometrie Algebrique en Liberte)","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/15/2024","Jose Rodriguez","WI","University of Wisconsin-Madison","Standard Grant","Tim Hodges","03/31/2025","$16,255.00","","jrodriguez43@wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","126400","7556","$0.00","This award funds participation of junior US mathematicians in the 31st edition of Gael (Géométrie Algébrique en Liberté) from June 17-21, 2024 at Turin, Italy, held jointly by Politecnico di Torino and Università di Torino. Géométrie Algébrique en Liberté is a series of annual meetings organized for and by junior researchers in algebraic geometry with a long tradition, drawing in 70-90 participants each year. There are both casual and structured career opportunities for junior mathematicians to interact with speakers and other attendees.

GAeL XXXI will bring together leading experts on a range of topics within Algebraic Geometry, providing an excellent opportunity for junior mathematicians to learn about major new developments. There will be three senior speakers giving mini-courses covering cutting edge results from a wide variety of topics so that GAeL appeals to all PhD students and junior postdocs in algebraic geometry. The rest of the talks are chosen from among the junior participants, often providing the first opportunity for many of these individuals to speak in front of an international audience. More information about GAeL XXXI may be found on the event website: https://sites.google.com/view/gaelxxxi

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2412921","Conference: CAAGTUS (Commutative Algebra and Algebraic Geometry in TUcSon)","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","02/14/2024","Debaditya Raychaudhury","AZ","University of Arizona","Standard Grant","Tim Hodges","04/30/2025","$15,000.00","Arvind Suresh, Zhengning Hu","draychaudhury@math.arizona.edu","845 N PARK AVE RM 538","TUCSON","AZ","85721","5206266000","MPS","126400","7556","$0.00","This award will support participation in a weekend conference to be held at the University of Arizona, Tucson on May 4 - 5. The aim of the conference is to establish a solid basis for contacts and collaborations among researchers in Commutative Algebra and Algebraic Geometry located in Arizona and its neighboring states. Its main purposes are to stimulate new directions of research, to provide opportunities to junior researchers to share their work, and to provide a venue for networking and collaboration in the southwest. Its other aim is to expand the network of algebraic and arithmetic geometers by providing an algebro-geometric complement of the Arizona Winter School.

The conference plans to host four leading researchers from Arizona and its neighboring states working in Commutative Algebra and Algebraic Geometry, who will give colloquium-style one-hour lectures on their respective areas of expertise. These hour-long lectures are expected to provide surveys of the current state of the research in these areas, and to provide suggestions for new avenues of research. There will be five or six 30-minute talks given by young researchers, as well as six to eight contributed short 20-minute talks and a poster session. Priority for these contributed talks and posters will be given to recent PhD recipients and members of groups underrepresented in mathematics. Further information is available at the conference website: https://sites.google.com/math.arizona.edu/caagtus/home

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348833","Studies in Categorical Algebra","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/03/2024","Chelsea Walton","TX","William Marsh Rice University","Continuing Grant","Tim Hodges","04/30/2027","$119,965.00","","notlaw@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126400","","$0.00","Algebraic structures have been employed for nearly two centuries to understand the behavior, particularly the symmetry, of various entities in nature. Now with the current technology of category theory (i.e., the study of objects and how they are transported), classical algebraic structures can be upgraded to provide information on natural phenomena that was not previously understood. This yields significant consequences in quantum physics. The work sponsored by this grant lies in the framework of monoidal categories, which are categories that come equipped with a way of combining objects and combining maps between objects. Several projects are earmarked for partial work by undergraduate and graduate students. Moreover, the PI will make significant progress on completing a three-volume, user-friendly textbook series on quantum algebra. The PI is also an active mentor for numerous members of underrepresented groups, particularly for those in groups to which the PI belongs (women, African-Americans, and first generation college students).

The first research theme of the projects sponsored by this grant is on algebras in monoidal categories. The PI will extend classical properties of algebras over a field to the monoidal context, and will also study properties that only have significant meaning in the categorical setting. In addition, the PI will examine other algebraic structures (e.g., Frobenius algebras) in monoidal categories, especially those tied to Topological Quantum Field Theories (TQFTs). Another theme of the PI's sponsored research work is on representations of certain monoidal categories that play a crucial role in 2-dimensional Conformal Field Theory (2d-CFTs), and that correspond to 3d-TQFTs. Of particular interest are representations of modular tensor categories, and the PI's work here will build on recent joint work with R. Laugwitz and M. Yakimov that constructs canonical representations of braided monoidal categories.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337830","CAREER: Quantifying congruences between modular forms","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/15/2024","01/18/2024","Preston Wake","MI","Michigan State University","Continuing Grant","Tim Hodges","07/31/2029","$85,593.00","","wakepres@msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","126400","1045","$0.00","Number theory is the study of the most basic mathematical objects, whole numbers. Because whole numbers are so fundamental, number theory has connections with all major areas of mathematics. For instance, consider the problem of finding the whole-number solutions to a given equation. One can consider the shape given by the graph of that equation, or the set of symmetries that the equation has, or the function whose coefficients come from counting the number of solutions over a variety of number systems. The geometric properties of this shape, the algebraic properties of these symmetries, and the analytic properties of this function are all intimately related to the behavior of the equation?s whole-number solutions. Number theorists use techniques from each of these mathematical areas, but also, in the process, uncover surprising connections between the areas whereby discoveries in one area can lead to growth in another. One part of number theory where the connections between geometry, algebra, and analysis are particularly strong is in the field of modular forms. The proposed research focuses on an important and well-known type of relation between different modular forms called congruence and aims to compute the number of forms that are congruent to a given modular form and uncover the number-theoretic significance of this computation. Many of the conjectures that drive this project were found experimentally, through computer calculations. The main educational objective is to contribute to the training of the next generation of theoretical mathematicians in computational and experimental methods. To achieve this, the Principal Investigator (PI) will design software modules for a variety of undergraduate algebra and number theory courses that provide hands-on experience with computation. In addition, the PI will supervise undergraduates in computational research experiments designed to numerically verify conjectures made in the project and to explore new directions.

Congruences between modular forms provide a link between two very different types of objects in number theory: algebraic objects, like Galois representations, and analytic objects, like L-functions. This link has been used as a tool for proving some of the most celebrated results in modern number theory, such as the Main Conjecture of Iwasawa theory. The proposed research pushes the study of congruences in a new, quantitative direction by counting the number of congruences, not just determining when a congruence exists. The central hypothesis is that this quantitative structure of congruences contains finer information about the algebraic and analytic quantities involved than the Main Conjecture and its generalizations (such as the Bloch?Kato conjecture) can provide.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347097","Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","12/19/2023","Melissa Emory","OK","Oklahoma State University","Standard Grant","Andrew Pollington","12/31/2026","$20,000.00","Maria Fox, Mahdi Asgari","melissa.emory@okstate.edu","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","126400","7556, 9150","$0.00","This award supports the TORA mathematics conference series. This series consists of annual meetings hosted by the University of North Texas, Oklahoma State University, and the University of Oklahoma on a rotating basis. This award provides support for three weekend conferences, one at the University of North Texas in Spring 2024 (TORA XIII), one at Oklahoma State University in Spring 2025 (TORA XIV), and another at the University of Oklahoma in Spring 2026 (TORA XV). Each conference will feature three prominent guest speakers from outside the Texas-Oklahoma region, in addition to other participants including students, post-doctoral researchers, and junior faculty. Regional graduate students and researchers will also give talks describing their work. These conferences will facilitate collaborations and interactions among the students and researchers in the region who work in the areas of Automorphic Forms, Representation Theory, and Number Theory.

Over the last century, the theories of automorphic forms and representations have grown enormously. Important applications impact various fields of research, ranging from number theory, coding theory, algebraic geometry, and topology to Kac-Moody algebras and quantum field theory. The interplay of automorphic forms and representation theory has been especially fruitful, and many surprising and deep results have emerged. The TORA conference series will emphasize the interplay between automorphic forms and representations, both in the classical and adelic languages, and related topics like analytic number theory and harmonic analysis.



The conference Texas-Oklahoma Representations and Automorphic forms XIII will take place on April 12-14, 2024, at the University of North Texas. Additional information can be found on the conference website: https://www.math.unt.edu/~richter/TORA/TORA13.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401353","Automorphic Forms and the Langlands Program","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/10/2024","Sug Woo Shin","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","06/30/2027","$87,594.00","","sug.woo.shin@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400","","$0.00","This award concerns research in number theory which studies integers, prime numbers, and solutions of a system of equations over integers or rational numbers following the long tradition from ancient Greeks. In the digital age, number theory has been essential in algorithms, cryptography, and data security. Modern mathematics has seen increasingly more interactions between number theory and other areas from a unifying perspective. A primary example is the Langlands program, comprising a vast web of conjectures and open-ended questions. Even partial solutions have led to striking consequences such as verification of Fermat's Last Theorem, the Sato-Tate conjecture, the Serre conjecture, and their generalizations.

The PI's projects aim to broaden our understanding of the Langlands program and related problems in the following directions: (1) endoscopic classification for automorphic forms on classical groups, (2) a formula for the intersection cohomology of Shimura varieties with applications to the global Langlands reciprocity, (3) the non-generic part of cohomology of locally symmetric spaces, and (4) locality conjectures on the mod p Langlands correspondence. The output of research would stimulate further progress and new investigations. Graduate students will be supported on the grant to take part in these projects. The PI also plans outreach to local high schools which have large under-represented minority populations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401098","Groups and Arithmetic","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/10/2024","Michael Larsen","IN","Indiana University","Continuing Grant","Adriana Salerno","06/30/2027","$92,099.00","","larsen@math.indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","126400","","$0.00","This award will support the PI's research program concerning group theory and its applications. Groups specify symmetry types; for instance, all bilaterally symmetric animals share a symmetry group, which is different from that of a starfish or of a sand dollar. Important examples of groups arise from the study of symmetry in geometry and in algebra (where symmetries of number systems are captured by ``Galois groups''). Groups can often be usefully expressed as finite sequences of basic operations, like face-rotations for the Rubik's cube group, or gates acting on the state of a quantum computer. One typical problem is understanding which groups can actually arise in situations of interest. Another is understanding, for particular groups, whether all the elements of the group can be expressed efficiently in terms of a single element or by a fixed formula in terms of varying elements. The realization of a particular group as the symmetry group of n-dimensional space is a key technical method to analyze these problems. The award will also support graduate student summer research.

The project involves using character-theoretic methods alone or in combination with algebraic geometry, to solve problems about finite simple groups. In particular, these tools can be applied to investigate questions about solving equations when the variables are elements of a simple group. For instance, Thompson's Conjecture, asserting the existence, in any finite simple group of a conjugacy class whose square is the whole group, is of this type. A key to these methods is the observation that, in practice, character values are usually surprisingly small. Proving and exploiting variations on this theme is one of the main goals of the project. One class of applications is to the study of representation varieties of finitely generated groups, for instance Fuchsian groups. In a different direction, understanding which Galois groups can arise in number theory and how they can act on sets determined by polynomial equations, is an important goal of this project and, indeed, a key goal of number theorists for more than 200 years.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401049","Conference: Representation Theory and Related Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/08/2024","Laura Rider","GA","University of Georgia Research Foundation Inc","Standard Grant","James Matthew Douglass","12/31/2024","$46,000.00","Mee Seong Im","laurajoymath@gmail.com","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126400","7556","$0.00","This is a grant to support participation in the conference ""Representation theory and related geometry: progress and prospects"" that will take place May 27-31, 2024 at the University of Georgia in Athens, GA. This conference will bring together a diverse set of participants to discuss two key areas of mathematics and their interplay. Talks will include historical perspectives on the area as well as the latest mathematical breakthroughs. A goal of the conference is to facilitate meetings between graduate students, junior mathematicians, and seasoned experts to share knowledge and inspire new avenues of research. In addition to the formally invited talks, the conference will include opportunities for contributed talks and discussion.

The interplay of representation theory and geometry is fundamental to many of the recent breakthroughs in representation theory. Topics will include the representation theory of Lie (super)algebras, and finite, algebraic, and quantum groups; cohomological methods in representation theory; modular representation theory; geometric representation theory; categorification; tensor triangular geometry and related topics in noncommutative algebraic geometry; among others. More specific topics of interest may include support varieties, cohomology and extensions, endotrivial modules, Schur algebras, tensor triangular geometry, and categorification. The conference website can be found at https://sites.google.com/view/representation-theory-geometry/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401380","Quasimaps to Nakajima Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/10/2024","Andrey Smirnov","NC","University of North Carolina at Chapel Hill","Continuing Grant","James Matthew Douglass","05/31/2027","$80,023.00","","asmirnov@live.unc.edu","104 AIRPORT DR STE 2200","CHAPEL HILL","NC","275995023","9199663411","MPS","126400","","$0.00","Counting curves in a given space is a fundamental problem of enumerative geometry. The origin of this problem can be traced back to quantum physics, and especially string theory, where the curve counting provides transition amplitudes for elementary particles. In this project the PI will study this problem for spaces that arise as Nakajima quiver varieties. These spaces are equipped with internal symmetries encoded in representations of quantum loop groups. Thanks to these symmetries, the enumerative geometry of Nakajima quiver varieties is extremely rich and connected with many areas of mathematics. A better understanding of the enumerative geometry of Nakajima quiver varieties will lead to new results in representation theory, algebraic geometry, number theory, combinatorics and theoretical physics. Many open questions in this field are suitable for graduate research projects and will provide ideal opportunities for students' rapid introduction to many advanced areas of contemporary mathematics.

More specifically, this project will investigate and compute the generating functions of quasimaps to Nakajima quiver varieties with various boundary conditions, uncover new dualities between these functions, and prove open conjectures inspired by 3D-mirror symmetry. The project will also reveal new arithmetic properties of the generating functions via the analysis of quantum differential equations over p-adic fields. The main technical tools to be used include the (algebraic) geometry of quasimap moduli spaces, equivariant elliptic cohomology, representation theory of quantum loop groups, and integral representations of solutions of the quantum Knizhnik-Zamolodchikov equations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401049","Conference: Representation Theory and Related Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/08/2024","Laura Rider","GA","University of Georgia Research Foundation Inc","Standard Grant","James Matthew Douglass","12/31/2024","$46,000.00","Mee Seong Im","laurajoymath@gmail.com","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126400","7556","$0.00","This is a grant to support participation in the conference ""Representation theory and related geometry: progress and prospects"" that will take place May 27-31, 2024 at the University of Georgia in Athens, GA. This conference will bring together a diverse set of participants to discuss two key areas of mathematics and their interplay. Talks will include historical perspectives on the area as well as the latest mathematical breakthroughs. A goal of the conference is to facilitate meetings between graduate students, junior mathematicians, and seasoned experts to share knowledge and inspire new avenues of research. In addition to the formally invited talks, the conference will include opportunities for contributed talks and discussion.

The interplay of representation theory and geometry is fundamental to many of the recent breakthroughs in representation theory. Topics will include the representation theory of Lie (super)algebras, and finite, algebraic, and quantum groups; cohomological methods in representation theory; modular representation theory; geometric representation theory; categorification; tensor triangular geometry and related topics in noncommutative algebraic geometry; among others. More specific topics of interest may include support varieties, cohomology and extensions, endotrivial modules, Schur algebras, tensor triangular geometry, and categorification. The conference website can be found at https://sites.google.com/view/representation-theory-geometry/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401351","Quantum Groups, W-algebras, and Brauer-Kauffmann Categories","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/12/2024","Weiqiang Wang","VA","University of Virginia Main Campus","Standard Grant","James Matthew Douglass","05/31/2027","$330,000.00","","ww9c@virginia.edu","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126400","","$0.00","Symmetries are patterns that repeat or stay the same when certain changes are made, like rotating a shape or reflecting it in a mirror. They are everywhere in nature, from the spirals of a seashell to the orbits of planets around the sun. They also hide behind mathematical objects and the laws of physics. Quantum groups and Lie algebras are tools mathematicians use to study these symmetries. This project is a deep dive into understanding the underlying structure of these patterns, even when they're slightly changed or twisted, and how they influence the behavior of everything around us. The project will also provide research training opportunities for graduate students.

In more detail, the PI will develop emerging directions in i-quantum groups arising from quantum symmetric pairs as well as develop applications in various settings of classical types beyond type A. The topics include braid group actions for i-quantum groups; Drinfeld presentations for affine i-quantum groups and twisted Yangians, and applications to W-algebras; character formulas in parabolic categories of modules for finite W-algebras; and categorification of i-quantum groups, and applications to Hecke, Brauer and Schur categories.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401178","Representation Theory and Symplectic Geometry Inspired by Topological Field Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/12/2024","David Nadler","CA","University of California-Berkeley","Standard Grant","James Matthew Douglass","05/31/2027","$270,000.00","","nadler@math.berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400","","$0.00","Geometric representation theory and symplectic geometry are two subjects of central interest in current mathematics. They draw original inspiration from mathematical physics, often in the form of quantum field theory and specifically the study of its symmetries. This has been an historically fruitful direction guided by dualities that generalize Fourier theory. The research in this project involves a mix of pursuits, including the development of new tools and the solution of open problems. A common theme throughout is finding ways to think about intricate geometric systems in elementary combinatorial terms. The research also offers opportunities for students entering these subjects to make significant contributions by applying recent tools and exploring new approaches. Additional activities include educational and expository writing on related topics, new interactions between researchers in mathematics and physics, and continued investment in public engagement with mathematics.

The specific projects take on central challenges in supersymmetric gauge theory, specifically about phase spaces of gauge fields, their two-dimensional sigma-models, and higher structures on their branes coming from four-dimensional field theory. The main themes are the cocenter of the affine Hecke category and elliptic character sheaves, local Langlands equivalences and relative Langlands duality, and the topology of Lagrangian skeleta of Weinstein manifolds. The primary goals of the project include an identification of the cocenter of the affine Hecke category with elliptic character sheaves as an instance of automorphic gluing, the application of cyclic symmetries of Langlands parameter spaces to categorical forms of the Langlands classification, and a comparison of polarized Weinstein manifolds with arboreal spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401025","Conference: Algebraic Cycles, Motives and Regulators","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/10/2024","Deepam Patel","IN","Purdue University","Standard Grant","Andrew Pollington","04/30/2025","$15,000.00","","patel471@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126400","7556","$0.00","This award is to support US participation in Regulators V, the fifth in a series of international conferences dedicated to the mathematics around the theory of regulators, that will take place June 3-13, 2024, at the University of Pisa. The Regulators conferences are an internationally recognized and well-respected series of conferences on topics surrounding the theory of Regulators, many of which have played a key role in recent breakthroughs in mathematics. The conference will bring together a diverse group of participants at a wide range of career stages, from graduate students to senior professors and provide a supportive environment for giving talks, exchanging ideas, and beginning new collaborations. This has traditionally been a fruitful place for early career researchers in these fields to connect with potential collaborators and mentors at other institutions, working on related topics. This award is mainly to support such participants.

Regulators play a central role in algebraic geometry and number theory, being the common thread relating algebraic cycles and motives to number theory and arithmetic. They are the central objects appearing in several well-known conjectures relating L-functions and algebraic cycles, including the Birch--Swinnerton-Dyer conjecture, and conjectures of Deligne, Beilinson, and Bloch-Kato relating special values of L-functions of varieties to algebraic cycles and K-theory. The study of these objects have led to the development of related fields including Iwasawa theory, K-theory, and motivic homotopy theory. They also appear in many areas of mathematics outside algebraic geometry and number theory, most notably in mathematical physics. The topics covered at Regulators V are likely to include recent developments in Iwasawa theory and p-adic L-functions, K-theory, motivic homotopy theory, motives and algebraic cycles, hodge theory, microlocal analysis in characteristic p, and special values of L-functions and additional related areas of research including applications to mathematical physics.


Additional information can be found on the conference website:
http://regulators-v.dm.unipi.it/regulators-v-web.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -83,11 +89,10 @@ "2401422","Algebraic Geometry and Strings","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Ron Donagi","PA","University of Pennsylvania","Continuing Grant","Adriana Salerno","06/30/2028","$95,400.00","","donagi@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","126400","","$0.00","Exploration of the interactions of physical theories (string theory and quantum field theory) with mathematics (especially algebraic geometry) has been extremely productive for decades, and the power of this combination of tools and approaches only seems to strengthen with time. The goal of this project is to explore and push forward some of the major issues at the interface of algebraic geometry with string theory and quantum field theory. The research will employ and combine a variety of techniques from algebraic geometry, topology, integrable systems, String theory, and Quantum Field theory. The project also includes many broader impact activities such as steering and organization of conferences and schools, membership of international boards and prize committees, revising Penn?s graduate program, curricular development at the graduate and undergraduate level, advising postdocs, graduate and undergraduate students, editing several public service volumes and editing of journals and proceedings volumes.

More specifically, the project includes, among other topics: a QFT-inspired attack on the geometric Langlands conjecture via non-abelian Hodge theory; a mathematical investigation of physical Theories of class S in terms of variations of Hitchin systems; applications of ideas from supergeometry to higher loop calculations in string theory; exploration of moduli questions in algebraic geometry, some of them motivated by a QFT conjecture, others purely within algebraic geometry; further exploration of aspects of F theory and establishment of its mathematical foundations; and exploration of categorical symmetries and defect symmetry TFTs. Each of these specific research areas represents a major open problem in math and/or in physics, whose solution will make a major contribution to the field.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349388","Analytic Langlands Correspondence","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Alexander Polishchuk","OR","University of Oregon Eugene","Continuing Grant","James Matthew Douglass","06/30/2027","$82,862.00","","apolish@uoregon.edu","1776 E 13TH AVE","EUGENE","OR","974031905","5413465131","MPS","126400","","$0.00","This is a project in the field of algebraic geometry with connections to number theory and string theory. Algebraic geometry is the study of geometric objects defined by polynomial equations, and related mathematical structures. Three research projects will be undertaken. In the main project the PI will provide a generalization of the theory of automorphic forms, which is an important classical area with roots in number theory. This project provides research training opportunities for graduate students.

In more detail, the main project will contribute to the analytic Langlands correspondence for curves over local fields. The goal is to study the action of Hecke operators on a space of Schwartz densities associated with the moduli stack of bundles on curves over local fields, and to relate the associated eigenfunctions and eigenvalues to objects equipped with an action of the corresponding Galois group. As part of this project, the PI will prove results on the behavior of Schwartz densities on the stack of bundles near points corresponding to stable and very stable bundles. A second project is related to the geometry of stable supercurves. The PI will develop a rigorous foundation for integrating the superstring supermeasure of the moduli space of supercurves. The third project is motivated by the homological mirror symmetry for symmetric powers of punctured spheres: the PI will construct the actions of various mapping class groups on categories associated with toric resolutions of certain toric hypersurface singularities and will find a relation of this picture to Ozsvath-Szabo's categorical knot invariants.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401472","Spheres of Influence: Arithmetic Geometry and Chromatic Homotopy Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS","09/01/2024","04/10/2024","Jared Weinstein","MA","Trustees of Boston University","Continuing Grant","Adriana Salerno","08/31/2027","$82,195.00","","jsweinst@math.bu.edu","1 SILBER WAY","BOSTON","MA","022151703","6173534365","MPS","126400, 126500","","$0.00","The principal investigator plans to build a bridge between two areas of mathematics: number theory and topology. Number theory is an ancient branch of mathematics concerned with the whole numbers and primes. Some basic results in number theory are the infinitude of primes and the formula which gives all the Pythagorean triples. Topology is the study of shapes, but one doesn't remember details like length and angles; the surfaces of a donut and a coffee mug are famously indistinguishable to a topologist. An overarching theme in topology is to invent invariants to distinguish among shapes. For instance, a pair of pants is different from a straw because ""number of holes"" is an invariant which assigns different values to them (2 and 1 respectively, but one has to be precise about what a hole is). The notion of ""hole"" can be generalized to higher dimensions: a sphere has no 1-dimensional hole, but it does have a 2-dimensional hole and even a 3-dimensional hole (known as the Hopf fibration, discovered in 1931). There are ""spheres"" in every dimension, and the determination of how many holes each one has is a major unsolved problem in topology. Lately, the topologists' methods have encroached into the domain of number theory. In particular the branch of number theory known as p-adic geometry, involving strange number systems allowing for decimal places going off infinitely far to the left, has made an appearance. The principal investigator will draw upon his expertise in p-adic geometry to make contributions to the counting-holes-in-spheres problem. He will also organize conferences and workshops with the intent of drawing together number theorists and topologists together, as currently these two realms are somewhat siloed from each other. Finally, the principal investigator plans to train his four graduate students in methods related to this project.

The device which counts the number of holes in a shape is called the ""homotopy group"". Calculating the homotopy groups of the spheres is notoriously difficult and interesting at the same time. There is a divide-and-conquer approach to doing this known as chromatic homotopy theory, which replaces the sphere with its K(n)-localized version. Here K(n) is the Morava K-theory spectrum. Work in progress by the principal investigator and collaborators has identified the homotopy groups of the K(n)-local sphere up to a torsion subgroup. The techniques used involve formal groups, p-adic geometry, and especially perfectoid spaces, which are certain fractal-like entities invented in 2012 by Fields Medalist Peter Scholze. The next step in the project is to calculate the Picard group of the K(n)-local category, using related techniques. After this, the principal investigator will turn his attention to the problem known as the ""chromatic splitting conjecture"", which has to do with iterated localizations of the sphere at different K(n). This is one of the missing pieces of the puzzle required to assemble the homotopy groups of the spheres from their K(n)-local analogues. This award is jointly supported by the Algebra and Number Theory and Geometric Analysis programs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401321","Euler Systems, Iwasawa Theory, and the Arithmetic of Elliptic Curves","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/05/2024","Francesc Castella","CA","University of California-Santa Barbara","Continuing Grant","Adriana Salerno","06/30/2027","$74,832.00","","castella@ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126400","","$0.00","Elliptic curves are a class of polynomial equations (of degree three in two variables) that have been studied for centuries, yet for which many basic questions remain open. For instance, at present there is no proven algorithm to decide whether or not a given elliptic curve has finite or infinitely many rational solutions. Over the past century, mathematicians conjectured that an answer to these questions could be extracted from certain functions of a complex variable, namely the L-function of the elliptic curve. Euler systems and Iwasawa theory are two of the most powerful tools available to date for the study of these and related conjectured links between arithmetic and analysis. This award will advance our understanding of the arithmetic of elliptic curves by developing new results and techniques in Euler systems and Iwasawa theory. The award will also support several mentoring, training, dissemination, and outreach activities.

More specifically, the research to be pursued by the PI and his collaborators will largely focus on problems whose solutions will significantly advance our understanding of issues at the core of the Birch and Swinnerton-Dyer conjecture and related questions in situations of analytic rank 1, and shed new light on the much more mysterious cases of analytic rank 2 and higher. In rank 1, they will prove the first p-converse to the celebrated theorem of Gross-Zagier and Kolyvagin in the case of elliptic curves defined over totally real fields. In rank 2, they will continue their investigations of the generalized Kato classes introduced a few years ago by Darmon-Rotger, establishing new nonvanishing results in the supersingular case. They will also study a systematic p-adic construction of Selmer bases for elliptic curves over Q of rank 2 in connection with the sign conjecture of Mazur-Rubin. For elliptic curves of arbitrary rank, they will establish various non-triviality results of associated Euler systems and Kolyvagin systems, as first conjectured by Kolyvagin and Mazur-Tate.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401337","Algebraic Cycles and L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/03/2024","Chao Li","NY","Columbia University","Standard Grant","Adriana Salerno","06/30/2027","$230,000.00","","chaoli@math.columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126400","","$0.00","The research in this project concerns one of the basic questions in mathematics: solving algebraic equations. The information of the solutions are encoded in various mathematical objects: algebraic cycles, automorphic forms and L-functions. The research will deepen the understanding of these mathematical objects and the connection between them, especially in high dimensions, which requires solving many new problems, developing new tools and interactions in diverse areas, and appealing to new perspectives which may shed new light on old problems. It will also advance the techniques for understanding the arithmetic of elliptic curves, particularly the Birch and Swinnerton-Dyer conjecture, one of the seven Millennium Prize Problems of the Clay Mathematics Institute. The PI will continue to mentor graduate students, organize conferences and workshops, and write expository articles.

The PI will work on several projects relating arithmetic geometry with automorphic L-function, centered around the common theme of the generalization and applications of the Gross--Zagier formula. The PI will investigate the Kudla--Rapoport conjecture for parahoric levels. The PI will extend the arithmetic inner product formula to orthogonal groups, and study the Bloch--Kato conjecture of symmetric power motives of elliptic curves and endoscopic cases of the arithmetic Gan--Gross--Prasad conjectures. The PI will also investigate a new arithmetic relative trace formula approach towards a Gross--Zagier type formula for orthogonal Shimura varieties.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400550","Splicing Summation Formulae and Triple Product L-Functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Jayce Getz","NC","Duke University","Standard Grant","Andrew Pollington","06/30/2027","$220,000.00","","jgetz@math.duke.edu","2200 W MAIN ST","DURHAM","NC","277054640","9196843030","MPS","126400","","$0.00","This award concerns the Langlands program which has been described as a grand unification theory within mathematics. In some sense the atoms of the theory are automorphic representations. The Langlands functoriality conjecture predicts that a collection of natural correspondences preserve these atoms. To even formulate this conjecture precisely, mathematical subjects as diverse as number theory, representation theory, harmonic analysis, algebraic geometry, and mathematical physics are required. In turn, work on the conjecture has enriched these subjects, and in some cases completely reshaped them.

One particularly important example of a correspondence that should preserve automorphic representations is the automorphic tensor product. It has been known for some time that in order to establish this particular case of Langlands functoriality it suffices to prove that certain functions known as L-functions are analytically well-behaved. More recently, Braverman and Kazhdan, Ngo, Lafforgue and Sakellaridis have explained that the expected properties of these L-functions would follow if one could obtain certain generalized Poisson summation formulae. The PI has isolated a particular family of known Poisson summation formulae and proposes to splice them together to obtain the Poisson summation formulae relevant for establishing the automorphic tensor product.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2420166","Conference: The Mordell conjecture 100 years later","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Bjorn Poonen","MA","Massachusetts Institute of Technology","Standard Grant","Andrew Pollington","06/30/2025","$29,970.00","","poonen@math.mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126400","7556","$0.00","The award will support a conference, ``The Mordell conjecture 100 years later'', at the Massachusetts Institute of Technology during the week July 8-12, 2024. The conference website, showing the list of invited speakers, is https://mordell.org/ . The Mordell conjecture, proved in 1983, is one of the landmarks of modern number theory. A conference on this topic is needed now, because in recent years, there have been advances on different aspects of the conjecture, while other key questions remain unsolved. This would be the first conference to bring together all the researchers coming from these different perspectives. The conference will feature 16 hour-long lectures, with speakers ranging from the original experts to younger mathematicians at the forefront of current research. Some lectures will feature surveys of the field, which have educational value especially for the next generation of researchers. The conference will also feature a problem session and many 5-minute lightning talk slots, which will give junior participants an opportunity to showcase their own research on a wide variety of relevant topics. The award will support the travel and lodging of a variety of mathematicians including those from underrepresented groups in mathematics and attendees from colleges and universities where other sources of funding are unavailable. Materials from the lectures, problem session, and lightning talks will be made publicly available on the website, to reach an audience broader than just conference attendees.

The Mordell conjecture motivated much of the development of arithmetic geometry in the 20th century, both before and after its resolution by Faltings. The conference will feature lectures covering a broad range of topics connected with the Mordell conjecture, its generalizations, and other work it has inspired. In particular, it will build on recent advances in the following directions: 1) nonabelian analogues of Chabauty's p-adic method; 2) the recent proof via p-adic Hodge theory; 3) uniform bounds on the number of rational points; 4) generalizations to higher-dimensional varieties, studied by various methods: analytic, cohomological, and computational.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401164","Conference: Latin American School of Algebraic Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/10/2024","Evgueni Tevelev","MA","University of Massachusetts Amherst","Standard Grant","Adriana Salerno","04/30/2025","$20,000.00","","tevelev@math.umass.edu","101 COMMONWEALTH AVE","AMHERST","MA","010039252","4135450698","MPS","126400","7556","$0.00","This award will provide travel support for graduate students and early career mathematicians from the United States to participate in the research school ""Latin American School of Algebraic Geometry"" that will take place in Cabo Frio, Brazil from August 12 to 23, 2024, and will be hosted by IMPA (Institute for Pure and Applied Mathematics), a renowned center for mathematical research and post-graduate education founded in 1952 and situated in Rio de Janeiro, Brazil. This will be the fifth edition of the ELGA series. The previous events were held in Buenos Aires (Argentina, 2011), Cabo Frio (Brazil, 2015), Guanajuato (Mexico, 2017), and Talca (Chile, 2019). ELGA is a major mathematical event in Latin America, a focal meeting point for the algebraic geometry community and a great opportunity for junior researchers to network and to learn from the world experts in the field. ELGA workshops are unique in their dedicated efforts to nurture the next generation of leaders in STEM in the Americas. The travel support for U.S. participants from the National Science Foundation will further strengthen the ties between the universities and promote scientific cooperation between future mathematicians in Latin America and the U.S. The website of the conference is https://impa.br/en_US/eventos-do-impa/2024-2/v-latin-american-school-of-algebraic-geometry-and-applications-v-elga/

Algebraic geometry has long enjoyed a central role in mathematics by providing a precise language to describe geometric shapes called algebraic varieties, with applications ranging from configuration spaces in physics to parametric models in statistics. This versatile language is used throughout algebra and has fueled multiple recent advances, not only in algebraic geometry itself but also in representation theory, number theory, symplectic geometry, and other fields. Over the course of two weeks, courses by Cinzia Casagrande (University of Torino, Italy), Charles Favre (École Polytechnique, France), Joaquin Moraga (UCLA, USA), Giancarlo Urzúa (Catholic University, Chile), and Susanna Zimmermann (University of Paris-Saclay, France) will cover a wide range of topics including geometry of Fano manifolds, singularities of algebraic varieties, Cremona groups of projective varieties, Higgs bundles, and geometry of moduli spaces. Each course will include two hours of tutorial sessions coordinated by the course lecturers with the assistance of advanced graduate students participating in the research workshop. Additional talks and presentations by a combination of senior and junior researchers are intended to give a panoramic view of algebraic geometry and its applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401337","Algebraic Cycles and L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/03/2024","Chao Li","NY","Columbia University","Standard Grant","Adriana Salerno","06/30/2027","$230,000.00","","chaoli@math.columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126400","","$0.00","The research in this project concerns one of the basic questions in mathematics: solving algebraic equations. The information of the solutions are encoded in various mathematical objects: algebraic cycles, automorphic forms and L-functions. The research will deepen the understanding of these mathematical objects and the connection between them, especially in high dimensions, which requires solving many new problems, developing new tools and interactions in diverse areas, and appealing to new perspectives which may shed new light on old problems. It will also advance the techniques for understanding the arithmetic of elliptic curves, particularly the Birch and Swinnerton-Dyer conjecture, one of the seven Millennium Prize Problems of the Clay Mathematics Institute. The PI will continue to mentor graduate students, organize conferences and workshops, and write expository articles.

The PI will work on several projects relating arithmetic geometry with automorphic L-function, centered around the common theme of the generalization and applications of the Gross--Zagier formula. The PI will investigate the Kudla--Rapoport conjecture for parahoric levels. The PI will extend the arithmetic inner product formula to orthogonal groups, and study the Bloch--Kato conjecture of symmetric power motives of elliptic curves and endoscopic cases of the arithmetic Gan--Gross--Prasad conjectures. The PI will also investigate a new arithmetic relative trace formula approach towards a Gross--Zagier type formula for orthogonal Shimura varieties.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401464","Conference: Solvable Lattice Models, Number Theory and Combinatorics","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/09/2024","Solomon Friedberg","MA","Boston College","Standard Grant","James Matthew Douglass","05/31/2025","$22,500.00","","friedber@bc.edu","140 COMMONWEALTH AVE","CHESTNUT HILL","MA","024673800","6175528000","MPS","126400","7556","$0.00","This award supports the participation of US-based researchers in the Conference on Solvable Lattice Models, Number Theory and Combinatorics that will take place June 24-26, 2024 at the Hamilton Mathematics Institute at Trinity College Dublin. Solvable lattice models first arose in the description of phase change in physics and have become useful tools in mathematics as well. In the past few years a group of researchers have found that they may be used to effectively model quantities arising in number theory and algebraic combinatorics. At the same time, other scholars have used different methods coming from representation theory to investigate these quantities. This conference will be a venue to feature these developments and to bring together researchers working on related questions using different methods and students interested in learning more about them.

This conference focuses on new and emerging connections between solvable lattice models and special functions on p-adic groups and covering groups, uses of quantum groups, Hecke algebras and other methods to study representations of p-adic groups and their covers, and advances in algebraic combinatorics and algebraic geometry. Spherical and Iwahori Whittaker functions are examples of such special functions and play an important role in many areas. The website for this conference is https://sites.google.com/bc.edu/solomon-friedberg/dublin2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401114","Parahoric Character Sheaves and Representations of p-Adic Groups","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Charlotte Chan","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","James Matthew Douglass","06/30/2027","$105,981.00","","charchan@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126400","","$0.00","In the past half century, cutting-edge discoveries in mathematics have occurred at the interface of three major disciplines: number theory (the study of prime numbers), representation theory (the study of symmetries using linear algebra), and geometry (the study of solution sets of polynomial equations). The interactions between these subjects has been particularly influential in the context of the Langlands program, arguably the most expansive single project in modern mathematical research. The proposed research aims to further these advances by exploring geometric techniques in representation theory, especially motivated by questions within the context of the Langlands conjectures. This project also provides research training opportunities for undergraduate and graduate students.

In more detail, reductive algebraic groups over local fields (local groups) and their representations control the behavior of symmetries in the Langlands program. This project aims to develop connections between representations of local groups and two fundamental geometric constructions: Deligne-Lusztig varieties and character sheaves. Over the past decade, parahoric analogues of these geometric objects have been constructed and studied, leading to connections between (conjectural) algebraic constructions of the local Langlands correspondence to geometric phenomena, and thereby translating open algebraic questions to tractable problems in algebraic geometry. In this project, the PI will wield these novel positive-depth parahoric analogues of Deligne-Lusztig varieties and character sheaves to attack outstanding conjectures in the local Langlands program.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2411537","Conference: Comparative Prime Number Theory Symposium","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/05/2024","Wanlin Li","MO","Washington University","Standard Grant","Adriana Salerno","04/30/2025","$10,000.00","","wanlin@wustl.edu","ONE BROOKINGS DR","SAINT LOUIS","MO","63110","3147474134","MPS","126400","7556","$0.00","The workshop Comparative Prime Number Theory Symposium, which is the first scientific event to focus predominantly on this subject, will take place on the UBC--Vancouver campus from June 17--21, 2024. One of the first and central topics in the research of number theory is to study the distribution of prime numbers. In 1853, Chebyshev observed that there seems to be more primes taking the form of a multiple of four plus three than a multiple of four plus one. This phenomenon is now referred to as Chebyshev's bias and its study led to a new branch of number theory, comparative prime number theory. As a subfield of analytic number theory, research in this area focuses on examining how prime counting functions and other arithmetic functions compare to one another. This field has witnessed significant growth and activity in the last three decades, especially after the publication of the influential article on Chebyshev's bias by Rubinstein and Sarnak in 1994. The primary goal of this award will be to provide participant support and fund US-based early career researchers to attend this unique event, giving them the opportunity to discuss new ideas, advance research projects, and interact with established researchers.

The symposium will bring together many leading and early-career researchers with expertise and interest in comparative prime number theory to present and discuss various aspects of current research in the field, with special emphasis on results pertaining to the distribution of counting functions in number theory and zeros of L-functions, consequences of quantitative Linear Independence, oscillations of the Mertens sum, and the frequency of sign changes. Through this symposium, we will advertise the recently disseminated survey ""An Annotated Bibliography for Comparative Prime Number Theory"" by Martin et al which aims to record every publication within the topic of comparative prime number theory, together with a summary of results, and presenting a unified system of notation and terminology for referring to the quantities and hypotheses that are the main objects of study. Another important outcome of the symposium will be compiling and publicizing a problem list, with the hope of stimulating future research and providing young researchers with potential projects. Information about the conference can be found at the website: https://sites.google.com/view/crgl-functions/comparative-prime-number-theory-symposium

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -95,16 +100,12 @@ "2334874","Conference: Pittsburgh Links among Analysis and Number Theory (PLANT)","DMS","ALGEBRA,NUMBER THEORY,AND COM, ANALYSIS PROGRAM","02/01/2024","01/19/2024","Carl Wang Erickson","PA","University of Pittsburgh","Standard Grant","James Matthew Douglass","01/31/2025","$20,000.00","Theresa Anderson, Armin Schikorra","carl.wang-erickson@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126400, 128100","7556","$0.00","This award will support the four-day conference ""Pittsburgh Links among Analysis and Number Theory (PLANT)"" that will take place March 4-7, 2024 in Pittsburgh, PA. The purpose of the conference is to bring together representatives of two disciplines with a shared interface: number theory and analysis. There is a large potential for deeper collaboration between these fields resulting in new and transformative mathematical perspectives, and this conference aims at fostering such an interchange. In particular, the conference is designed to attract PhD students and post-doctoral scholars into working on innovations at this interface.

To encourage the development of new ideas, the conference speakers, collectively, represent many subfields that have developed their own distinctive blend of analysis and number theory, such as analytic number theory, arithmetic statistics, analytic theory of modular and automorphic forms, additive combinatorics, discrete harmonic analysis, and decoupling. While there have been a wide variety of conferences featuring these subfields in relative isolation, the PIs are excited at PLANT's potential for sparking links among all of these subfields and giving early-career participants the opportunity to be part of this exchange. The conference website is https://sites.google.com/view/plant24/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401041","Conference: Singularities in Ann Arbor","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","03/28/2024","Mircea Mustata","MI","Regents of the University of Michigan - Ann Arbor","Standard Grant","Adriana Salerno","04/30/2025","$33,758.00","Qianyu Chen","mmustata@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126400","7556","$0.00","The conference ""Singularities in Ann Arbor"", scheduled for May 13-17, 2024, at the University of Michigan, Ann Arbor, will explore recent progress in the study of singularities in algebraic geometry. Algebraic geometry, in simple terms, concerns itself with studying geometric objects defined by polynomial equations. This conference will focus on several recent advances concerning singularities: these are points where the geometric objects behave in unexpected ways (such as the bumps or dents on a normally flat surface). Understanding these singularities not only satisfies intellectual curiosity but also plays a crucial role in classifying and comprehending global complex geometric structures. More details about the conference, as well as the list of confirmed lecturers, are available on the conference website, at https://sites.google.com/view/singularitiesinaa.

The conference will feature four lecture series presented by leading experts and rising stars in the field, covering recent advancement related to singularities. These lectures will introduce fresh perspectives and tools, including Hodge Theory, D-modules, and symplectic topology, to address challenging questions in algebraic geometry. The conference aims to make these complex ideas accessible to a younger audience, fostering engagement and understanding among participants. Additionally, the conference will provide a platform for young researchers to showcase their work through a poster session, encouraging collaboration and discussion among participants. This award will provide travel and lodging support for about 35 early-career conference participants.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2344680","Conference: Tensor Invariants in Geometry and Complexity Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS, Algorithmic Foundations","03/15/2024","02/20/2024","Luke Oeding","AL","Auburn University","Standard Grant","James Matthew Douglass","02/28/2025","$40,000.00","","oeding@auburn.edu","321-A INGRAM HALL","AUBURN","AL","368490001","3348444438","MPS","126400, 126500, 779600","7556, 9150","$0.00","The conference Tensor Invariants in Geometry and Complexity Theory will take place May 13-17, 2024 at Auburn University. This conference aims to bring together early-career researchers and experts to study tensor invariants, their appearance in pure algebraic and differential geometry, and their application in Algebraic Complexity Theory and Quantum Information. The workshop will feature talks from both seasoned experts and promising young researchers. The event is designed to facilitate new research connections and to initiate new collaborations. The conference will expose the participants to state-of-the-art research results that touch a variety of scientific disciplines. The activities will support further development of both pure mathematics and the ""down-stream"" applications in each area of scientific focus (Algebraic and Differential Geometry, Algebraic Complexity, Quantum Information).

The conference is centered on invariants in geometry, divided into three themes: Algebraic and Differential Geometry, Tensors and Complexity, and Quantum Computing and Quantum Information. Geometry has long been a cornerstone of mathematics, and invariants are the linchpins. Regarding Algebraic and Differential Geometry, the organizers are inviting expert speakers on topics such as the connections between projective and differential geometry. Considerations in these areas, such as questions about dimensions and defining equations of secant varieties, have led to powerful tools both within geometry and applications in areas such as computational complexity and quantum information. Likewise, the organizers are inviting application-area experts in Algebraic Complexity and Quantum Information. This natural juxtaposition of pure and applied mathematics will lead to new and interesting connections and help initiate new research collaborations. In addition to daily talks by seasoned experts, the conference will include young researchers in a Poster Session and provide networking opportunities, including working group activities, to help early career researchers meet others in the field, which will provide opportunities for new (and ongoing) research collaborations. It is anticipated that these collaborations will continue long after the meeting is over. The conference webpage is: https://webhome.auburn.edu/~lao0004/jmlConference.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2342225","RTG: Numbers, Geometry, and Symmetry at Berkeley","DMS","ALGEBRA,NUMBER THEORY,AND COM, WORKFORCE IN THE MATHEMAT SCI","08/01/2024","03/18/2024","Tony Feng","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","07/31/2029","$1,196,058.00","Martin Olsson, David Nadler, Sug Woo Shin, Yunqing Tang","fengt@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400, 733500","","$0.00","The project will involve a variety of activities organized around the research groups in number theory, geometry, and representation theory at UC Berkeley. These subjects study the structure and symmetries of mathematical equations, and have applications to (for example) cryptography, codes, signal processing, and physics. There will be an emphasis on training graduate students to contribute to society as scientists, educators, and mentors.

More precisely, RTG will be used to organize annual graduate research workshops, with external experts, as well as weekly research seminars to keep up-to-date on cutting-edge developments. Summer programs on Research Experiences of Undergraduates will provide valuable research exposure to undergraduates, and also mentorship training to graduate students. Postdocs will be hired to help lead these activities. Finally, the project will fund outreach to local schools. At the core of all these activities is the goal of training students and postdocs as strong workforce in their dual roles as mentors and mentees, recruiting students into the ?eld with a good representation of underrepresented groups, and providing a setting for collaboration between all levels and across di?erent areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2402436","Conference: Visions in Arithmetic and Beyond","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","03/26/2024","Akshay Venkatesh","NJ","Institute For Advanced Study","Standard Grant","Andrew Pollington","05/31/2025","$44,975.00","Alexander Gamburd","akshay@math.ias.edu","1 EINSTEIN DR","PRINCETON","NJ","085404952","6097348000","MPS","126400","7556","$0.00","This award provides funding to help defray the expenses of participants in the conference ""Visions in Arithmetic and Beyond"" (conference website https://www.ias.edu/math/events/visions-in-arithmetic-and-beyond ) to be held at the Institute for Advanced Study and Princeton University from June 3 to June 7, 2024. Those speaking at the meeting include the leading researchers across arithmetic, analysis and geometry.

The conference will provide high-level talks by mathematicians who are both outstanding researchers and excellent speakers. These will synthesize and expose a broad range of recent advances in number theory as well as related developments in analysis and dynamics. In addition to the talks by leading researchers there is also time allotted for a session on the best practices for mentoring graduate students and postdocs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401152","Conference: Modular forms, L-functions, and Eigenvarieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/26/2024","John Bergdall","AR","University of Arkansas","Standard Grant","Adriana Salerno","11/30/2024","$15,000.00","","bergdall@uark.edu","1125 W MAPLE ST STE 316","FAYETTEVILLE","AR","727013124","4795753845","MPS","126400","7556, 9150","$0.00","This award supports US-based scientists to attend the conference ""Modular Forms, L-functions, and Eigenvarieties"". The event will take place in Paris, France from June 18, 2024, until June 21, 2024. Whole numbers are the atoms of our mathematical universe. Number theorists study why patterns arise among whole numbers. In the 1970's, Robert Langlands proposed connections between number theory and mathematical symmetry. His ideas revolutionized the field. Some of the most fruitful approaches to his ideas have come via calculus on geometric spaces. The conference funded here will expose cutting edge research on such approaches. The ideas disseminated at the conference will have a broad impact on the field. The presentations of leading figures will propel junior researchers toward new theories. The US-based participants will make a written summary of the conference. The summaries will encourage the next generation to adopt the newest perspectives. Writing them will also engender a spirit of collaboration within the research community. The summaries along with details of the events will be available on the website https://www.eventcreate.com/e/bellaiche/.

The detailed aim of the conference is exposing research on modular forms and L-functions in the context of eigenvarieties. An eigenvariety is a p-adic space that encodes congruence phenomena in number theory. Families of eigenforms, L-functions, and other arithmetic objects find their homes on eigenvarieties. The conference's primary goal is exposing the latest research on such families. The presentations will place new research and its applications all together in one place, under the umbrella of the p-adic Langlands program.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2341365","Conference: Southern Regional Number Theory Conference","DMS","ALGEBRA,NUMBER THEORY,AND COM","02/01/2024","01/19/2024","Gene Kopp","LA","Louisiana State University","Standard Grant","James Matthew Douglass","01/31/2026","$35,000.00","Fang-Ting Tu","gkopp@lsu.edu","202 HIMES HALL","BATON ROUGE","LA","708030001","2255782760","MPS","126400","9150","$0.00","Southern Regional Number Theory Conferences (SRNTCs) are planned to be held in the Gulf Coast region March 9?11, 2024, and in Spring 2025, at Louisiana State University in Baton Rouge. The 2024 conference will be the 10th anniversary of the conference series. The SRNTC series serves as an annual number theory event for the Gulf Coast region. It brings together researchers from the region and beyond to disseminate and discuss fundamental research in various branches of number theory, in turn fostering communication and collaboration between researchers. Local students and early-career researchers attending the conferences are exposed to a wide array of problems and techniques, including specialized topics that may have no local experts at their home institutions. Students and early-career researchers are given opportunities to present their research through contributed talks and to expand their professional network.

SRNTC 2024 will feature about ten invited talks by established experts from four countries, speaking on topics in algebraic number theory, analytic number theory, and automorphic forms. It will also feature about twenty-five contributed talks, mostly by regional graduate students and early-career researchers. Information about SRNTC 2024 and SRNTC 2025, including a registration form and the schedule for each conference, is available at the conference website (https://www.math.lsu.edu/srntc).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2342225","RTG: Numbers, Geometry, and Symmetry at Berkeley","DMS","ALGEBRA,NUMBER THEORY,AND COM, WORKFORCE IN THE MATHEMAT SCI","08/01/2024","03/18/2024","Tony Feng","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","07/31/2029","$1,196,058.00","Martin Olsson, David Nadler, Sug Woo Shin, Yunqing Tang","fengt@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400, 733500","","$0.00","The project will involve a variety of activities organized around the research groups in number theory, geometry, and representation theory at UC Berkeley. These subjects study the structure and symmetries of mathematical equations, and have applications to (for example) cryptography, codes, signal processing, and physics. There will be an emphasis on training graduate students to contribute to society as scientists, educators, and mentors.

More precisely, RTG will be used to organize annual graduate research workshops, with external experts, as well as weekly research seminars to keep up-to-date on cutting-edge developments. Summer programs on Research Experiences of Undergraduates will provide valuable research exposure to undergraduates, and also mentorship training to graduate students. Postdocs will be hired to help lead these activities. Finally, the project will fund outreach to local schools. At the core of all these activities is the goal of training students and postdocs as strong workforce in their dual roles as mentors and mentees, recruiting students into the ?eld with a good representation of underrepresented groups, and providing a setting for collaboration between all levels and across di?erent areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2333970","Conference: Collaborative Workshop in Algebraic Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","03/21/2024","Sarah Frei","NH","Dartmouth College","Standard Grant","Andrew Pollington","05/31/2025","$24,400.00","Ursula Whitcher, Rohini Ramadas, Julie Rana","sarah.frei@dartmouth.edu","7 LEBANON ST","HANOVER","NH","037552170","6036463007","MPS","126400","7556, 9150","$0.00","This award supports participants to attend a collaborative algebraic geometry research workshop at the Institute for Advanced Study (IAS) during the week of June 24-28, 2024. The goals of the workshop are to facilitate significant research in algebraic geometry and to strengthen the community of individuals in the field from underrepresented backgrounds. We will place a particular focus on forming connections across different career stages. Participants will join project groups composed of a leader and co-leader together with two to three junior participants and will spend the workshop engaged in focused and substantive research.

The projects to be initiated during this workshop represent a wide range of subfields of algebraic geometry (e.g. intersection theory, toric geometry and arithmetic geometry), as well as connections to other fields of math (e.g. representation theory). Specifically, topics include: abelian covers of varieties, del Pezzo surfaces over finite fields, positivity of toric vector bundles, Chow rings of Hurwitz spaces with marked ramification, Ceresa cycles of low genus curves, and the geometry of Springer fibers and Hessenberg varieties. More information is available at https://sites.google.com/view/wiag2024/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349888","Conference: International Conference on L-functions and Automorphic Forms","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/15/2024","Larry Rolen","TN","Vanderbilt University","Standard Grant","Adriana Salerno","03/31/2025","$25,000.00","Jesse Thorner, Andreas Mono","larry.rolen@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126400","7556","$0.00","This award provides support for the conference entitled ""International Conference on L-functions and Automorphic Forms'', which will take place at Vanderbilt University in Nashville, Tennessee on May 13--16 2024. This is part of an annual series hosted by Vanderbilt, known as the Shanks conference series. The main theme will be on new developments and recent interactions between the areas indicated in the title. The interplay between automorphic forms and L-functions has a long and very fruitful history in number theory, and bridging both fields is still a very active area of research. This conference is oriented at establishing and furthering dialogue on new developments at the boundary of these areas. This will foster collaboration between researchers working in these fields.

One beautiful feature of modern number theory is that many problems of broad interest, in areas of study as diverse as arithmetic geometry to mathematical physics, can be solved in an essentially optimal way if the natural extension of the Riemann hypothesis holds for L-functions associated to automorphic representations. Although many generalizations and applications around L-functions have have already been worked out, there are still various fundamental open problems among them to tackle, including bounds for and the value distribution of L-functions. The former is related to the pursuit of so-called sub-convexity bounds for L-functions. The latter is related to the Birch and Swinnterton-Dyer conjecture (another ?Millenium problem? posed by the Clay Mathematics institute). These pursuits are closely connected with the Langlands program, a ?grand unifying theory? relating automorphic forms. Further details can be found on the conference website https://my.vanderbilt.edu/shanksseries/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2400006","Conference: Underrepresented Students in Algebra and Topology Research Symposium (USTARS)","DMS","INFRASTRUCTURE PROGRAM, ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","03/15/2024","03/12/2024","Ryan Moruzzi","CA","California State University, East Bay Foundation, Inc.","Standard Grant","Adriana Salerno","02/28/2025","$36,000.00","Christopher ONeill, Robyn Brooks","ryan.moruzzi@csueastbay.edu","25800 CARLOS BEE BLVD","HAYWARD","CA","945423000","5108854212","MPS","126000, 126400, 126700","7556","$0.00","This award will support the Underrepresented Students in Topology and Algebra Research Symposium (USTARS). A goal of this conference is to highlight research being conducted by underrepresented students in the areas of algebra and topology. At this unique meeting, attendees are exposed to a greater variety of current research, ideas, and results in their areas of study and beyond. Participants are also given the opportunity to meet and network with underrepresented professors and students who may later become collaborators and colleagues. This is particularly important for students with great academic potential who do not attend top-tier research institutions; students that are often overlooked, despite a strong faculty and graduate student population. Furthermore, USTARS promotes diversity in the mathematical sciences by encouraging women and minorities to attend and give talks. Participants of USTARS continue to influence the next generation of students in positive ways by serving as much needed mentors and encouraging students in the mathematical sciences to advance themselves and participate in research and conference events. USTARS exposes all participants to the research and activities of underrepresented mathematicians, encouraging a more collaborative mathematics community.

The Underrepresented Students in Topology and Algebra Research Symposium (USTARS) is a project proposed by a group of underrepresented young mathematicians. The conference organizing committee is diverse in gender, ethnicity, and educational background, and is well-positioned to actively encourage participation by women and minorities. The symposium includes networking sessions along with research presentations. Speakers will give 30-minute parallel research talks. Graduate students will give at least 75% of these presentations. Two distinguished graduate students and one invited faculty member are chosen to give 1-hour presentations and a poster session featuring invited undergraduates is also planned. Additionally, a discussion panel and creative math session will provide networking, guidance, and mentorship opportunities from past USTARS participants that have transitioned to full-time faculty positions. The conference website is https://www.ustars.org/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401305","Conference: ANTS XVI: Algorithmic Number Theory Symposium 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM, Secure &Trustworthy Cyberspace","07/01/2024","02/27/2024","Andrew Sutherland","MA","Massachusetts Institute of Technology","Standard Grant","Andrew Pollington","06/30/2025","$36,000.00","","drew@math.mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126400, 806000","7556","$0.00","This award provides funds for early-career researchers (graduate students, postdocs, and tenure-track faculty not having other NSF support) to attend the sixteenth edition of the Algorithmic Number Theory Symposium (ANTS-XVI) held July 15-19, 2024 at the Massachusetts Institute of Technology (MIT). The ANTS meetings, held biannually since 1994, are the premier international forum for new research in computational number theory. As an established conference series, ANTS attracts invited and contributed lectures of the highest quality, and serves as a forum for dissemination of new ideas and techniques throughout the research community in the area of computational number theory and number-theoretic aspects of cryptography. In addition to numerous applications to theoretical mathematics, these fields have immense importance through real world connections to computer security.

The ANTS meetings are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, arithmetic algebraic geometry, modular forms, finite fields, and applications of number theory to cryptography. Participants include academic researchers in both mathematics and computer science, as well as mathematicians in industry who work on cryptography and other areas of application; similarly, the topics presented include both pure and applied topics. The review process for contributed lectures and the subsequent production of a proceedings volume provides documentation of the presented results at a quality level comparable to an international research journal in mathematics. This award funds lodging and US-based travel for researchers who might not otherwise be able to participate in this premier event. Funding priority will be given to those contributing papers or posters; the organizers also seek to actively promote participation by women and underrepresented minorities.

More information about the conference can be found at https://antsmath.org/ANTSXVI/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2349244","Conference: Texas Algebraic Geometry Symposium (TAGS) 2024-2026","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","01/19/2024","Frank Sottile","TX","Texas A&M University","Continuing Grant","James Matthew Douglass","03/31/2027","$15,000.00","","sottile@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126400","","$0.00","The Texas Algebraic Geometry Symposium (TAGS) will be held at Texas A&M University April 5,6, and 7, 2024, and in Spring 2025 and Spring 2026. TAGS is an annual regional conference which is jointly organized by faculty at Rice University, Texas A&M University, and the University of Texas at Austin. The conference series began in 2005, and serves to enhance the educational and research environment in Texas and the surrounding states, providing an important opportunity for interaction and sharing of ideas for students and researchers in this region.

TAGS serves to ensure that members of the algebraic geometry community in the Texas region stay in regular contact and brings distinguished mathematicians and rising stars to an area with no other comparable regular gatherings in algebraic geometry. The 2024 TAGS will have nine lectures delivered by a diverse group of speakers, and will include accessible lectures for graduate students and a juried poster session for students and junior researchers. It will be held in conjunction with the annual Maxson lectures at Texas A&M the week before and delivered by Prof. David Eisenbud. The TAGS website is https://franksottile.github.io/conferences/TAGS24/index.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400553","Conference: Arithmetic quantum field theory","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/01/2024","02/12/2024","Daniel Freed","MA","Harvard University","Standard Grant","Andrew Pollington","02/28/2025","$45,000.00","David Ben-Zvi","dafr@math.harvard.edu","1033 MASSACHUSETTS AVE STE 3","CAMBRIDGE","MA","021385366","6174955501","MPS","126400","7556","$0.00","The conference Arithmetic Quantum Field Theory will be held at the Harvard Center of Mathematical Sciences and Applications (CMSA) on March 25-29 2024. This will be an in-person gathering of approximately 70 researchers - graduate students, postdocs, and faculty in mathematics and physics, available in hybrid mode to an unlimited number of outside participants. A central focus of the conference - and the dedicated aim of its first day - is to encourage a high level of participation by women in math and physics. The first day is designed to encourage junior researchers to come and network, give talks in a friendly environment, and participate without concern over the precise fit of their research to the narrow theme of the workshop.

The conference Arithmetic Quantum Field Theory, and the two-month program of the same title it concludes, are aimed at catalyzing interactions between mathematicians and physicists by disseminating exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions. On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds. On the other hand, the arithmetic topology dictionary provides a sturdy bridge between the topology of manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory. The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions, and conversely to explore potential geometric and physical consequences of arithmetic ideas.
The conference website is https://cmsa.fas.harvard.edu/event/aqftconf/ where recordings of the talks and notes from lectures will be made widely available.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2338485","CAREER: Moduli Spaces, Fundamental Groups, and Asphericality","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/01/2024","02/02/2024","Nicholas Salter","IN","University of Notre Dame","Continuing Grant","Swatee Naik","06/30/2029","$67,067.00","","nsalter@nd.edu","836 GRACE HALL","NOTRE DAME","IN","465566031","5746317432","MPS","126400, 126700","1045","$0.00","This NSF CAREER award provides support for a research program at the interface of algebraic geometry and topology, as well as outreach efforts aimed at improving the quality of mathematics education in the United States. Algebraic geometry can be described as the study of systems of polynomial equations and their solutions, whereas topology is the mathematical discipline that studies notions such as ?shape? and ?space"" and develops mathematical techniques to distinguish and classify such objects. A notion of central importance in these areas is that of a ?moduli space? - this is a mathematical ?world map? that gives a complete inventory and classification of all instances of a particular mathematical object. The main research objective of the project is to better understand the structure of these spaces and to explore new phenomena, by importing techniques from neighboring areas of mathematics. While the primary aim is to advance knowledge in pure mathematics, developments from these areas have also had a long track record of successful applications in physics, data science, computer vision, and robotics. The educational component includes an outreach initiative consisting of a ?Math Circles Institute? (MCI). The purpose of the MCI is to train K-12 teachers from around the country in running the mathematical enrichment activities known as Math Circles. This annual 1-week program will pair teachers with experienced instructors to collaboratively develop new materials and methods to be brought back to their home communities. In addition, a research conference will be organized with the aim of attracting an international community of researchers and students and disseminating developments related to the research objectives of the proposal.

The overall goal of the research component is to develop new methods via topology and geometric group theory to study various moduli spaces, specifically, (1) strata of Abelian differentials and (2) families of polynomials. A major objective is to establish ?asphericality"" (vanishing of higher homotopy) of these spaces. A second objective is to develop the geometric theory of their fundamental groups. Asphericality occurs with surprising frequency in spaces coming from algebraic geometry, and often has profound consequences. Decades on, asphericality conjectures of Arnol?d, Thom, and Kontsevich?Zorich remain largely unsolved, and it has come to be regarded as a significantly challenging topic. This project?s goal is to identify promising-looking inroads. The PI has developed a method called ""Abel-Jacobi flow"" that he proposes to use to establish asphericality of some special strata of Abelian differentials. A successful resolution of this program would constitute a major advance on the Kontsevich?Zorich conjecture; other potential applications are also described. The second main focus is on families of polynomials. This includes linear systems on algebraic surfaces; a program to better understand the fundamental groups is outlined. Two families of univariate polynomials are also discussed, with an eye towards asphericality conjectures: (1) the equicritical stratification and (2) spaces of fewnomials. These are simple enough to be understood concretely, while being complex enough to require new techniques. In addition to topology, the work proposed here promises to inject new examples into geometric group theory. Many of the central objects of interest in the field (braid groups, mapping class groups, Artin groups) are intimately related to algebraic geometry. The fundamental groups of the spaces the PI studies here should be just as rich, and a major goal of the project is to bring this to fruition.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2337451","CAREER: Higgs bundles and Anosov representations","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS","07/01/2024","02/02/2024","Brian Collier","CA","University of California-Riverside","Continuing Grant","Swatee Naik","06/30/2029","$79,647.00","","brian.collier@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","126400, 126500","1045","$0.00","This project focuses on the mathematical study of curved surfaces by connecting algebraic objects to them and thereby generalizing the scope of their application. One of the main notions used is that of a surface group representation, a concept which connects surfaces to generalizations of classical geometries such as Euclidean and hyperbolic geometry. The study of surfaces has surprising applications throughout many fields of mathematics and physics. Consequently, the project lies at the intersection of multiple disciplines. In addition to cutting edge mathematical research, the project will promote the progress of science and mathematics through different workshops aimed at graduate students as well as community outreach events. The educational component will also focus on creating an engaging and inclusive place for mathematical interactions for students and early career researchers.

In the past decades, both the theories of Higgs bundles and Anosov dynamics have led to significant advancements in our understanding of the geometry of surface groups. Recent breakthroughs linking these approaches are indirect and mostly involve higher rank generalizations of hyperbolic geometry known as higher rank Teichmuller spaces. The broad aim of this project is to go beyond higher rank Teichmuller spaces by using Higgs bundles to identify subvarieties of surface group representations which generalize the Fuchsian locus in quasi-Fuchsian space. The cornerstone for the approach is the role of Slodowy slices for Higgs bundles. Specifically, the PI aims to establish Anosov properties of surface group representations associated to Slodowy slices in the Higgs bundle moduli space. This approach will significantly extend applications of Higgs bundles to both Anosov representations and (G,X) geometries. It will complete the component count for moduli of surface group representations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2347096","Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","12/19/2023","Lea Beneish","TX","University of North Texas","Standard Grant","Andrew Pollington","12/31/2026","$20,000.00","Anne Shepler, Olav Richter","lea.beneish@unt.edu","1112 DALLAS DR STE 4000","DENTON","TX","762051132","9405653940","MPS","126400","7556","$0.00","This award supports the TORA mathematics conference series. This series consists of annual meetings hosted by the University of North Texas, Oklahoma State University, and the University of Oklahoma on a rotating basis. This award provides support for three weekend conferences, one at the University of North Texas in Spring 2024 (TORA XIII), one at Oklahoma State University in Spring 2025 (TORA XIV), and another at the University of Oklahoma in Spring 2026 (TORA XV). Each conference will feature three prominent guest speakers from outside the Texas-Oklahoma region, in addition to other participants including students, post-doctoral researchers, and junior faculty. Regional graduate students and researchers will also give talks describing their work. These conferences will facilitate collaborations and interactions among the students and researchers in the region who work in the areas of Automorphic Forms, Representation Theory, and Number Theory.

Over the last century, the theories of automorphic forms and representations have grown enormously. Important applications impact various fields of research, ranging from number theory, coding theory, algebraic geometry, and topology to Kac-Moody algebras and quantum field theory. The interplay of automorphic forms and representation theory has been especially fruitful, and many surprising and deep results have emerged. The TORA conference series will emphasize the interplay between automorphic forms and representations, both in the classical and adelic languages, and related topics like analytic number theory and harmonic analysis.



The conference Texas-Oklahoma Representations and Automorphic forms XIII will take place on April 12-14, 2024, at the University of North Texas. Additional information can be found on the conference website: https://www.math.unt.edu/~richter/TORA/TORA13.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Analysis/Awards-Analysis-2024.csv b/Analysis/Awards-Analysis-2024.csv index 54eaa33..807d70e 100644 --- a/Analysis/Awards-Analysis-2024.csv +++ b/Analysis/Awards-Analysis-2024.csv @@ -1,7 +1,17 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" "2424267","Conference: East Coast Operator Algebras Symposium 2024","DMS","ANALYSIS PROGRAM","09/01/2024","07/25/2024","Corey Jones","NC","North Carolina State University","Standard Grant","Wing Suet Li","08/31/2025","$29,950.00","","cmjones6@ncsu.edu","2601 WOLF VILLAGE WAY","RALEIGH","NC","276950001","9195152444","MPS","128100","7556","$0.00","The East Coast Operator Algebra Symposium (ECOAS) is an annual research conference centered around the theory of operator algebras and their applications. The first meeting was at Vanderbilt University in the Fall of 2003, and since then meetings have occurred annually. This award will partially support participants for this year's event, the 20th meeting of ECOAS, held at North Carolina State University in Raleigh, North Carolina, November 9-10, 2024. The conference will provide a venue for early career researchers to learn about developments at the forefront of their field, to share their work with the broader community, and to network with other early career researchers as well as more senior members of the community.

This event focuses on C*-algebras, von Neumann algebras and a wide variety of applications, including to quantum physics, representation theory, and dynamical systems. Thirty to sixty participants are expected. The plenary speakers will review recent advances, enabling participants to keep abreast of recent developments in a vast and rapidly expanding subject. More information is available at the conference website https://www.coreyjonesmath.com/ecoas-2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2400115","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Kate Juschenko","TX","University of Texas at Austin","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","","kate.juschenko@gmail.com","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400112","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Zhizhang Xie","TX","Texas A&M University","Standard Grant","Wing Suet Li","03/31/2027","$16,400.00","","xie@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2400111","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Mehrdad Kalantar","TX","University of Houston","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","","kalantar@math.uh.edu","4300 MARTIN LUTHER KING BLVD","HOUSTON","TX","772043067","7137435773","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2349322","Banach Spaces: Theory and Applications","DMS","ANALYSIS PROGRAM","07/01/2024","06/20/2024","Thomas Schlumprecht","TX","Texas A&M University","Standard Grant","Wing Suet Li","06/30/2027","$257,986.00","","t-schlumprecht@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","128100","","$0.00","Logistics planning, including optimal distribution of products, leads to questions about maps with weighted distances, and routes that minimize these distances. Transportation cost spaces, also known as Lipschitz-free spaces, Wasserstein spaces, Arens-Eals spaces, and Earthmover spaces, have been used to model such problems. They can be viewed as a framework to study nonlinear metric spaces by embedding them isometrically and linearly densely into Banach spaces and provide powerful tools to study the nonlinear geometry of Banach spaces using well-known linear techniques for nonlinear problems. These spaces play a fundamental role in many areas of applied mathematics, engineering, physics, computer science, finance, and social sciences. Finding an optimal embedding is known to be a computationally hard problem and it has become a central problem in computer science to find low distortion embeddings. Using methods from the structure theory of Banach spaces and computational graph theory, the investigator?s goal is to achieve more precise estimates of these embeddings. He will obtain a deeper understanding of the structure of these spaces, which will result in several applications to the areas mentioned above. The principal investigator plans to organize conferences as well as mentor Ph.D. students as a part of this project.

A crucial connection exists between the L1-distortion of Transportation Cost Spaces and stochastic embeddings of the underlying metric space into trees. The investigator will further study this connection to obtain lower and upper estimations on the distortion. The second part of the project represents a contribution to Lindenstrauss?s program in determining Banach spaces that are primary, and that cannot be decomposed into essentially different subspaces. The investigator will continue to determine primary function spaces. This project concentrates on studying the primarity and related factorization properties of function spaces in two parameters, combining methods from Functional and Harmonic Analysis and Probability Theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2340465","CAREER: Gauge-theoretic Floer invariants, C* algebras, and applications of analysis to topology","DMS","TOPOLOGY, ANALYSIS PROGRAM","09/01/2024","02/02/2024","Sherry Gong","TX","Texas A&M University","Continuing Grant","Qun Li","08/31/2029","$89,003.00","","sgongli@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126700, 128100","1045","$0.00","The main research goal of this project is to apply analytic tools coming from physics, such as gauge theory and operator algebras, to topology, which is the study of geometric shapes. This research is divided into two themes: low dimensional topology and operator K-theory. In both fields, the aforementioned analytic tools are used to build invariants to study the geometric structure of manifolds, which are spaces modelled on Euclidean spaces, like the 3-dimensional space we live in. In both low dimensional topology and operator K-theory, the PI will use analytic tools to study questions about these spaces, such as how they are curved or how objects can be embedded inside them. These questions have a wide range of applications in biology and physics. The educational and outreach goals of this project involve math and general STEM enrichment programs at the middle and high school levels, with a focus on programs aimed at students from underserved communities and underrepresented groups, as well as mentorship in research at the high school, undergraduate and graduate levels.

In low dimensional topology, this project focuses on furthering our understanding of instanton and monopole Floer homologies and their relation to Khovanov homology, and using this to study existence questions of families of metrics with positive scalar curvature on manifolds, as well as questions about knot concordance. Separately this project also involves computationally studying knot concordance, both by a computer search for concordances and by computationally studying certain local equivalence and almost local equivalence groups that receive homomorphisms from the knot concordance groups. In operator algebras, this project focuses on studying their K-theory and its applications to invariants in geometry and topology. The K-theory groups of operator algebras are the targets of index maps of elliptic operators and have important applications to the geometry and topology of manifolds. This project involves studying the K-theory of certain C*-algebras and using them to study infinite dimensional spaces; studying the noncommutative geometry of groups that act on these infinite dimensional spaces and, in particular, the strong Novikov conjecture for these groups; and studying the coarse Baum-Connes conjecture for high dimensional expanders.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2402022","Conference: Dynamical Systems and Fractal Geometry","DMS","ANALYSIS PROGRAM","04/15/2024","04/03/2024","Pieter Allaart","TX","University of North Texas","Standard Grant","Jan Cameron","03/31/2025","$32,017.00","Kiko Kawamura, Kirill Lazebnik","allaart@unt.edu","1112 DALLAS DR STE 4000","DENTON","TX","762051132","9405653940","MPS","128100","7556","$0.00","This award provides support for participants to attend the conference ?Dynamical Systems and Fractal Geometry? to be held at the University of North Texas from May 14-17, 2024. The primary goal of the conference is to foster interaction and collaboration between researchers in several fields of mathematics: fractal geometry, complex dynamics, thermodynamic formalism, random dynamical systems, and open dynamical systems. These fields are interrelated through both the methods used and in the fundamental questions of their study. The conference will bring together mathematicians from these fields ranging from senior experts to graduate students; experts will give standard 45?50-minute plenary lectures, and students will have the opportunity to give 5-10 minute ?lightning talks?. The conference will also include a career panel. More information on the conference, including a list of speakers, can be found on the conference website: https://pcallaart3.wixsite.com/conference.

The fields represented in this conference have broad motivations and applications in several classical areas of mathematics and physics beyond dynamical systems and geometry, including number theory, probability theory, and statistical mechanics. Thermodynamic formalism is a framework for unifying many aspects of these fields, and its investigation triggers research and collaboration on the problem of the existence and uniqueness of equilibrium states of the various systems studied in these fields. Limit sets of conformal dynamical systems, and in particular Julia sets arising in complex dynamics, are typically of a fractal nature and understanding their fine fractal properties such as Hausdorff, packing, Assouad and Fourier dimensions provides a true challenge for fractal geometers. The conference aims to advance research in these directions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2400008","A description of surface dynamics","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Enrique Pujals","NY","CUNY Graduate School University Center","Standard Grant","Jeremy Tyson","06/30/2026","$249,103.00","","epujals@gc.cuny.edu","365 5TH AVE STE 8113","NEW YORK","NY","100164309","2128177526","MPS","128100","5913, 5918","$0.00","This project seeks to understand the mechanisms that underlie the transition of a dynamical system from an ordered state to a random (chaotic) state. In other words, the aim is to understand the processes through which a system's behavior evolves from periodicity toward chaos, as one or more governing parameters are varied. A related goal is to identify the primary bifurcation responsible for qualitative changes exhibited by a dynamical system. While such comprehension has previously been attained for low-dimensional dynamical systems, this project introduces a novel approach to transcend the low-dimensional limitation. The project will offer new conceptual ideas and approaches to provide fresh perspectives on advances in mathematics and science. Additionally, the project will facilitate the training of graduate students directly engaged in the research, and will afford educational opportunities to undergraduate students through the organization of a summer school presenting topics in mathematics, including topics related to dynamical systems.

The theory of one-dimensional dynamical systems successfully explains the depth and complexity of chaotic phenomena in concert with a description of the dynamics of typical orbits for typical maps. Its remarkable universality properties supplement this understanding with powerful geometric tools. In the two-dimensional setting, the range of possible dynamical scenarios that can emerge is at present only partially understood, and a general framework for those new phenomena that do not occur for one-dimensional dynamics remains to be developed. In prior work supported by the NSF, the principal investigator introduced a large open class of two-dimensional dynamical systems, including the classical Henon family without the restriction of large area contraction, that is amenable to obtaining results as in the one-dimensional case. Moreover, major progress was reached to understand the transition from zero entropy to positive entropy using renormalization schemes. The present project has several components. First, existing renormalization schemes will be adapted to the positive entropy realm. Next, initial steps towards a characterization of dissipative diffeomorphisms in more general contexts will be addressed. Finally, the principal investigator will seek to develop the theory of differentiable renormalization without an a priori assumption of proximity to the one-dimensional setting. These results will open the door to a global description of dissipative diffeomorphisms and their behavior under perturbation, bringing both new tools and new perspectives to smooth dynamical systems theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348305","Viscosity Solutions: Beyond the Wellposedness Theory","DMS","ANALYSIS PROGRAM","09/01/2024","07/26/2024","Hung Tran","WI","University of Wisconsin-Madison","Continuing Grant","Marian Bocea","08/31/2027","$100,972.00","","hung@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","128100","","$0.00","This project studies some nonlinear partial differential equations (PDE) that appear naturally in chemistry, physics, and engineering and which arise, for example, in the study of crystal growth, combustion, coagulation-fragmentation processes, game theory, and optimal control theory. These equations have connections with a host of other areas of mathematics, including the calculus of variations, differential games, dynamical systems, geometry, homogenization theory, and probability. The main goal of the project is to discover new underlying principles and general methods to understand the properties of solutions of the PDE under investigation. A key object of the research is a crystal growth model in which the crystal grows in both the horizontal direction, by adatoms, and the vertical direction, by dislocations or nucleation in a supersaturated media. To make practical use of the model, it is important to understand the qualitative and quantitative aspects of the growth speed and the shape of the crystal. The mentoring of graduate students in research is an important educational component of the project.

The work of the project involves two themes. The first is about critical Coagulation-Fragmentation equations and their connections with Hamilton-Jacobi equations. The Principal Investigator (PI) is interested in regularity and large-time behavior results for Hamilton-Jacobi equations which give implications on the existence of mass-conserving solutions of Coagulation-Fragmentation equations and their behavior. The second involves level-set mean curvature flow equations with driving and source terms and applications in crystal growths and turbulent combustions. The focus is on the regularity, the large-time average, and the large-time behavior of the solutions. The PI and his collaborators have recently developed new approaches which led to solutions to several open problems in these and related areas. The new approaches are expected to be developed further in this project, thereby bringing fresh perspectives on and insights into the study of nonlinear PDE and viscosity solutions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2350252","Regular and Singular Incompressible Fluid Flows","DMS","ANALYSIS PROGRAM","08/01/2024","07/26/2024","Camillo De Lellis","NJ","Princeton University","Standard Grant","Marian Bocea","07/31/2027","$300,000.00","","camillo.delellis@math.ias.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","128100","","$0.00","A variety of systems in natural sciences are described through physically measurable quantities which depend on each other. For instance, we routinely measure the pressure and the temperature of the air in the Earth?s atmosphere, and such measurements depend upon the time and the location of the device used. Several fundamental laws discovered by scientists during the last three centuries give relations among the rates of change of such physical quantities and the resulting mathematical objects, called partial differential equations, are therefore ubiquitous in modern science and engineering. The partial differential equations describing the motion of incompressible, viscous and ideal fluids date back to the seventeenth and eighteenth centuries. Nonetheless, a rigorous mathematical understanding of many properties of their solutions is still lacking and some reverberates in a poor understanding of certain fundamental phenomena. A pivotal example is the apparent incompatibility of the classical mathematical treatment of these equations with the basic observation in the theory of fully developed turbulence that, in the limit of the viscosity of the fluid tending to zero, turbulent flows dissipate kinetic energy. In fact, regular solutions of the equations describing the zero-viscosity limit can be proved to conserve the kinetic energy and are therefore at odds with the latter phenomenon. Starting from the latter problem as a pivotal one, this project aims to advance our understanding of other basic properties of solutions, such as regularity, uniqueness, and stability. The project provides research training opportunities for graduate students and supports the engagement of the principal investigator in popularizing mathematics to the general public.

The project investigates two fundamental questions in incompressible fluid dynamics. The first goal is to find rigorous examples of the so-called ""zero law of fully developed turbulence"", namely the presence of anomalous dissipation in the zero-viscosity limit. The ideal solution of the latter problem is to give a proof of existence of a sequence of solutions to the incompressible Navier-Stokes equations with vanishing viscosity for which the dissipation rate of kinetic energy stays positive in the limit, without the introduction of spurious oscillations in the initial data. The second is the investigation of blow-up scenarios for smooth solutions of the Navier-Stokes and Euler equations. Both problems are formidable, and they have defied the efforts of mathematicians for decades. Given the size of the challenge, some effort will be dedicated to the investigation of simpler situations. An important example in the case of anomalous dissipation is the effect of forcing terms in the equations. An example in the case of the blow-up problem is understanding suitable deformations of the Navier-Stokes equations which embeds them in a higher parameter family of equations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349919","Ergodic Schrödinger Operators","DMS","ANALYSIS PROGRAM","08/01/2024","07/24/2024","David Damanik","TX","William Marsh Rice University","Standard Grant","Marian Bocea","07/31/2027","$291,253.00","","damanik@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","128100","7203","$0.00","This project aims to improve the understanding of how the amount of disorder present in an environment can promote or suppress transport in a system. This issue is studied in the context of quantum mechanics at the atomic level. Applications of new insights about quantum systems include the development of quantum computing devices and quantum algorithms. The project supports education and diversity though the mentoring of postdoctoral scholars, the training of graduate students, and the supervision of undergraduate research.

This project addresses the general theory of Schrödinger operators with ergodic potentials. These operators are relevant in many areas, primarily in quantum mechanics and approximation theory. The objective is to establish results for general base transformations and for large classes of sampling functions. The methods employed range from functional analysis via harmonic analysis to dynamical systems and ergodic theory. The investigator seeks to identify the almost sure spectral type of an ergodic family of Schrödinger operators, while establishing a version of Simon's Wonderland Theorem in this setting and answering a question of Walters about the existence of non-uniform cocycles as byproducts, to develop further gap labelling theory based on the Schwartzman group, along with a comparison with gap labelling based on K-theory, to study the Laplacian on Penrose and other aperiodically ordered tilings, and to obtain proofs of Cantor spectra via cocycle perturbation techniques beyond the two-dimensional time-discrete setting.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348522","Advances in Spectral Theory, Several Complex Variables, and the Geometry of Eigenfunctions of the Laplacian","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","07/01/2024","07/01/2024","Hamid Hezari","CA","University of California-Irvine","Standard Grant","Jeremy Tyson","06/30/2027","$246,525.00","","hezari@math.uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126500, 128100","","$0.00","The project resides at the intersection of the fields of mathematical analysis, partial differential equations, and geometry. Specific questions to be investigated concern the inverse spectral problem, the structure of Laplacian eigenfunctions, and the asymptotic behavior of Bergman kernels. These topics are crucial for understanding how geometric structure influences spectral properties, and are deeply connected to various concepts in mathematics and mathematical physics. The inverse spectral problem investigates how much information about the shape of a (not necessarily round) drum can be obtained solely from its frequencies of vibration. This is a classical question famously popularized by Mark Kac with the phrase `Can one hear the shape of a drum?? A second set of problems focuses on the shape and the size of the set (`nodal set?) on which an eigenstate of the Laplacian operator vanishes. The size (in the sense of Hausdorff measure) of the nodal set is conjectured to be comparable to the frequency of the eigenstate. Finally, the Bergman kernel is an essential concept in the fields of complex analysis and complex geometry. Bergman kernel approximations arise naturally in mathematical physics, especially in string theory, where they have been proposed as a tool for the search for geometrically well-behaved complex metric structures. The broader impacts of the project contribute to education and diversity. The principal investigator actively supervises graduate students and postdoctoral researchers. Additionally, the PI participates in outreach activities such as organizing math competitions for middle school students and mentoring students from diverse backgrounds through summer research programs.

The planned research lies in three main areas. Building on previous work with Steve Zelditch, in which nearly circular ellipses were shown to be spectrally unique among smooth domains, the PI aims to generalize such results to generic ellipses and to domains with constant width. Another direction of interest resides in strong inverse spectral results for generic polygons. Next, recent work by the PI resulted in new explicit upper bounds for the Hausdorff measure of nodal sets of eigenfunctions on compact Riemannian manifolds with Gevrey or quasianalytic regularity. The PI seeks to extend these results to manifolds with boundaries and to improve the current upper bounds using innovative methods. Finally, in collaboration with Hang Xu, the PI investigates asymptotic properties of Bergman kernels. This includes establishing new off-diagonal asymptotics for smooth Kaehler potentials and improving extant upper bounds for Bergman kernels. In addition, the PI will explore convergence properties of the Fefferman expansion for domains with real analytic boundaries.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2337911","CAREER: Mixing and Equidistribution in Number Theory and Geometry","DMS","ANALYSIS PROGRAM","06/01/2024","01/23/2024","Osama Khalil","IL","University of Illinois at Chicago","Continuing Grant","Jan Cameron","05/31/2029","$69,724.00","","okhalil@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","128100","1045","$0.00","Dynamics is the study of the evolution of a system under a transformation rule governing its behavior over time. It encompasses such varied examples as planetary motion, the spread of disease and the flow of electric currents in conductive material. It turns out that many fundamental problems in number theory and geometry can also be understood in terms of the long-time behavior of certain dynamical systems of algebraic origin. Furthermore, the algebraic nature of these systems makes it possible to employ tools from a wide array of mathematical disciplines for their investigation. This project aims to develop new methods in the theory of algebraic dynamical systems with the goal of resolving central questions in the fields of Diophantine approximation and surface geometry. The educational component aims at training early-career mathematicians and providing mentorship to students at all levels. This includes a workshop geared towards training graduate students and postdocs on active research directions in dynamics, as well as outreach workshops aimed at encouraging students from underrepresented backgrounds to pursue careers in the mathematical sciences.

The research program has three interrelated goals. One goal is to study the distribution of rational points near self-similar sets from the perspective of homogeneous dynamics. The PI will also investigate limits of horocycle-invariant measures on moduli spaces of Abelian differentials, A third aim is to establish rates of mixing of geodesic flows on negatively curved manifolds. Progress on these questions will involve development of dynamical methods at the intersection of representation theory, geometry, and additive combinatorics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350115","Analysis of Fluids and Nonlinear Waves","DMS","ANALYSIS PROGRAM","08/15/2024","07/24/2024","Chongchun Zeng","GA","Georgia Tech Research Corporation","Standard Grant","Marian Bocea","07/31/2027","$299,998.00","","zengch@math.gatech.edu","926 DALNEY ST NW","ATLANTA","GA","303186395","4048944819","MPS","128100","","$0.00","Partial differential equations (PDE) are widely used to model various problems involving spatial and temporal variables arising in physics, engineering, biology, finance, etc. The aims of the efforts to understand rigorously these mathematical models are twofold. On the one hand, the physical relevance and the validity of these ideal models are established through the comparison between the results from theoretical analysis and the experimental observations. On the other hand, once the meaningfulness of a mathematical model is supported by available experimental data to certain extent, the theoretical studies on these ideal models can provide properties and predictions of the original physical problems that are difficult to obtain from experiments. For physical systems involving temporal evolution, of particular interest are certain structural and asymptotic properties. These include special structures, such as equilibria, periodic and quasi-periodic orbits, chaotic orbits, and their qualitative properties like stability or asymptotic stability. In general, on the one hand, only stable states are physically observable in a system, while the ideal, but unstable, states are hardly observed due to their extremely sensitive dependence on the parameters. On the other hand, unstable states are also very important, in part because they and some of their associated structures serve as the boundaries separating different collections of stable states in a system. In this project, the principal investigator (PI) plans to focus on the local dynamics near steady states in several classical nonlinear PDE systems which belong to the general category of nonlinear waves and incompressible fluids. The complicated nonlinearity poses tremendous challenges in their mathematical analysis. A substantial part of the project is suitable for graduate students and postdocs and provides research training opportunities for these early-career mathematicians.

More specifically, the project will study the dynamics of incompressible fluid PDE (inviscid, weakly viscous, or with density stratification) with free surfaces as well as a class of nonlinear Hamiltonian PDE. They are standard models arising in fluids, atmosphere-oceans, nonlinear waves, etc. Their solution flows generate infinite dimensional dynamical systems in function spaces. There has been extensive research on these systems with many important advances in recent years. However, due to the complicated spectra of the linearized problems, the highly nonlinear nature, regularity issues, and the multiple scales in space and time they involve, many questions, including some fundamental ones, are still not well understood. First, the PI will work on the two-dimensional water waves linearized at shear flows, including the bifurcation of instability and the linear inviscid damping for the gravity water waves and the spectra and linear flows of the stratified water waves. The second focus of the project is the nonlinear local dynamics of a class of Hamiltonian PDE including the local invariant manifolds for quasilinear Hamiltonian PDE, where the regularity issue poses a major challenge, and the unfolding bifurcation of small homoclinic type solutions in a singular perturbation framework. The PI will also study a potential flow approximation to weakly viscous water waves including formal justification via detailed multi-scale expansions involving boundary layers followed by rigorous proofs. Understanding and solving these problems, expected to be largely based on their specific mechanical and geometric structures, would result in substantial theoretical advances in these areas and possibly lead to the discovery of new physical and mathematical phenomena in the underlying systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348908","Low Regularity and Long Time Dynamics in Nonlinear Dispersive Flows","DMS","ANALYSIS PROGRAM","08/01/2024","04/02/2024","Mihaela Ifrim","WI","University of Wisconsin-Madison","Standard Grant","Marian Bocea","07/31/2027","$343,401.00","","ifrim@wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","128100","","$0.00","The primary objective of this project is to examine solutions to a broad class of equations that can be described as nonlinear waves. These mathematical equations model a wide range of physical phenomena arising in fluid dynamics (oceanography), quantum mechanics, plasma physics, nonlinear optics, and general relativity. The equations being studied range from semilinear to fully nonlinear, and from local to nonlocal equations, and we aim to investigate them in an optimal fashion both locally and globally in time. This research develops and connects ideas and methods in partial differential equations, and in some cases also draws a clear path towards other problems in fields such as geometry, harmonic analysis, complex analysis, and microlocal analysis. The project provides research training opportunities for graduate students.

The strength of the nonlinear wave interactions is the common feature in the models considered in this proposal, and it significantly impacts both their short-time and their long-time behavior. The project addresses a series of very interesting questions concerning several classes of nonlinear dispersive equations: (i) short-time existence theory in a low regularity setting; (ii) breakdown of waves, and here a particular class of equations is provided by the water wave models; and (iii) long-time persistence and/or dispersion and decay of waves, which would involve either a qualitative aspect attached to it, that is, an asymptotic description of the nonlinear solution, or a quantitative description of it, for instance nontraditional scattering statements providing global in time dispersive bounds. All of this also depends strongly on the initial data properties, such as size, regularity and localization.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348715","Differentiability in Carnot Groups and Metric Measure Spaces","DMS","ANALYSIS PROGRAM","09/01/2024","07/17/2024","Gareth Speight","OH","University of Cincinnati Main Campus","Standard Grant","Jeremy Tyson","08/31/2027","$263,078.00","","gareth.speight@uc.edu","2600 CLIFTON AVE","CINCINNATI","OH","452202872","5135564358","MPS","128100","5918, 5920, 5935, 5946, 5952","$0.00","A function is considered to be smooth or differentiable if at every point it is has a derivative, or in other words, a well-defined rate of change. Many familiar functions are smooth, and smoothness properties are convenient and prevalent in scientific applications. However, non-smooth functions also frequently arise in mathematics and its applications, such as optimization. This project concerns differentiability phenomena in non-smooth environments. Specifically, it seeks to understand when non-smooth objects possess hidden smoothness structures. While non-smooth objects are more difficult to understand, they are often equipped with additional structure that is not initially visible. For instance, Lipschitz functions (i.e., those functions which expand distances by at most a multiplicative factor) are differentiable at most points of their domain. The project investigates these and related phenomena, it seeks to describe when a partially defined function can be extended to a smooth function, and explores when a function can be approximated by a smooth function. The project will promote research collaboration and will generate research training opportunities for both graduate and undergraduate students.

The project centers on two broad topics of research. First, the PI seeks a deeper understanding of the Whitney extension and Lusin approximation questions for mappings between Carnot groups. A significant complication, not present in the Euclidean case, is that the maps to be constructed must satisfy nonlinear constraints reflecting the underlying geometry of these non-Euclidean environments. A second line of study investigates the differentiability properties of Lipschitz functions in Euclidean spaces, Carnot groups, and metric or Banach spaces. A fundamental theorem due to Rademacher states that every Lipschitz function defined in a Euclidean domain is differentiable almost everywhere. However, in many situations one in fact finds differentiability points inside measure zero sets. This observation led to the modern study of sets of universal differentiability. The project seeks to test the limits of Rademacher?s theorem through an improved understanding of universal differentiability sets, via the use of maximal directional derivatives and other methods.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -15,7 +25,6 @@ "2349942","Dynamics of Polynomials","DMS","OFFICE OF MULTIDISCIPLINARY AC, ANALYSIS PROGRAM","09/01/2024","07/17/2024","Alexander Blokh","AL","University of Alabama at Birmingham","Standard Grant","Jeremy Tyson","08/31/2027","$205,606.00","","ablokh@math.uab.edu","701 S 20TH STREET","BIRMINGHAM","AL","352940001","2059345266","MPS","125300, 128100","5905, 9150","$0.00","This project analyzes the structure and dynamical properties of families of complex polynomials of degree three. Nonlinear mappings arise in mathematical models across a host of scientific and applied fields, and a key issue is to understand how the behavior of such mappings changes as the underlying parameters vary. Among the simplest nonlinear mappings are complex polynomials. The structure and dynamical properties of the space of complex quadratic polynomials has been intensively studied since the early 1980s, culminating in a detailed understanding of the celebrated Mandelbrot set. Analyzing the structure of spaces of complex cubic polynomials is at the heart of this project. The project also provides research opportunities for graduate students and contributes to the training and mentoring of undergraduate students. In addition, the principal investigator continues to serve as director of an outreach program aimed at Alabama high school students.

The project develops the dynamical and structural theory of moduli spaces of complex polynomials of degree three from several perspectives. A first line of inquiry concerns the construction of locally connected models of the cubic connectedness locus. By analogy with classical combinatorial models for the Mandelbrot set, the project also studies a combinatorial model in the cubic case based upon critical portraits. This work relies on recent laminational results recently developed by the PI and collaborators. A further approach to be investigated involves analytic tools. Estimates for the moduli of annuli will be used to show that Julia sets of polynomials of degree three are generated by rational cuts and admit a description in terms of rational laminations. If successful, this line of inquiry will validate conjectural laminational models of such Julia sets as well as certain subsets of the cubic connectedness locus.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348806","RUI: PDE and Geometry in non-smooth spaces","DMS","ANALYSIS PROGRAM","07/15/2024","07/15/2024","Luca Capogna","MA","Smith College","Standard Grant","Wing Suet Li","06/30/2027","$275,939.00","","lcapogna@smith.edu","10 ELM ST","NORTHAMPTON","MA","010636304","4135842700","MPS","128100","9229","$0.00","This award supports a project which investigates topics in the theory of partial differential equations in the setting of non-smooth spaces. Partial differential equations provide a powerful mathematical tool to gain insights about equilibrium states of complex physical systems which arise as solutions of certain equations. The properties of the solutions to these equations depend on a ?background geometry? that models physical features such as the non-homogeneity of materials or the presence of constraints (such as the constraints inherent in the motion of a robotic arm). In many important physical applications, one encounters non-smooth geometries (for instance, fractals) which differ fundamentally from the familiar geometry of Euclidean space, so that standard notions from calculus must be reformulated from a broader perspective. One of the most ubiquitous instances of such ?background geometry? is known as sub-Riemannian geometry, which models spaces in which motion is possible only along a given set of directions. This non-smooth geometry is widely useful in modeling physical phenomena, for example, in robotics, quantum mechanics, and neuroscience. This project will also provide opportunities for undergraduate and graduate students to work on research projects arising from the proposed work.

The PI will study sub-Riemannian analogues of the curve shortening flow; the regularity of solutions of certain degenerate elliptic parabolic PDE and non-local PDE in the general setting of certain metric spaces endowed with a doubling measure. The common thread between these investigations is the interplay between the non-smooth structure of the space and the behavior of solutions of equations describing critical points of interesting energy functionals. Some of the proposed research will provide a theoretical basis for implementing numerical simulations of real-world systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348739","RUI: Topics in Free Boundary Problems","DMS","ANALYSIS PROGRAM","09/01/2024","07/10/2024","Mariana Smit Vega Garcia","WA","Western Washington University","Standard Grant","Marian Bocea","08/31/2027","$208,780.00","","mariana.smitvegagarcia@wwu.edu","516 HIGH ST","BELLINGHAM","WA","982255996","3606502884","MPS","128100","9229, 9251","$0.00","Partial Differential Equations (PDE) describe many physical phenomena, including heat or wave propagation, and electromagnetism. The scientific part of this project focuses on families of PDE that model stochastic control, image processing, chemical diffusion, and combustion. The investigator develops new tools which allow her to better understand questions at the interface of mathematics and other sciences, leading to a deeper understanding of the problems being modeled. Furthermore, the investigator organizes a week-long mathematics workshop focused on first-generation freshmen and sophomore students, addressing a large group that is severely underserved. The students participate in minicourses, attend research talks, and have informal conversations with mathematicians who work in different sectors. The workshop is designed to maximize the chance of success of these students, promoting the progress of science and contributing to the development of a mathematically well-versed and diverse workforce. Finally, the investigator organizes a yearly event to help advanced undergraduates and masters? students prepare their applications for graduate school in mathematics.

This project focuses on questions arising in free boundary problems and geometric measure theory. Free boundaries often appear in the applied sciences, in situations where the solution to a problem consists of a pair: a function (often satisfying a PDE), and a set related to this function. The main questions investigated by this project are related to the regularity of the function and the geometry of the associated set. The investigator answers these questions for problems modeled by nonlocal equations, almost minimizers with free boundaries, and minimizers for anisotropic energies. The first class of problems involves PDE which have fundamental importance for mathematical modeling. In particular, numerous applied phenomena give rise to nonlocal equations, such as nonlocal image processing and liquid crystals. In this part of the project, the investigator develops a technique to obtain results for parabolic, nonlocal equations, from their elliptic counterparts. Secondly, the study of almost minimizers with free boundaries has outstanding potential to treat a new group of physically motivated problems, as the almost minimizing property can be understood as a minimizing problem with noise. Finally, minimizers for anisotropic energies lead to non-uniformly elliptic PDE, generating new, challenging questions in geometric PDE.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2400111","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Mehrdad Kalantar","TX","University of Houston","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","","kalantar@math.uh.edu","4300 MARTIN LUTHER KING BLVD","HOUSTON","TX","772043067","7137435773","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349550","Weights in Harmonic Analysis and PDEs","DMS","OFFICE OF MULTIDISCIPLINARY AC, ANALYSIS PROGRAM","07/15/2024","07/11/2024","David Cruz-Uribe","AL","University of Alabama Tuscaloosa","Standard Grant","Wing Suet Li","06/30/2027","$249,454.00","","dcruzuribe@ua.edu","801 UNIVERSITY BLVD","TUSCALOOSA","AL","354012029","2053485152","MPS","125300, 128100","9150","$0.00","This project concerns two areas within the field of mathematical analysis, namely harmonic analysis and partial differential equations. Both have proved to be very effective in understanding a variety of physical phenomena and have wide applications in engineering and the natural sciences. Partial differential equations are a natural way to model dynamic processes (that is, processes that evolve or change in some way). Harmonic analysis provides both a firm theoretical foundation on which to construct these models and effective tools for analyzing their behavior. One of the main goals of this research is to expand our knowledge of harmonic analysis and its applications to the study of partial differential equations. Significant parts of this project include education and mentoring of graduate students, particularly women and under-represented minorities, and the development of new international research collaborations.

The principal investigator (PI) is working on two projects in harmonic analysis and partial differential equations. In the first, the PI is studying matrix weighted estimates for singular and fractional integrals. He is proving generalizations of the Rubio de Francia extrapolation theorem in this setting and developing a theory of matrix weighted Hardy spaces and matrix weighted variable Lebesgue spaces. These results generalize the extensive literature on scalar weighted inequalities and highlight the differences between scalar and matrix weights. New techniques involving convex-set valued functions are used to overcome various technical obstacles that arise in the passage from scalar to matrix weights. In the second project, the PI is studying the existence, uniqueness, and regularity properties of solutions of second order, degenerate elliptic equations with lower order terms. The goal is to construct a theory on as general an equation as possible with the fewest assumptions on the coefficients and the region. These assumptions are expressed in terms of the existence of matrix weighted Sobolev and Poincare ? inequalities. This approach unites and extends a number of results that are already in the literature. The PI is also studying the existence of such Sobolev and Poincare ? inequalities by applying the theory of matrix weighted norm inequalities.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349380","Ergodic Theory for Weakly Hyperbolic Dynamical Systems","DMS","ANALYSIS PROGRAM","09/01/2024","07/10/2024","Davi Obata","UT","Brigham Young University","Standard Grant","Jan Cameron","08/31/2027","$184,985.00","","davi.obata@mathematics.byu.edu","A-153 ASB","PROVO","UT","846021128","8014223360","MPS","128100","","$0.00","The mathematical field of dynamical systems concerns the long-term behavior of systems which evolve in time according to specified rules. Dynamical systems arise naturally in many areas of science and engineering, including statistical mechanics, neurophysiology, and climate science. This project will focus on the dynamics of certain systems ? known as weakly hyperbolic systems -- that display chaotic behavior, in which small perturbations of initial conditions can lead to widely varying trajectories for the system. Because these systems are inherently difficult to predict, they are often studied from a statistical point of view, that is, one analyzes the properties of the system that are expressed through various types of average. This is the focus of ergodic theory, a subfield of dynamical systems, and the conceptual framework for this project, in which the PI will investigate the statistical properties of systems with different types of hyperbolicity. The project will also contribute to education and training, through mentorship of graduate students and the development of new seminars on the topics studied.

The project has three distinct parts. Previously, the PI used measure rigidity results to identify new open sets of dynamical systems with a unique physical measure. The first part of the project aims to address questions related to the utilization of quantified non-joint integrability in establishing the existence and finiteness of physical measures, as well as to understand how often these conditions occur in the partially hyperbolic setting. In the second part of the project, the PI and his co-authors aim to understand different types of transversality to obtain absolute continuity of stationary measures for certain types of random products of surface diffeomorphisms. One goal of this part is to obtain a Benoist-Quint type of result in a non-homogeneous setting. The third part of the project focuses on applying coding techniques to study measures of maximal entropy for non-invertible systems possibly having singularities. Some of the goals include understanding conditions that guarantee existence and finiteness of measures of maximal entropy in these settings, and understanding new examples of such maps.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349929","Renormalization and Rescaling in Conformal Dynamics","DMS","ANALYSIS PROGRAM","08/01/2024","07/09/2024","Yusheng Luo","NY","Cornell University","Standard Grant","Jeremy Tyson","07/31/2027","$262,205.00","","yusheng.luo@cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","128100","","$0.00","The theory of dynamical systems describes how mathematical structures change over time according to prescribed constraints and laws. Dynamical systems model a host of complex phenomena, ranging from celestial mechanics to financial systems to human social behavior. An important but difficult question is to understand when small perturbations of the initial state of a system will qualitatively change the long-term behavior. The stability problem is frequently investigated through a rigorous study of the classifying space of all relevant dynamical systems, known as moduli space. This project focuses on a broad class of one-dimensional dynamical systems satisfying a geometric constraint known as conformality, along with the associated moduli spaces. Tools from complex analysis, hyperbolic geometry, and arithmetic geometry will be combined to address longstanding conjectures and to open new directions for investigation. The project will generate research opportunities for undergraduate and graduate students and will facilitate collaboration among early-career researchers via the organization of seminars and workshops. The research will also result in visually compelling representations, including intricate fractal images and videos, which will be shared with the broader public.

Three distinct but interrelated directions lie at the core of this research project. First, the investigator will use recently developed techniques for the study of degenerations of rational maps and a priori renormalization bounds to study boundedness questions in conformal dynamics. These methods suggest promising approaches to tackle longstanding conjectures about the boundaries of hyperbolic components for rational maps. Next, the investigator will extend the correspondence between rational maps and Kleinian groups. This extension yields novel hybrid dynamical systems combining rational maps and Kleinian groups, where renormalization and rescaling methods can be used to understand rigidity and the deformation spaces. Finally, the investigator will pursue a recently developed renormalization theory for infinite circle packings. These new techniques hold promise in solving various conjectures regarding the quasiconformal geometry of circle packings, thereby addressing some open questions about uniformization and offering insights into conjectures from geometric group theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -27,12 +36,10 @@ "2407511","CAREER: Singularities in fluids","DMS","APPLIED MATHEMATICS, ANALYSIS PROGRAM","04/15/2024","07/07/2024","Tristan Buckmaster","NY","New York University","Continuing Grant","Pedro Embid","08/31/2027","$257,049.00","","tb97@nyu.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","126600, 128100","1045","$0.00","Innumerable hydrodynamical phenomena are described in terms of singularities, of which perhaps the most well-known is the formation of shock waves resulting from a disturbance in a medium such as air or water moving faster than the local speed of sound. The goal of this project is to create a broad program for both research and pedagogical activities centered around the study of singularities in fluids. The award will provide research opportunities and training for postdoctoral scholars and will leverage its research elements to design projects suitable for undergraduate students. The project will also aim at producing a foundational graduate textbook on shock waves in compressible fluids.

The research component is split into three projects: formation and development of shock waves, radial implosions from smooth initial data, and self-similar blow-up via neural networks. Building on previous work of the PI and his collaborators, the aim of the first project will be to provide the first full description of shock wave formation and development for the multi-dimensional compressible Euler equations. The second project involves further developing prior work on self-similar imploding solutions for isentropic compressible flows to investigate the possibility of new types of singularities. The third project involves utilizing physically informed neural networks to search for new forms of singularities in fluid, whose existence will be made rigorous through the aid of computer assisted proofs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350454","Morrey Inequalities, the Pressureless Euler System, and Semipermeable Obstacle Problems","DMS","ANALYSIS PROGRAM","07/01/2024","07/01/2024","Ryan Hynd","PA","University of Pennsylvania","Standard Grant","Marian Bocea","06/30/2027","$291,367.00","","rhynd@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","128100","","$0.00","This project addresses several questions regarding the solvability of certain partial differential equations (PDE). Solutions of these PDE are used to provide information about the models from which they are derived. One of the main challenges is to extract information about these solutions without knowing the functions explicitly. The Principal Investigator (PI) aims to refine and build upon techniques from PDE theory to overcome this challenge. The project focuses on an array of problems at the junction of several areas of mathematics. Moreover, it addresses fundamental problems involving function spaces, the theory of adhesion dynamics, and optimization. As part of this project, the PI mentors a postdoctoral scholar, disseminates results to a broad scientific audience, and continues his involvement in creating opportunities for members of underrepresented groups in mathematics.

The methods of calculus of variations have been used to solve optimization problems in mathematics, physics, and engineering for hundreds of years. These methods continue to play an important role in science, and they also help bridge the gap between PDE theory and optimization. The topics studied by this project involve applications of this interplay to modern questions of interest in mathematical analysis. Morrey's inequality is one of the most important inequalities in the theory of Sobolev spaces. The PI has characterized Morrey extremals as solutions of a nonlinear PDE reminiscent of the equation which arises in the study of the classical electric dipole. In this project, he will develop ways to extend these considerations to Hardy-type inequalities in which the admissible functions are constrained to be supported in certain regions of Euclidean space. The pressureless Euler system is one of the basic model equations in cosmology. They were introduced a generation ago to understand low temperature settings in which galaxies form. The PI recently established an existence theorem for solutions in one spatial dimension. This will be further developed by establishing the uniqueness of solutions and by investigating the large time behavior of solutions. In addition, the project considers obstacle problems in which the competitor curve or shape can permeate the obstacle up to a given threshold. The PI aims to develop this optimization theory from scratch by considering the very basic problems which capture the essence of a semipermeable obstacle problem. In particular, he will study associated Hamilton-Jacobi equations and applications to minimal surfaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2342349","RTG: Frontiers in Applied Analysis","DMS","APPLIED MATHEMATICS, ANALYSIS PROGRAM, WORKFORCE IN THE MATHEMAT SCI","09/01/2024","02/05/2024","Dejan Slepcev","PA","Carnegie-Mellon University","Continuing Grant","Pedro Embid","08/31/2029","$1,474,838.00","Noel Walkington, Irene Fonseca, Gautam Iyer, Robin Neumayer","slepcev@math.cmu.edu","5000 FORBES AVE","PITTSBURGH","PA","152133815","4122688746","MPS","126600, 128100, 733500","7301","$0.00","The increased use of sophisticated mathematical models in applied fields calls for a mathematical workforce with a strong theoretical foundation and a clear vision of how concepts of analysis can be applied to meet challenges at the frontiers of science and technology. The research and training of this RTG focuses on applied analysis, which encompasses partial differential equations, calculus of variations, geometric analysis, stochastic analysis, numerical analysis, optimal transportation, and their applications to relevant models in materials science, geometry processing, and machine learning. This RTG will create a rich ecosystem of activities that is attentive to the needs of trainees at each level. Undergraduate students will be introduced to research in applied analysis and will work alongside graduate students and faculty in innovative course-based undergraduate research and intense summer undergraduate research programs. An undergraduate research conference will provide a venue for presentations, networking, and learning about career opportunities in applied mathematics. This RTG will provide comprehensive mentorship for graduate students and postdocs in a stimulating environment with topics courses, weekly working groups, seminars (including a new seminar series focused on uses of applied analysis across disciplines), workshops, and summer schools. The training will be enhanced by regular professional development activities and visits to international partners from leading research groups in Europe. Particular attention will be given to recruiting and ensuring the success of trainees from underrepresented groups. Overall, the RTG will help attract students to applied mathematics, and will create a technically trained US workforce with expertise in advanced tools of applied analysis ready to engage with future challenges that arise in applied disciplines.

Scientifically, the RTG will spark collaborative efforts to address compelling problems in applied analysis; in particular, variational problems for novel materials, geometric structures in minimization problems, new descriptions of geometry processing tasks, quantitative study of mixing and enhanced dissipation, innovative geometries and gradient flows allowing for accurate computation in high dimensions, and modeling and simulation of problems involving thermomechanics. These collaborations will bridge disciplines, and lead to the creation of new mathematics necessary to address applied challenges.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348522","Advances in Spectral Theory, Several Complex Variables, and the Geometry of Eigenfunctions of the Laplacian","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","07/01/2024","07/01/2024","Hamid Hezari","CA","University of California-Irvine","Standard Grant","Jeremy Tyson","06/30/2027","$246,525.00","","hezari@math.uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126500, 128100","","$0.00","The project resides at the intersection of the fields of mathematical analysis, partial differential equations, and geometry. Specific questions to be investigated concern the inverse spectral problem, the structure of Laplacian eigenfunctions, and the asymptotic behavior of Bergman kernels. These topics are crucial for understanding how geometric structure influences spectral properties, and are deeply connected to various concepts in mathematics and mathematical physics. The inverse spectral problem investigates how much information about the shape of a (not necessarily round) drum can be obtained solely from its frequencies of vibration. This is a classical question famously popularized by Mark Kac with the phrase `Can one hear the shape of a drum?? A second set of problems focuses on the shape and the size of the set (`nodal set?) on which an eigenstate of the Laplacian operator vanishes. The size (in the sense of Hausdorff measure) of the nodal set is conjectured to be comparable to the frequency of the eigenstate. Finally, the Bergman kernel is an essential concept in the fields of complex analysis and complex geometry. Bergman kernel approximations arise naturally in mathematical physics, especially in string theory, where they have been proposed as a tool for the search for geometrically well-behaved complex metric structures. The broader impacts of the project contribute to education and diversity. The principal investigator actively supervises graduate students and postdoctoral researchers. Additionally, the PI participates in outreach activities such as organizing math competitions for middle school students and mentoring students from diverse backgrounds through summer research programs.

The planned research lies in three main areas. Building on previous work with Steve Zelditch, in which nearly circular ellipses were shown to be spectrally unique among smooth domains, the PI aims to generalize such results to generic ellipses and to domains with constant width. Another direction of interest resides in strong inverse spectral results for generic polygons. Next, recent work by the PI resulted in new explicit upper bounds for the Hausdorff measure of nodal sets of eigenfunctions on compact Riemannian manifolds with Gevrey or quasianalytic regularity. The PI seeks to extend these results to manifolds with boundaries and to improve the current upper bounds using innovative methods. Finally, in collaboration with Hang Xu, the PI investigates asymptotic properties of Bergman kernels. This includes establishing new off-diagonal asymptotics for smooth Kaehler potentials and improving extant upper bounds for Bergman kernels. In addition, the PI will explore convergence properties of the Fefferman expansion for domains with real analytic boundaries.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347868","Geometric Inverse Problems and Dynamics","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","07/01/2024","07/01/2024","Gabriel Paternain","WA","University of Washington","Standard Grant","Jeremy Tyson","06/30/2027","$335,956.00","","gpp24@uw.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","126500, 128100","5918, 5935, 5936, 5950","$0.00","This project will center on the study of inverse problems, particularly those involving transport-type partial differential equations. The theory of inverse problems lies at the borderline between pure and applied mathematics, with connections to statistics, physics, engineering, and biology. The diverse array of applications which can be addressed via this theory include X-ray computed tomography, geophysical prospection, and parameter identification for partial differential equations. An effective approach to tackle such questions often involves the use of a geometric framework and geometric tools, facilitating the reconstruction of internal structure from local or boundary measurements. This project focuses specifically on geometric inverse problems. The relevant equations feature velocity fields capable of generating chaotic dynamics, an aspect which presents new challenges for the analysis. The project will also generate opportunities for research and professional training for graduate and undergraduate students.

The project addresses several novel strands of research situated at the interface of geometric inverse problems, dynamical systems, microlocal analysis, and complex geometry. At its core, the planned research is motivated by the desire to comprehend and characterize distinguished solutions to transport problems, a pursuit with potentially far-reaching consequences including the resolution of certain longstanding geometric inverse problems. Among those are the determination of the range of the scattering relation (the first return map of the geodesic flow), deciphering the information encoded within the Ruelle zeta function at zero, and determining topological features of the underlying space from the periods of closed trajectories of the velocity field. The study of distinguished solutions to transport equations necessitates an in-depth analysis of X-ray transforms and the spectral theory of hyperbolic flows.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349077","The Mathematics of Interacting Particle Systems","DMS","ANALYSIS PROGRAM","07/01/2024","07/01/2024","Ian Jauslin","NJ","Rutgers University New Brunswick","Standard Grant","Marian Bocea","06/30/2027","$198,463.00","","ian.jauslin@rutgers.edu","3 RUTGERS PLZ","NEW BRUNSWICK","NJ","089018559","8489320150","MPS","128100","","$0.00","One of the great successes of modern science has been the understanding that simple objects can combine to form complicated structures. For instance, most of the matter that surrounds us is made up of protons, neutrons, and electrons. These building blocks, taken individually, are rather simple, but, when enough of them interact with each other, they produce complex and varied structures, from the intricate patterns of tiny snowflakes to enormous spiraling galaxies. This is a very powerful idea: in principle, it suffices to understand the behavior of simple particles to derive everything. However, in practice, this is a very challenging task, as keeping track of large numbers of interacting particles is impossibly difficult. Instead, sophisticated techniques need to be developed to extract the relevant collective behaviors. This project consists in developing and investigating several such techniques. This project focuses on three types of particle systems, both classical and quantum, which exhibit different types of collective behavior. The first is a model of interacting quantum particles called Bosons. This is a toy model for helium atoms, which are known to form a superfluid phase at low temperature, in which the helium flows without viscosity. The principal investigator (PI) is studying the so-called ""Simplified Approach"", which has been shown to reproduce much of the complex behavior of the interacting Bose gas, while being much more tractable. The second is a classical model in which the PI is proving the existence of crystalline phases, in which infinite large-scale regular patterns spontaneously emerge. The third is a model of interacting quantum particles called Fermions. This is a toy model for the electrons in conductors, which are known to form a superconducting phase at low temperature, in which electricity flows without resistance. The PI is investigating ""hierarchical models"", for which exact solutions can be found, and complex behavior can be proved. This project includes a significant educational component at various levels. The PI is developing graduate, undergraduate, and master's level courses that incorporate the techniques developed in the project, thus introducing students to the tools and techniques of mathematical research. In addition, the PI is producing and distributing educational videos aimed at high school students, undergraduates, and the general public, which are informed by the PI's perspective as a researcher. In addition, the PI is involved in a project to design new mathematical reasoning courses at Rutgers, based on the formal proof assistant called ""Lean"".

This project lies in the field of mathematical physics and aims to develop new tools and refine existing ones to analyze the effect of interactions in a systematic and mathematically rigorous way. Specifically, it consists of the analysis of three types of systems: interacting Bose gases, classical hard-core particle models at high density, and interacting lattice Fermi gases. To analyze the interacting Bose gas, the PI is investigating the ""Simplified Approach"", which is a nonlinear, nonlocal partial differential equation (PDE) in three dimensions. Its analysis has yielded very promising results: it reproduces all known and conjectured behavior of the Bose gas for all densities. The objectives of this part are to solve the more important problems that are still open about this PDE and study its relation to the original many-Boson problem. The PI has developed a framework to study a large class of hard-core particle models at high density and prove that these behave like crystals in that regime. The objectives of this part are to extend the family of hard-core particle models for which we can rigorously prove ordering phase transitions to include three dimensional models, liquid crystals, as well as continuum models. To study interacting lattice Fermi gases, the PI is using the Renormalization Group (RG), which is a powerful tool to study systems of interacting quantum particles, but it is notoriously difficult to implement. The PI has introduced a family of models for which the RG analysis can be carried out easily, rigorously, and exactly, and nontrivial properties can be proved. The main objective of this part is to define and study Fermionic hierarchical models that exhibit superconductivity.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337630","CAREER: Isoperimetric and Minkowski Problems in Convex Geometric Analysis","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","06/01/2024","12/28/2023","Yiming Zhao","NY","Syracuse University","Continuing Grant","Eriko Hironaka","05/31/2029","$69,246.00","","yzhao197@syr.edu","900 S CROUSE AVE","SYRACUSE","NY","13244","3154432807","MPS","126500, 128100","1045","$0.00","Isoperimetric problems and Minkowski problems are two central ingredients in Convex Geometric Analysis. The former compares geometric measurements (such as volume and surface area) while the latter recovers the shape of geometric figures using local versions of these measurements. The two types of problems are inherently connected. This project will exploit this connection to seek answers to either isoperimetric problems or Minkowski problems in various settings when answers to one exist while answers to the other remain elusive. Although these problems originate from a geometric background, their applications extend beyond mathematics into engineering and design, including areas like antenna reflector design and urban planning. The principal investigator will organize a series of events and workshops at local science museums, community centers, and schools, involving high school teachers and students as well as undergraduate and graduate students. These events and workshops aim to expose the fun and exploratory side of the principal investigator?s research and mathematics in general to students early in their educational careers, raise society's awareness and interest in mathematics, and promote mathematics among historically underrepresented populations.

The existence of solutions to the dual Minkowski problem (that characterizes dual curvature measures) in the original symmetric case has been largely settled (by the principal investigator and his collaborators) through techniques from geometry and analysis. This naturally leads to conjectures involving isoperimetric problems connected to the dual Minkowski problem. Such conjectured isoperimetric inequalities are also connected to an intriguing question behind many other conjectures in convexity: how does certain symmetry improve estimates? The principal investigator will also study Minkowski problems and isoperimetric inequalities coming from affine geometry. Special cases of these isoperimetric inequalities are connected to an affine version of the sharp fractional Sobolev inequalities of Almgren-Lieb. The techniques involved in studying these questions are from Convex Geometric Analysis and PDE. In the last few decades (particularly the last two), there has been a community-wide effort to extend results in the theory of convex bodies to their counterparts in the space of log-concave functions. In this project, the principal investigator will also continue his past work to extend dual curvature measures, their Minkowski problems, and associated isoperimetric inequality to the space of log-concave functions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400238","Problems in Harmonic Analysis: interplay between non-zero and zero curvature","DMS","ANALYSIS PROGRAM","07/01/2024","06/20/2024","Victor Lie","IN","Purdue University","Standard Grant","Wing Suet Li","06/30/2027","$276,250.00","","vlie@math.purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","128100","","$0.00","This project in classical harmonic analysis focuses on time-frequency analysis and its connections with other fields such as combinatorics, ergodic theory and fluid dynamics. Time-frequency analysis originates in signal processing and considers the properties of a signal in both the time and frequency domains simultaneously. Historically, the development of time-frequency analysis was motivated in quantum mechanics (e.g. the celebrated Heisenberg uncertainty principle and related work of Wigner and Gabor) and radar detection. Modern applications relying on time-frequency techniques include areas such as image sampling, satellite transmission/GPS location and biomedicine. The PI will continue the development of powerful analytical methods to advance time-frequency analysis from a theoretical perspective. The PI will organize a series of educational activities that include outreach and mentoring for high school and undergraduate students, Putnam exam preparation, reading-course offerings, supervision of graduate students and postdoctoral researchers, and co-organization of seminars, conferences, and summer schools.

This project involves important problems in harmonic analysis with connections to additive combinatorics, ergodic theory and PDE. Relying on time-frequency analysis, the main focus is on the interplay between non-zero and zero curvature settings, with special attention paid to hybrid situations that encapsulate features from both extremes of the scale. The main themes include: (I) Multilinear maximal/singular/oscillatory operators: Building on a natural hierarchical structure that includes the Carleson operator and the bilinear Hilbert transform, this topic studies several relevant model problems in connection to two celebrated open questions: (a) the behavior of the pointwise convergence of bilinear Fourier series, and (b) the boundedness properties of the trilinear Hilbert transform. (II) Multidimensional maximal/singular/oscillatory operators along variable curves: This theme focuses on Carleson-Radon type behavior as well as on an array of problems related to Zygmund's differentiation conjecture. The crucial difficulty here lies in the multivariable dependence of the curves involved in the representation of the operators under study. This creates a series of new difficulties in part due to the existence of Kakeya/Besicovitch type phenomena. (III) Pointwise convergence of Fourier Series, end-point behavior: This topic revolves around the century-old problem regarding the behavior of Fourier Series and discusses some long-standing conjectures on which the investigator has made relevant progress. The main interest in this study relies on the new methods to be developed in order to exploit subtle connections with additive combinatorics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2349322","Banach Spaces: Theory and Applications","DMS","ANALYSIS PROGRAM","07/01/2024","06/20/2024","Thomas Schlumprecht","TX","Texas A&M University","Standard Grant","Wing Suet Li","06/30/2027","$257,986.00","","t-schlumprecht@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","128100","","$0.00","Logistics planning, including optimal distribution of products, leads to questions about maps with weighted distances, and routes that minimize these distances. Transportation cost spaces, also known as Lipschitz-free spaces, Wasserstein spaces, Arens-Eals spaces, and Earthmover spaces, have been used to model such problems. They can be viewed as a framework to study nonlinear metric spaces by embedding them isometrically and linearly densely into Banach spaces and provide powerful tools to study the nonlinear geometry of Banach spaces using well-known linear techniques for nonlinear problems. These spaces play a fundamental role in many areas of applied mathematics, engineering, physics, computer science, finance, and social sciences. Finding an optimal embedding is known to be a computationally hard problem and it has become a central problem in computer science to find low distortion embeddings. Using methods from the structure theory of Banach spaces and computational graph theory, the investigator?s goal is to achieve more precise estimates of these embeddings. He will obtain a deeper understanding of the structure of these spaces, which will result in several applications to the areas mentioned above. The principal investigator plans to organize conferences as well as mentor Ph.D. students as a part of this project.

A crucial connection exists between the L1-distortion of Transportation Cost Spaces and stochastic embeddings of the underlying metric space into trees. The investigator will further study this connection to obtain lower and upper estimations on the distortion. The second part of the project represents a contribution to Lindenstrauss?s program in determining Banach spaces that are primary, and that cannot be decomposed into essentially different subspaces. The investigator will continue to determine primary function spaces. This project concentrates on studying the primarity and related factorization properties of function spaces in two parameters, combining methods from Functional and Harmonic Analysis and Probability Theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409251","Conference: Maryland Dynamics Conference","DMS","ANALYSIS PROGRAM","04/15/2024","04/04/2024","Adam Kanigowski","MD","University of Maryland, College Park","Standard Grant","Jeremy Tyson","03/31/2027","$49,800.00","Giovanni Forni, Rodrigo Trevino, Bassam Fayad","adkanigowski@gmail.com","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","128100","7556","$0.00","This award provides funding for three years for an annual workshop, to be held in the spring, on dynamical systems and related topics. The workshop will take place on the campus of the University of Maryland at College Park. The event provides a forum for both early career and established researchers to exchange ideas with each other and with their counterparts from around the world. Conference proceedings will be produced at the conclusion of each workshop; these publications will help early career mathematicians to gain familiarity with the presented material. Funding from the award will be prioritized for the reimbursement of travel expenses incurred by junior participants and participants without access to other sources of support.

The goals of this workshop are to promote the dissemination of mathematical results; to facilitate interaction and research progress in dynamical systems and related fields; to nurture the sense of community and common mission in these fields; to promote the participation and visibility of women and under-represented groups in the field; and to contribute to the training of graduate students and recent Ph.D. recipients and to their integration into the dynamics community. Talks at the conference come from widely varying areas of dynamical systems, as well as related areas such as analysis, geometry, and topology. At the same time, each instance of the conference incorporates a particular thematic focus within the overall field of dynamical systems. Special effort will be taken to promote the involvement of early career researchers and individuals from groups under-represented in mathematics research. For instance, graduate students and postdocs in attendance at the conference will be invited to contribute to the creation of a post-conference booklet based on notes of the lectures, which will be made available on the conference?s website. (https://www-math.umd.edu/dynamics-conference.html)

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2411574","Conference: New Frontiers in Parabolic Dynamics and Renormalization","DMS","ANALYSIS PROGRAM","07/01/2024","06/17/2024","Rodrigo Trevino","MD","University of Maryland, College Park","Standard Grant","Jan Cameron","06/30/2025","$39,900.00","David Aulicino","rodrigo@umd.edu","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","128100","7556","$0.00","This award will support U.S.-based mathematicians ? with a priority on early-career researchers ? to participate in the dynamical systems conference ?New Frontiers in Parabolic Dynamics and Renormalization,? to be held at the University of Bologna, Italy, July 24-28, 2024. The mathematical field of dynamical systems concerns the evolution of systems over time, including real-world systems such as the weather, traffic patterns, and planetary systems. Some of the most important examples exhibit chaotic behavior. Parabolic dynamics encompasses one class of dynamical systems with chaotic behavior, and renormalization is a powerful tool for uncovering its properties. This conference seeks to bring leading international researchers together to discuss systems that extend beyond parabolic systems and understand techniques that would expand the scope of renormalization and discover new techniques for studying such systems.

Examples of parabolic dynamical systems include horocycle flows on hyperbolic surfaces and, more generally, unipotent flows in homogeneous dynamics, smooth area-preserving flows on surfaces, and nilflows on nilmanifolds. If we allow for the presence of singularities, it also encompasses the study of interval exchange transformations (IETs) and translation flows. More recently, another example that has attracted a lot of attention is the horocycle flow in the moduli space of translation surfaces. Many important examples of parabolic flows also arise from models in mathematical physics, such as the Ehrenfest model of Lorentz gases, systems of Eaton lenses, and the Novikov model, leading to flows on Fermi energy level surfaces in solid-state physics. A key technique used to study parabolic systems is renormalization, an idea that originated from physics, entered dynamical systems decades ago, and has become an increasingly powerful tool for understanding the long-term behavior of many classes of parabolic dynamical systems. This conference seeks to bring together leading researchers from around the world to share their recent advances with the community, which would include US-based graduate students and postdocs. More information about the conference can be found at https://events.unibo.it/parabolicdynamics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400046","Conference: 2024 Great Plains Operator Theory Symposium","DMS","ANALYSIS PROGRAM","05/15/2024","01/23/2024","David Pitts","NE","University of Nebraska-Lincoln","Standard Grant","Wing Suet Li","12/31/2024","$50,000.00","Allan Donsig, Christopher Schafhauser","dpitts2@math.unl.edu","2200 VINE ST # 830861","LINCOLN","NE","685032427","4024723171","MPS","128100","7556, 9150","$0.00","This grant will provide partial participants support for the 2024 Great Plains Operator Theory Symposium (GPOTS) conference at the University of Nebraska-Lincoln, June 3-7, 2024. GPOTS is the largest annual national conference in operator algebras and operator theory held in the United States. Operator algebras and operator theory are major research areas in mathematics, with many connections to other branches of mathematics and with applications across the sciences, particularly to quantum phenomena. Since its beginning in 1981, GPOTS has grown into a major international conference with attendance approximately between 100-150 each year. Researchers will learn about the latest developments and early-career participants will have the opportunity to share their work and connect with other researchers in this part of Mathematics.

The themes of the conference have connections both to many areas of mathematics, including dynamical systems, logic, group theory, ring theory, and to a range of applications, including in quantum phenomena, such quantum computing, and in mathematical physics. Topics which will be featured at GPOTS 2024 include: C*-algebras, operator spaces, operator theory, non-commutative geometry, von Neumann algebras, and quantum information theory. Aside from plenary lectures, GPOTS 2024 will have contributed talks, with many given by early-career researchers, graduate students and postdocs. A significant portion of the proposed funding will be used to support participation by early-career researchers. More information is available at https://math.unl.edu/events/special/gpots2024

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -46,7 +53,6 @@ "2405032","Groups Acing on Hyperbolic Spaces and Operator Algebras","DMS","TOPOLOGY, ANALYSIS PROGRAM","06/01/2024","05/01/2024","Denis Osin","TN","Vanderbilt University","Standard Grant","Eriko Hironaka","05/31/2027","$303,150.00","","denis.osin@gmail.com","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126700, 128100","","$0.00","Geometric group theory studies groups by visualizing them as sets of transformations of metric spaces. This approach is particularly effective when the metric space satisfies certain negative curvature conditions, such as being hyperbolic. The proposed project builds upon the recent work of the PI in this direction. Specifically, the PI will make further advances in the study of groups acting on hyperbolic spaces and their operator algebras. Progressing toward the research objectives of this project requires expertise across various areas, including group theory, functional analysis, geometry, and dynamical systems. The PI will organize a series of week-long conferences aimed at fostering collaboration among experts and young researchers in these fields. Additionally, the project includes a range of educational activities targeting undergraduate and graduate students.

The research project consists of three parts. The main goal of the first part is to study rigidity properties of the class of acylindrically hyperbolic groups. Driven by two major open problems regarding quasi-isometric and measure equivalence rigidity, the PI will address several auxiliary questions and conjectures that connect analytic and geometric properties of groups. In the second part, the PI will study groups acting cocompactly on simply connected, hyperbolic, simplicial complexes. Examples of groups admitting such actions with good control over the local data include hyperbolic and relatively hyperbolic groups, fundamental groups of graphs of groups and their small cancellation quotients, mapping class groups, many Artin groups, etc. The PI will generalize their previous results for relatively hyperbolic groups in this broader context. Lastly, the PI will continue work with collaborators on automorphisms of von Neumann algebras and reduced C*-algebras of countable groups.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424018","CAREER: Oscillatory Integrals and the Geometry of Projections","DMS","ANALYSIS PROGRAM","04/15/2024","04/24/2024","Hong Wang","NY","New York University","Continuing Grant","Jeremy Tyson","08/31/2028","$163,054.00","","hongwang@math.ucla.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","128100","1045","$0.00","This project involves research at the interface of Fourier analysis and geometric measure theory. Fourier analysis studies the relation between a function and its Fourier transform. The Fourier transform of a function, in rough terms, represents the function via a superposition of frequencies. Geometric measure theory studies the geometric properties of sets and measures under transformations. Fractal sets, or sets with highly irregular geometry, are of particular interest in this regard. Recently, the connection between Fourier analysis and geometric measure theory has led to substantial progress in both fields. This project explores the interaction between these two fields, along with possible applications to other fields such as dynamics and number theory. The project also supports workshops for graduate students and early-career mathematicians: these events will promote mathematical expertise within the indicated research areas, will contribute to the professional training of participants, and will foster new research collaborations.

The project combines work in restriction theory (within Fourier analysis) and the theory of projections (within geometric measure theory). One component of the planned research involves the study of the mass of a function, with Fourier transform supported on the sphere, on a fractal set. Another component investigates the dimensions of fractal sets under certain linear or nonlinear maps parametrized by curved manifolds. A final component concerns the Kakeya conjecture, which asks how large must a set be if it contains a unit line segment in every direction. These three components, while distinct, are highly interrelated, and progress in each area is anticipated to inform ongoing work in all of these areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2403501","Conference: Travel to the 21st International Congress on Mathematical Physics, July 1-6, 2024, Strasbourg, France, and Related Events","DMS","ANALYSIS PROGRAM","05/01/2024","04/23/2024","Ilya Kachkovskiy","MI","Michigan State University","Standard Grant","Marian Bocea","04/30/2025","$50,000.00","","ikachkov@msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","128100","7556","$0.00","This award supports the participation of researchers based at institutions in the United States to the 21st International Congress on Mathematical Physics (ICMP) and its satellite events. The ICMP conferences are held every three years, sponsored by the International Association of Mathematical Physics. They are the most important conferences in the field, covering all areas of mathematical physics and demonstrating its richness and vitality. The 21st ICMP takes place July 1-6, 2024, in Strasbourg, France. Similarly to all the congresses since 2000, it is preceded by a Young Researchers Symposium on June 28-29, 2024, at University of Strasbourg.

Combined, these events in mathematical physics make the second half of 2024 a peak time for mathematical physics and attract a large number of international researchers including many of the leading experts in a broad range of mathematical disciplines and their applications in physics. In particular, the conference focuses on recent developments in Analysis that are related to and motivated by mathematical physics. This award provides U.S. graduate students, postdoctoral scholars, early career researchers, members of underrepresented groups, and researchers with limited external funding an opportunity to attend and participate in the Congress. More information is available at https://icmp2024.org. Applications for funding supported by this award are collected through the website https://sites.google.com/msu.edu/icmp-2024-for-us.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2340465","CAREER: Gauge-theoretic Floer invariants, C* algebras, and applications of analysis to topology","DMS","TOPOLOGY, ANALYSIS PROGRAM","09/01/2024","02/02/2024","Sherry Gong","TX","Texas A&M University","Continuing Grant","Qun Li","08/31/2029","$89,003.00","","sgongli@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126700, 128100","1045","$0.00","The main research goal of this project is to apply analytic tools coming from physics, such as gauge theory and operator algebras, to topology, which is the study of geometric shapes. This research is divided into two themes: low dimensional topology and operator K-theory. In both fields, the aforementioned analytic tools are used to build invariants to study the geometric structure of manifolds, which are spaces modelled on Euclidean spaces, like the 3-dimensional space we live in. In both low dimensional topology and operator K-theory, the PI will use analytic tools to study questions about these spaces, such as how they are curved or how objects can be embedded inside them. These questions have a wide range of applications in biology and physics. The educational and outreach goals of this project involve math and general STEM enrichment programs at the middle and high school levels, with a focus on programs aimed at students from underserved communities and underrepresented groups, as well as mentorship in research at the high school, undergraduate and graduate levels.

In low dimensional topology, this project focuses on furthering our understanding of instanton and monopole Floer homologies and their relation to Khovanov homology, and using this to study existence questions of families of metrics with positive scalar curvature on manifolds, as well as questions about knot concordance. Separately this project also involves computationally studying knot concordance, both by a computer search for concordances and by computationally studying certain local equivalence and almost local equivalence groups that receive homomorphisms from the knot concordance groups. In operator algebras, this project focuses on studying their K-theory and its applications to invariants in geometry and topology. The K-theory groups of operator algebras are the targets of index maps of elliptic operators and have important applications to the geometry and topology of manifolds. This project involves studying the K-theory of certain C*-algebras and using them to study infinite dimensional spaces; studying the noncommutative geometry of groups that act on these infinite dimensional spaces and, in particular, the strong Novikov conjecture for these groups; and studying the coarse Baum-Connes conjecture for high dimensional expanders.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404675","Conference: Young Mathematicians in C*-Algebras 2024","DMS","ANALYSIS PROGRAM","04/15/2024","04/09/2024","Adam Fuller","OH","Ohio University","Standard Grant","Jan Cameron","03/31/2025","$49,665.00","Priyanga Ganesan","fullera@ohio.edu","1 OHIO UNIVERSITY","ATHENS","OH","457012979","7405932857","MPS","128100","7556","$0.00","This award provides funding for U.S.-based participants, including members of underrepresented groups in the mathematical sciences, to participate in the conference Young Mathematicians in C*-Algebras (YMC*A), to be held August 5 -9, 2024 at The University of Glasgow, United Kingdom. This meeting is organized for and by graduate students and postdoctoral researchers in operator algebras and related areas, with the goal of fostering scientific and social interaction among early-career researchers. In each of its previous seven editions, YMC*A has provided an excellent opportunity for over one hundred early-career operator algebraists from around the world to attend mini-courses on current research topics in operator algebras. This grant significantly boosts the participation of U.S.-based researchers and their institutions at this conference, exemplifying U.S. research and furnishing opportunities for researchers to expand their professional networks.

The conference focuses on recent developments in operator algebras, noncommutative geometry, and related areas of mathematical analysis, with a particular emphasis on the interplay between operator algebras and group theory, dynamical systems and quantum information theory. The conference features three mini-courses by established researchers alongside many contributed talks by participants, and mentoring activities designed to increase retention of underrepresented groups in operator algebras. More information about the conference is available at: https://ymcstara.org.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2336118","CAREER: Gravitational and Electromagnetic Waves on Black Holes","DMS","APPLIED MATHEMATICS, ANALYSIS PROGRAM","07/01/2024","01/22/2024","Elena Giorgi","NY","Columbia University","Continuing Grant","Dmitry Golovaty","06/30/2029","$67,323.00","","elena.giorgi@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126600, 128100","1045","$0.00","The field of Mathematical General Relativity has played a fundamental role in the analysis of solutions to the Einstein equation, such as black holes - arguably one of the most fundamental objects in our understanding of the universe. Understanding stability of black holes has been central to the mathematical endeavor of confirming their relevance as realistic physical objects. If stable, black holes perturbed with gravitational or other form of radiation, after a temporary change, would eventually return to their initial state. The investigator aims to advance the current knowledge of perturbations dynamics by including interaction of electromagnetic radiation with gravitational waves. This interaction is significant as astrophysical black holes are thought to be surrounded by an accretion disk of matter which, in particular, contains electromagnetic waves. The results of this work are shared with the mathematical and physical communities through peer-reviewed publications and seminars and disseminated to the general public through media articles, public lectures and outreach events in schools. The research of the investigator is integrated with educational activities that increase representation of women in mathematics and promote engagement in mathematics among students. Graduate students and postdocs are also to be involved in this research.

The project is focused on building a comprehensive approach to analyze interactions between gravitational waves and electromagnetic radiation on rotating and charged black holes. The investigator incorporates new techniques to obtain precise decay for the gravitational and electromagnetic waves on charged black holes by developing a universal method involving a combined energy-momentum tensor for coupled system of wave equations. The goal of the project is to prove the non-linear stability of the most general charged and rotating black hole family and extend the investigator?s collaborative work on the resolution for the Kerr family. In addition, the investigator aims to obtain conservation laws for charged black holes in connection with their canonical energy while allowing control of the gravitational and electromagnetic energy radiated at infinity.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401258","Collaborative Research: Conference: Great Lakes Mathematical Physics Meetings 2024-2025","DMS","ANALYSIS PROGRAM","04/15/2024","04/12/2024","Jeffrey Schenker","MI","Michigan State University","Standard Grant","Jan Cameron","03/31/2026","$25,000.00","Ilya Kachkovskiy","jeffrey@math.msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","128100","7556, 9150","$0.00","This award will support participants in the Great Lakes Mathematical Physics Meetings (GLaMP) in 2024 at Michigan State University and in 2025 at the University of Kentucky. The GLaMP meetings are typically held over 3 days in June, with an attendance of 45-50 researchers. The annual conference series, which began in 2016 at Michigan State, focuses on early-career mathematicians working in mathematical physics. Each meeting features invited talks by experts in the field, a minicourse on a topic in mathematical physics, contributed talks by participants, and an interactive career development panel. The main goals of the GLaMP series are: 1) to provide a forum for early-career researchers in mathematical physics ? including advanced undergraduates, graduate students, and early-career postdoctoral scholars ? to present their research and enhance their career development; 2) to maintain communication and collaboration among scientists working in mathematical physics throughout the United States and, in particular, in the greater Midwest; 3) to encourage participation by women and underrepresented minorities in the field of mathematical physics; and 4) to raise the research profile of mathematical physics within the mathematical and scientific community of the United States. All details about the 2024 meeting and links to web pages of previous GLaMP meetings can be found at https://sites.google.com/msu.edu/glamp/home.


Mathematical Physics is one of the oldest scientific disciplines and is a very active field worldwide, with researchers working in both mathematics and physics departments. The roots of the field can be traced to the classical mathematics of Newton, Euler, and Gauss. In the twentieth century, there were many developments at the boundary between mathematics and physics, for example, in scattering theory, non-relativistic quantum mechanics, constructive quantum field theory, the foundations of statistical mechanics, and applications of geometry and topology to high energy physics. The field is supported by the International Association of Mathematical Physics, which organizes an international congress every three years. Although there are many mathematical physicists working in the United States, there are few regular conferences representing the field in the US. The GLaMP meetings have evolved to be the main annual meetings focused on mathematical physics in the US. Minicourse topics have included non-equilibrium quantum statistical mechanics, disordered quantum spin chains and many-body localization, non-self-adjoint operators and quantum resonances, the mathematics of aperiodic order, random matrix theory and supersymmetry techniques, quantum trajectories, and mathematical general relativity. Besides the location, we believe that the distinguishing feature of the GLaMP meeting is its emphasis on early-career researchers. The majority of contributed talks are given by early-career faculty, postdocs, and advanced graduate students. In addition to providing a forum that showcases the work of young researchers, the GLaMP meeting also offers career development opportunities, specifically through a three-hour mini-course on an active area of research given by a world-class expert and a career round table with panelists representing different career paths in mathematical physics, both in academia and in industry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -59,7 +65,6 @@ "2401019","Conference: Supplementary funding for the BIRS-CMO workshop Optimal Transport and Dynamics (24s5198)","DMS","ANALYSIS PROGRAM","04/15/2024","04/05/2024","Jun Kitagawa","MI","Michigan State University","Standard Grant","Jan Cameron","03/31/2025","$14,420.00","","jun@msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","128100","7556","$0.00","The funds from this award will support local expenses for additional participants from US institutions to the Banff International Research Station-Casa Matemática Oaxaca workshop 24w5198, ?Optimal Transport and Dynamics? which will be held August 11 to August 16, 2024, in Oaxaca, Mexico. This workshop will focus on applications of the optimal transport problem, a mathematical problem where the goal is to minimize the total cost of transporting mass from one location to another, to problems involving physical processes that change with time. Such processes include interface motion (such as how water spreads on a surface), models for tumor growth, modeling fluid flows, multi-species population dynamics, and reconstruction of the state of the early universe. The workshop will provide a unique opportunity for early-career researchers to develop connections with and be exposed to the cutting-edge research of well-established leaders in the field. Additionally, the workshop will establish connections between mathematicians and cosmologists, to further accelerate development of the tools and theory behind computation in early universe reconstruction. More information on the workshop may be found at https://www.birs.ca/events/2024/5-day-workshops/24w5198.


The workshop will bring together experts working in optimal transport (Monge-Kantorovich) theory with connections to dynamics interpreted in a broad sense. This includes using optimal transport and related tools to analyze and model fluid flows, interface motion in evolutionary PDE, and also the use of dynamical techniques such as the theory of the parabolic Monge-Ampère PDE for computational and theoretical analysis of optimal transport itself. Optimal transport theory has also been used as a computational model for early universe reconstruction that is consistent with the Zel?dovich approximation, by cosmologists with great success. With recent developments in cosmological surveying and the availability of new data, this area is currently experiencing a revival and is a particularly timely topic. The workshop will consist of a combination of short and long talks solicited from participants, with priority given to presentations by early-career researchers (i.e., graduate students, postdoctoral researchers, and pre-tenure faculty). To take advantage of the international diversity present in the participant list, there will also be a panel discussion on differences in academic job search procedures in different countries.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401257","Collaborative Research: Conference: Great Lakes Mathematical Physics Meetings 2024-2025","DMS","ANALYSIS PROGRAM","04/15/2024","04/12/2024","Peter Hislop","KY","University of Kentucky Research Foundation","Standard Grant","Jan Cameron","03/31/2026","$25,000.00","","peter.hislop@uky.edu","500 S LIMESTONE","LEXINGTON","KY","405260001","8592579420","MPS","128100","7556, 9150","$0.00","This award will support participants in the Great Lakes Mathematical Physics Meetings (GLaMP) in 2024 at Michigan State University and in 2025 at the University of Kentucky. The GLaMP meetings are typically held over 3 days in June, with an attendance of 45-50 researchers. The annual conference series, which began in 2016 at Michigan State, focuses on early-career mathematicians working in mathematical physics. Each meeting features invited talks by experts in the field, a minicourse on a topic in mathematical physics, contributed talks by participants, and an interactive career development panel. The main goals of the GLaMP series are: 1) to provide a forum for early-career researchers in mathematical physics ? including advanced undergraduates, graduate students, and early-career postdoctoral scholars ? to present their research and enhance their career development; 2) to maintain communication and collaboration among scientists working in mathematical physics throughout the United States and, in particular, in the greater Midwest; 3) to encourage participation by women and underrepresented minorities in the field of mathematical physics; and 4) to raise the research profile of mathematical physics within the mathematical and scientific community of the United States. All details about the 2024 meeting and links to web pages of previous GLaMP meetings can be found at https://sites.google.com/msu.edu/glamp/home.


Mathematical Physics is one of the oldest scientific disciplines and is a very active field worldwide, with researchers working in both mathematics and physics departments. The roots of the field can be traced to the classical mathematics of Newton, Euler, and Gauss. In the twentieth century, there were many developments at the boundary between mathematics and physics, for example, in scattering theory, non-relativistic quantum mechanics, constructive quantum field theory, the foundations of statistical mechanics, and applications of geometry and topology to high energy physics. The field is supported by the International Association of Mathematical Physics, which organizes an international congress every three years. Although there are many mathematical physicists working in the United States, there are few regular conferences representing the field in the US. The GLaMP meetings have evolved to be the main annual meetings focused on mathematical physics in the US. Minicourse topics have included non-equilibrium quantum statistical mechanics, disordered quantum spin chains and many-body localization, non-self-adjoint operators and quantum resonances, the mathematics of aperiodic order, random matrix theory and supersymmetry techniques, quantum trajectories, and mathematical general relativity. Besides the location, we believe that the distinguishing feature of the GLaMP meeting is its emphasis on early-career researchers. The majority of contributed talks are given by early-career faculty, postdocs, and advanced graduate students. In addition to providing a forum that showcases the work of young researchers, the GLaMP meeting also offers career development opportunities, specifically through a three-hour mini-course on an active area of research given by a world-class expert and a career round table with panelists representing different career paths in mathematical physics, both in academia and in industry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400191","Group Actions, Rigidity, and Invariant Measures","DMS","ANALYSIS PROGRAM","06/01/2024","04/05/2024","Aaron Brown","IL","Northwestern University","Standard Grant","Jan Cameron","05/31/2027","$353,236.00","","awb@northwestern.edu","633 CLARK ST","EVANSTON","IL","602080001","3125037955","MPS","128100","","$0.00","This project focuses on questions at the interface of dynamical systems and rigidity of group actions. Many mathematical objects admit large groups of symmetries. The structure of such groups may highly constrain the underlying object or properties of the action. Questions across fields of mathematics can often be reformulated as questions about the (non-)fractal nature of invariant geometric structures (particularly sets and measures) for certain group actions. The project will employ tools from the field of dynamical systems to study group actions, with broad aims of classifying actions and the objects on which groups act, classifying certain invariant geometric structures, and showing certain actions do not admit fractal invariant structures. The project will also support the training of PhD students.

The project will focus on actions of groups, including higher-rank abelian groups and higher-rank lattices, with an emphasis on classifying actions with certain dynamical properties, classifying the underlying spaces on the group acts, or classifying invariant measures and orbit closures. The project will employ tools from hyperbolic dynamical systems (dynamical systems with positive Lyapunov exponents) with a common theme of studying invariant measures for the action (or certain subgroups). Classifying or ruling out fractal properties of certain invariant measures will produce further rigidity properties of the action including additional invariance of the measure, local homogeneous structures for the action, or dimension constraints on the space.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2400115","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Kate Juschenko","TX","University of Texas at Austin","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","","kate.juschenko@gmail.com","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349756","Harmonic and functional analysis of wavelet and frame expansions","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Marcin Bownik","OR","University of Oregon Eugene","Standard Grant","Wing Suet Li","06/30/2027","$245,960.00","","mbownik@uoregon.edu","1776 E 13TH AVE","EUGENE","OR","974031905","5413465131","MPS","128100","","$0.00","The project involves research and education activities in harmonic and functional analysis concerning the mathematical theory of multi-dimensional wavelet and frame expansions. Wavelet and frame theory is not only mathematically interesting as a subject of the study by itself, but this area has found many applications outside of pure mathematics ranging from applied and computational harmonic analysis to signal processing and data compression. Some well-known examples where wavelets are a key tool include the JPEG 2000 digital image standard and fingerprint compression for data storage. The broader impacts of the project deal with the education and training of undergraduate and graduate students in the area of harmonic analysis and wavelets.

The project aims to answer some of the most fundamental questions in wavelet and frame theory. One of the main research directions of the project is the development of techniques for the construction of well-localized orthogonal wavelets for large classes of non-isotropic expanding dilations. A closely related complementary topic is the study of wavelets for non-expanding dilations. A recent solution of the wavelet set problem by the PI and Speegle, characterizing dilations for which there exist minimally supported frequency (MSF) wavelets, is connected with the geometry of numbers, more specifically, with the estimate on the number of lattice points of dilates of balls. Another direction of the project is the construction of frames with desired properties such as with prescribed norms and frame operator. This line of research is closely related to the infinite-dimensional generalizations of the Schur-Horn theorem. The problem of characterizing diagonals of self-adjoint operators has not only implications for frame theory but it has also been extensively studied in the setting of von Neumann algebras. Finally, the PI aims to investigate the Akemann-Weaver conjecture, which is a higher-rank extension of Weaver?s conjecture that was proven by Marcus, Spielman, and Srivastava in their breakthrough solution of the Kadison-Singer problem.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348797","Averaging operators and related topics in harmonic analysis","DMS","ANALYSIS PROGRAM","09/01/2024","04/01/2024","Andreas Seeger","WI","University of Wisconsin-Madison","Standard Grant","Wing Suet Li","08/31/2027","$335,000.00","","seeger@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","128100","","$0.00","This project is in harmonic analysis and approximation theory, areas within the mathematical discipline of analysis. The methods have found many applications in understanding phenomena in the natural sciences and engineering. Harmonic analysis seeks to provide efficient mathematical tools for these disciplines and contributes to the unification of seemingly unrelated areas. One of the main objectives of this project is to expand the current mathematical toolbox in harmonic analysis to contribute towards a deeper theoretical understanding which will ultimately be beneficial for applications. The mentoring of graduate students in research is an important educational component of the project.

The principal investigator will work on several projects in harmonic analysis. (i) The first project is concerned with the precise regularity properties of certain averages over sub-manifolds of Euclidean space and the boundedness of associated maximal operators in Lebesgue spaces. The PI will consider mainly non-convolution variants and emphasize various classes of spherical maximal operators on nilpotent groups. (ii) In a second project the PI will study versions of the local smoothing problem for solutions of the wave equation when the dilation set is restricted. New phenomena show up even in the simplified version for radial functions. One expects that the outcomes depend on various notions of dimensions of the dilation sets, the Minkowski dimension, the quasi-Assouad dimension and intermediate scales of dimensions. The PI will also study the related problem concerns the Lp improving bounds for spherical maximal operators with restricted dilation sets, for the open case when the dilation set is not Assouad regular. (iii) The PI will pursue various projects on endpoint estimates in sparse domination, focusing on true multiscale phenomena. Atomic decompositions techniques and sharp Lp improving results for single-scaled operators play a crucial role. (iv) A fourth project is in approximation theory and concerns the characterization of approximation spaces for nonlinear wavelet approximation. The PI and his collaborators will focus on the interesting cases when the order of approximation is high, and the approximation spaces will not be normed spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2346736","Conference: CIRM 2024: Operators on analytic function spaces","DMS","ANALYSIS PROGRAM","08/01/2024","03/22/2024","Pamela Gorkin","PA","Bucknell University","Standard Grant","Wing Suet Li","07/31/2025","$40,200.00","Elodie Pozzi, Kelly Bickel","pgorkin@bucknell.edu","1 DENT DR","LEWISBURG","PA","178372005","5705773510","MPS","128100","7556","$0.00","The conference ""Operators on analytic function spaces"" will take place at the Centre International de Rencontres Mathematiques (CIRM) in Marseille, France from December 2 - 6, 2024. The goal is to create a diverse group of mathematicians poised to solve an important set of problems in function and operator theory, and to allow attendees to develop new directions and partnerships. Funding will be used for US participant support, with priority going to members of underrepresented groups and early career researchers. CIRM provides facilities and equipment as well as an excellent library and serves as a place for collaborative work.

The focus of the conference is on recent progress on Hilbert and Banach spaces of holomorphic functions and the operators acting on them. During the week at CIRM participants will discuss important open questions in function theory and operator theory, including operators on model spaces, Toeplitz and Hankel operators, cyclic vectors, sampling, frames, interpolation and reproducing kernels, and the Crouzeix conjecture. In addition to the talks, the conference will offer activities for attendees to interact and discuss future directions for research. More information may be found at the conference webpage, https://conferences.cirm-math.fr/3085.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -69,8 +74,6 @@ "2350049","Entropy and Boundary Methods in von Neumann Algebras","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Srivatsav Kunnawalkam Elayavalli","CA","University of California-San Diego","Continuing Grant","Jan Cameron","06/30/2027","$47,255.00","","srivatsavke@gmail.com","9500 GILMAN DR","LA JOLLA","CA","920930021","8585344896","MPS","128100","","$0.00","The theory of von Neumann algebras, originating in the 1930's as a mathematical foundation for quantum physics, has since evolved into a beautifully rich subfield of modern functional analysis. Studying the precise structure of von Neumann algebras is rewarding for many reasons, as they appear naturally in diverse areas of modern mathematics such as dynamical systems, ergodic theory, analytic and geometric group theory, continuous model theory, topology, and knot theory. They also continue to be intimately involved in a variety of fields across science and engineering, including quantum physics, quantum computation, cryptography, and algorithmic complexity. The PI will focus on developing a new horizon for research on structural properties of von Neumann algebras, by combining entropy (quantitative) and boundary (qualitative) methods, with applications to various fundamental open questions. This project will also contribute to US workforce development through diversity initiatives and mentoring of graduate students and early career researchers.

In this project, the PI will develop two new research directions in the classification theory of finite von Neumann algebras: applications of Voiculescu's free entropy theory to the structure of free products and of ultrapowers of von Neumann algebras; the small at infinity compactification and structure of von Neumann algebras arising from relatively properly proximal groups. This will involve a delicate study of structure, rigidity and indecomposability properties via innovative interplays between three distinct successful approaches: Voiculescu's free entropy theory, Popa's deformation rigidity theory, Ozawa's theory of small at infinity boundaries and amenable actions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348720","Advances in rational operations in free analysis","DMS","ANALYSIS PROGRAM","06/01/2024","04/01/2024","Jurij Volcic","PA","Drexel University","Standard Grant","Wing Suet Li","05/31/2027","$155,009.00","","jurij.volcic@drexel.edu","3141 CHESTNUT ST","PHILADELPHIA","PA","191042875","2158956342","MPS","128100","","$0.00","The order of actions or operations typically matters; for example, one should first wash the clothes and then dry them, not the other way around. In other words, operations typically do not commute; this is why matrices, which encode noncommutativity in mathematics, are omnipresent in science. While matrix and operator theory has been profoundly developed in the past, the fast-evolving technological advances raise new challenges that have to be addressed. Concretely, expanding quantum technologies, complex control systems, and new resources in optimization and computability pose questions about ensembles of matrices and their features that are independent of the matrix size. The common framework for studying such problems is provided by free analysis (""free"" as in size-free), which investigates functions in matrix and operator variables. This project focuses on such functions that are built only using variables and arithmetic operations, and are therefore called noncommutative polynomials and rational functions. While these are more tangible and computationally accessible than general noncommutative functions, most of their fundamental features are yet to be explored. The scope of the project is to investigate noncommutative rational functions and their variations, develop a theory that allows resolving open problems about them, and finally apply these resolutions to tackle emerging challenges in optimization, control systems, and quantum information. This project provides research training opportunities for graduate students.

The scope of this project is twofold. Firstly, the project aims to answer several function-theoretic open problems on rational operations in noncommuting variables. Among these are singularities and vanishing of rational expressions in bounded operator variables, geometric and structural detection of composition in noncommutative rational functions using control-theoretic tools, noncommutative tensor-rational functions and their role in computational complexity, and existence of low-rank values of noncommutative polynomials with a view towards noncommutative algebraic geometry and approximate zero sets. These fundamental problems call for new synergistic methods that combine complex analysis, representation theory, algebraic geometry and operator theory. Secondly, the project aims to advance the framework of positivity and optimization in several operator variables without dimension restrictions, where the objective functions and constraints are noncommutative polynomials and their variations. The approach to this goal leads through functional analysis, real algebraic geometry and operator algebras. Moreover, the project seeks to apply these new optimization algorithms in quantum information theory, to study nonlinear Bell inequalities in complex quantum networks and the self-testing phenomenon in device-independent certification and cryptographic security.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348633","Free Information Theory Techniques in von Neumann Algebras","DMS","ANALYSIS PROGRAM","07/01/2024","03/27/2024","Dimitri Shlyakhtenko","CA","University of California-Los Angeles","Standard Grant","Jan Cameron","06/30/2027","$421,000.00","","shlyakht@ipam.ucla.edu","10889 WILSHIRE BLVD STE 700","LOS ANGELES","CA","900244200","3107940102","MPS","128100","","$0.00","Von Neumann algebras arose in the 1930s as a mathematical framework for quantum mechanics. In classical mechanics it is possible to simultaneously observe and measure various properties of a physical system ? for example, the locations and velocities of all of its components. Such properties are often called observables. Observables be viewed as functions of the underlying system and form an algebra ? they can be added and multiplied. In quantum mechanics, simultaneous measurements are no longer possible. Mathematically this is reflected by the non-commutativity of the algebra of observables for quantum systems. Nonetheless, many of the operations that can be done with ordinary functions have quantum analogs. The current proposal studies such non-commutative algebras of observables from the angle of Voiculescu?s free probability theory, which treats observables as random variables. This results in an extremely rich theory that leads to free probability generalizations of classical objects such as partial differential equations and Brownian motion, amenable to analysis by techniques inspired by classical information theory. This project will promote human resource development through graduate and undergraduate research opportunities and will support students under the auspices of the UCLA Olga Radko Endowed Math Circle.

The proposed research deals with several questions in von Neumann algebras which are approached by free probability and free information methods, including free entropy theory. This includes further developing PDE based methods in the non-commutative context and strengthening the connection between free probability and random matrix theory. Among the research directions is a notion of dimension that is based on the behavior of optimal transportation distance, as well as applications of free information theory techniques to von Neumann algebra theory. The project includes a mixture of problems, some coming from existing research directions and some exploring new lines of inquiry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2337911","CAREER: Mixing and Equidistribution in Number Theory and Geometry","DMS","ANALYSIS PROGRAM","06/01/2024","01/23/2024","Osama Khalil","IL","University of Illinois at Chicago","Continuing Grant","Jan Cameron","05/31/2029","$69,724.00","","okhalil@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","128100","1045","$0.00","Dynamics is the study of the evolution of a system under a transformation rule governing its behavior over time. It encompasses such varied examples as planetary motion, the spread of disease and the flow of electric currents in conductive material. It turns out that many fundamental problems in number theory and geometry can also be understood in terms of the long-time behavior of certain dynamical systems of algebraic origin. Furthermore, the algebraic nature of these systems makes it possible to employ tools from a wide array of mathematical disciplines for their investigation. This project aims to develop new methods in the theory of algebraic dynamical systems with the goal of resolving central questions in the fields of Diophantine approximation and surface geometry. The educational component aims at training early-career mathematicians and providing mentorship to students at all levels. This includes a workshop geared towards training graduate students and postdocs on active research directions in dynamics, as well as outreach workshops aimed at encouraging students from underrepresented backgrounds to pursue careers in the mathematical sciences.

The research program has three interrelated goals. One goal is to study the distribution of rational points near self-similar sets from the perspective of homogeneous dynamics. The PI will also investigate limits of horocycle-invariant measures on moduli spaces of Abelian differentials, A third aim is to establish rates of mixing of geodesic flows on negatively curved manifolds. Progress on these questions will involve development of dynamical methods at the intersection of representation theory, geometry, and additive combinatorics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2402022","Conference: Dynamical Systems and Fractal Geometry","DMS","ANALYSIS PROGRAM","04/15/2024","04/03/2024","Pieter Allaart","TX","University of North Texas","Standard Grant","Jan Cameron","03/31/2025","$32,017.00","Kiko Kawamura, Kirill Lazebnik","allaart@unt.edu","1112 DALLAS DR STE 4000","DENTON","TX","762051132","9405653940","MPS","128100","7556","$0.00","This award provides support for participants to attend the conference ?Dynamical Systems and Fractal Geometry? to be held at the University of North Texas from May 14-17, 2024. The primary goal of the conference is to foster interaction and collaboration between researchers in several fields of mathematics: fractal geometry, complex dynamics, thermodynamic formalism, random dynamical systems, and open dynamical systems. These fields are interrelated through both the methods used and in the fundamental questions of their study. The conference will bring together mathematicians from these fields ranging from senior experts to graduate students; experts will give standard 45?50-minute plenary lectures, and students will have the opportunity to give 5-10 minute ?lightning talks?. The conference will also include a career panel. More information on the conference, including a list of speakers, can be found on the conference website: https://pcallaart3.wixsite.com/conference.

The fields represented in this conference have broad motivations and applications in several classical areas of mathematics and physics beyond dynamical systems and geometry, including number theory, probability theory, and statistical mechanics. Thermodynamic formalism is a framework for unifying many aspects of these fields, and its investigation triggers research and collaboration on the problem of the existence and uniqueness of equilibrium states of the various systems studied in these fields. Limit sets of conformal dynamical systems, and in particular Julia sets arising in complex dynamics, are typically of a fractal nature and understanding their fine fractal properties such as Hausdorff, packing, Assouad and Fourier dimensions provides a true challenge for fractal geometers. The conference aims to advance research in these directions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400040","Approximation properties in von Neumann algebras","DMS","ANALYSIS PROGRAM","06/01/2024","03/27/2024","Jesse Peterson","TN","Vanderbilt University","Standard Grant","Wing Suet Li","05/31/2027","$291,569.00","","jesse.d.peterson@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","128100","","$0.00","Von Neumann algebras were introduced in the 1930's and 40's to study representation theory of groups, and to use as a tool for developing a mathematical foundation for quantum physics. They have since developed into a full area of study as a natural noncommutative notion of measure theory. The noncommutative setting of topology (C*-algebras) emerged shortly after, and the two subjects have historically been closely connected. This project explores these connections to develop new ideas, to reach a broad mathematical community and providing engagement and support for new students in the field. The investigator is actively participating in the training of students and postdocs in von Neumann algebras and the research from this project will directly impact these students and postdocs.

The project investigator is studying approximation properties (or the lack thereof) in von Neumann algebras and C*-algebras, especially relating to group von Neumann algebras and group measure space constructions. This has historically been a significant area of study in the classification of operator algebras, with amenability/injectivity playing a major role in the development of von Neumann algebras, and nuclearity playing a major corresponding role in the theory of C*-algebras. The emergence of Popa's deformation/rigidity theory has led to numerous breakthroughs in the classification of von Neumann algebras beyond the amenability setting, and approximation properties, such as Ozawa's notion of a biexact group, have created new opportunities to study approximation properties in the setting of von Neumann algebras. The research developed in this project investigates these approximation properties, creating new connections between C* and von Neumann algebras. This allows new C*-algebraic tools to be used in the setting of von Neumann algebras, leading to new structural results for group and group measure space von Neumann algebras, and giving a deeper insight into interactions between operator algebras, ergodic theory, and geometric group theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350079","RUI: Nonuniformly Hyperbolic and Extended Dynamical Systems","DMS","ANALYSIS PROGRAM","09/01/2024","04/08/2024","Mark Demers","CT","Fairfield University","Standard Grant","Jan Cameron","08/31/2027","$242,456.00","","mdemers@fairfield.edu","1073 N BENSON RD","FAIRFIELD","CT","068245171","2032544000","MPS","128100","9229","$0.00","The PI will investigate the properties of chaotic dynamical systems that are out of equilibrium due to the influence of either external forces or interconnected components. Research in dynamical systems is often focused on closed systems in which the dynamics are self-contained. In many modeling situations, however, such a global view is not possible, and it becomes necessary to study local systems influenced by external dynamics, possibly on different spatial or temporal scales. To better understand these phenomena, the PI will study open systems in which mass or energy may enter or exit through deterministic or random mechanisms, as well as large-scale systems of smaller interacting components that exchange mass or energy. These problems are strongly motivated by connections with statistical mechanics and seek to advance our understanding of fundamental questions related to energy transport and diffusion. This award will also support the involvement of undergraduates in mathematics research. The highly visual nature and physical motivation of the problems will enable the investigator to recruit undergraduate students to participate in related research projects. Special emphasis will be given to recruiting students from underrepresented groups in research mathematics. Students will disseminate results of their research via poster sessions, conference presentations and publications in peer-reviewed journals. By stimulating interest in research careers in mathematics and creating a peer community supportive of that interest, this award will contribute to the important goal of integrating research and education.

The funded research includes three specific projects. The first project investigates the statistical and thermodynamic properties of both classical and non-equilibrium particle systems with collision interactions, an important class of models from statistical mechanics. The second concerns open systems, which relate on the one hand to physical systems in which mass or energy is allowed to escape, and on the other to the study of metastable states. The third project generalizes open systems to include linked and extended dynamical systems comprised of two or more components that exchange mass or energy through deterministic or random mechanisms. Important examples include the aperiodic Lorentz gas and mechanical models of heat conduction. The investigator will bring to bear several analytical techniques that he has been instrumental in developing for these classes of systems, including his recent work concerning the spectral decomposition of transfer operators for dispersing particle systems, contractions in projective cones due to Birkhoff, and the construction of Markov extensions adapted to open systems. None of these techniques require Markovian assumptions on the dynamics, making them widely applicable to a wide variety of nonuniformly hyperbolic and physically important systems. The application of these techniques to central models from equilibrium and non-equilibrium statistical mechanics will represent significant advances in the study of such systems. Efforts to understand these tools in one context strengthens them and aids in their application to other areas of mathematics. Their intellectual interest is enhanced by the application of these ideas to resolve problems posed and approached formally in the physics literature.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348384","Geometric Harmonic Analysis: Advances in Radon-like Transforms and Related Topics","DMS","ANALYSIS PROGRAM","07/01/2024","04/05/2024","Philip Gressman","PA","University of Pennsylvania","Standard Grant","Wing Suet Li","06/30/2027","$239,068.00","","gressman@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","128100","","$0.00","The mathematics of geometric averages known as Radon-like operators is of fundamental importance in a host of technological applications related to imaging and data analysis: CT, SPECT, and NMR, as well as RADAR and SONAR applications, all depend on a deep understanding of the Radon transform, and related ideas appear in optical-acoustic tomography, scattering theory, and even some motion-detection algorithms. Somewhat surprisingly, there are many basic theoretical problems in this area of mathematics which remain unsolved despite the many incredible successes the field has already achieved. This project studies a family of questions in the area of geometric averages which, for example, correspond to quantifying the relationship between small changes in the imaged objects and the expected changes in measured data (which in practice would be processed computationally to recover an approximate picture of the original object). The theoretical challenge in a problem such as this is to precisely quantify the notion of change and to establish essentially exact relationships between the magnitude of input and output changes. Thanks to recent advances in the PI's work to understand these objects, the project is well-positioned to yield important results. Achieving the main goals of this project would lead to advances in a number of related areas of mathematics and may influence future imaging technologies. The project furthermore provides unique opportunities for the advanced mathematical training of both undergraduate and PhD students, who can transfer these skills to other areas of critical need once in the workforce.

The PI studies topics in mathematical analysis related to the development of new geometric approaches to Radon-like transforms, oscillatory integrals, and Fourier restriction problems. This work includes various special cases of both sublevel set and oscillatory integral problems. Major special cases deserving mention include multiparameter sublevel set estimates, maximal curvature for Radon-like transforms of intermediate dimension, degenerate Radon transforms in low codimension, Fourier restriction and related generalized determinant functionals, and multilinear oscillatory integrals of convolution and related types. The PI's approach to these involves a variety of new tools developed within the last 5 years which incorporate techniques from Geometric Invariant Theory, geometric measure theory, decoupling theory, and other areas. Among these new tools is a recent result of the PI which provides an entirely new way to estimate norms of Radon-Brascamp-Lieb inequalities in terms of geometric quantities which can be understood as analogous to Lieb's formula for the Brascamp-Lieb constant. A major goal of this project is to understand the local geometric criteria which implicitly govern the finiteness of the nonlocal integrals appearing in the Radon-Brascamp-Lieb condition. The project has numerous potential applications to other problems of interest at the intersection of harmonic analysis, geometric measure theory, and incidence geometry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -89,12 +92,11 @@ "2349794","Regularity Problems in Free Boundaries and Degenerate Elliptic Partial Differential Equations","DMS","ANALYSIS PROGRAM","07/01/2024","04/02/2024","Ovidiu Savin","NY","Columbia University","Standard Grant","Marian Bocea","06/30/2027","$273,927.00","","os2161@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","128100","","$0.00","The goal of this project is to develop new methods for the mathematical theory in several problems of interest involving partial differential equations (PDE). The problems share some common features and are motivated by various physical phenomena such as the interaction of elastic membranes in contact with one another, jet flows of fluids, surfaces of minimal area, and optimal transportation between the elements of two regions. Advancement in the theoretical knowledge about these problems would be beneficial to the scientific community in general and possibly have applications to more concrete computational aspects of solving these equations numerically. The outcomes of the project will be disseminated at a variety of seminars and conferences.

The project focuses on the regularity theory of some specific free boundary problems and nonlinear PDE. The first part is concerned with singularity formation in the Special Lagrangian equation. The equation appears in the context of calibrated geometries and minimal submanifolds. The Principal Investigator (PI) studies the stability of singular solutions under small perturbations together with certain degenerate Bellman equations that are relevant to their study. The second part of the project is devoted to free boundary problems. The PI investigates regularity questions that arise in the study of the two-phase Alt-Phillips family of free boundary problems. Some related questions concern rigidity of global solutions in low dimensions in the spirit of the De Giorgi conjecture. A second problem of interest involves coupled systems of interacting free boundaries. They arise in physical models that describe the configuration of multiple elastic membranes that are interacting with each other according to some specific potential. Another part of the project is concerned with the regularity of nonlocal minimal graphs and some related questions about the boundary Harnack principle for nonlocal operators.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400090","Microlocal Analysis and Hyperbolic Dynamics","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Semyon Dyatlov","MA","Massachusetts Institute of Technology","Continuing Grant","Marian Bocea","06/30/2027","$120,678.00","","dyatlov@MATH.MIT.EDU","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","128100","","$0.00","This project investigates a broad range of topics at the intersection of microlocal analysis and hyperbolic dynamics. Microlocal analysis, with its roots in physical phenomena such as geometric optics and quantum/classical correspondence, is a powerful mathematical theory relating classical Hamiltonian dynamics to singularities of waves and quantum states. Hyperbolic dynamics is the mathematical theory of strongly chaotic systems, where a small perturbation of the initial data leads to exponentially divergent trajectories after a long time. The project takes advantage of the interplay between these two fields, studying the behavior of waves and quantum states in situations where the underlying dynamics is strongly chaotic, and also exploring the applications of microlocal methods to purely dynamical questions. The project provides research training opportunities for graduate students.

One direction of this project is in the highly active field of quantum chaos, the study of spectral properties of quantum systems where the underlying classical system has chaotic behavior. The Principal Investigator (PI) has introduced new methods in the field coming from harmonic analysis, fractal geometry, additive combinatorics, and Ratner theory, combined together in the concept of fractal uncertainty principle. The specific goals of the project include: (1) understanding the macroscopic concentration of high energy eigenfunctions of closed chaotic systems, such as negatively curved Riemannian manifolds and quantum cat maps; and (2) proving essential spectral gaps (implying in particular exponential local energy decay of waves) for open systems with fractal hyperbolic trapped sets. A second research direction is the study of forced waves in stratified fluids (with similar problems appearing also for rotating fluids), motivated by experimentally observed internal waves in aquaria and by applications to oceanography. A third direction is to apply microlocal methods originally developed for the theory of hyperbolic partial differential equations to study classical objects such as dynamical zeta functions, which is a rare example of the reversal of quantum/classical correspondence. In particular, the PI and his collaborators study (1) how the special values of the dynamical zeta function for a negatively curved manifold relate to the topology of the manifold; and (2) whether dynamical zeta functions can be meromorphically continued for systems with singularities such as dispersive billiards.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2334874","Conference: Pittsburgh Links among Analysis and Number Theory (PLANT)","DMS","ALGEBRA,NUMBER THEORY,AND COM, ANALYSIS PROGRAM","02/01/2024","01/19/2024","Carl Wang Erickson","PA","University of Pittsburgh","Standard Grant","James Matthew Douglass","01/31/2025","$20,000.00","Theresa Anderson, Armin Schikorra","carl.wang-erickson@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126400, 128100","7556","$0.00","This award will support the four-day conference ""Pittsburgh Links among Analysis and Number Theory (PLANT)"" that will take place March 4-7, 2024 in Pittsburgh, PA. The purpose of the conference is to bring together representatives of two disciplines with a shared interface: number theory and analysis. There is a large potential for deeper collaboration between these fields resulting in new and transformative mathematical perspectives, and this conference aims at fostering such an interchange. In particular, the conference is designed to attract PhD students and post-doctoral scholars into working on innovations at this interface.

To encourage the development of new ideas, the conference speakers, collectively, represent many subfields that have developed their own distinctive blend of analysis and number theory, such as analytic number theory, arithmetic statistics, analytic theory of modular and automorphic forms, additive combinatorics, discrete harmonic analysis, and decoupling. While there have been a wide variety of conferences featuring these subfields in relative isolation, the PIs are excited at PLANT's potential for sparking links among all of these subfields and giving early-career participants the opportunity to be part of this exchange. The conference website is https://sites.google.com/view/plant24/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2349865","Analysis and Dynamics in Several Complex Variables","DMS","ANALYSIS PROGRAM","06/01/2024","03/21/2024","Xianghong Gong","WI","University of Wisconsin-Madison","Standard Grant","Jeremy Tyson","05/31/2027","$333,182.00","","gong@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","128100","","$0.00","This award supports research at the interface of several complex variables, differential geometry, and dynamical systems. Complex analysis studies the behavior and regularity of functions defined on and taking values in spaces of complex numbers. It remains an indispensable tool across many domains in the sciences, engineering, and economics. This project considers the smoothness of transformations on a domain defined by complex valued functions when the domain is deformed. Using integral formulas, the PI will study how invariants of a domain vary when the underlying structure of the domain changes. Another component of the project involves the study of resonance. The PI will use small divisors that measure non-resonance to classify singularities of the complex structure arising in linear approximations of curved manifolds. The project will involve collaboration with researchers in an early career stage and will support the training of graduate students.

Motivated by recent counterexamples showing that smooth families of domains may be equivalent by a discontinuous family of biholomorphisms, the PI will study the existence of families of biholomorphisms between families of domains using biholomorphism groups and other analytic tools such as Bergman metrics. The PI will construct a global homotopy formula with good estimates for suitable domains in a complex manifold. One of the goals is to construct a global formula in cases when a local homotopy formula fails to exist. The PI will use such global homotopy formulas to investigate the stability of holomorphic embeddings of domains with strongly pseudoconvex or concave boundary in a complex manifold, when the complex structure on the domains is deformed. The PI will use this approach to investigate stability of global Cauchy-Riemann structures on Cauchy-Riemann manifolds of higher codimension. The project seeks a holomorphic classification of neighborhoods of embeddings of a compact complex manifold in complex manifolds via the Levi-form and curvature of the normal bundle. In addition, the PI will study the classification of Cauchy-Riemann singularities for real manifolds using methods from several complex variables and small-divisor conditions in dynamical systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350530","Analysis and Geometry of Conformal and Quasiconformal Mappings","DMS","ANALYSIS PROGRAM","06/01/2024","04/02/2024","Malik Younsi","HI","University of Hawaii","Standard Grant","Jeremy Tyson","05/31/2027","$211,262.00","","malik.younsi@gmail.com","2425 CAMPUS RD SINCLAIR RM 1","HONOLULU","HI","968222247","8089567800","MPS","128100","9150","$0.00","This project aims to better understand the analytic and geometric properties of conformal and quasiconformal mappings. Conformal mappings are planar transformations which locally preserve angles. An important example is the Mercator projection in cartography, used to project the surface of the Earth to a two-dimensional map. More recently, much attention has been devoted to the study of quasiconformal mappings, a generalization of conformal mappings where a controlled amount of angle distortion is permitted. Because of this additional flexibility, quasiconformal mappings have proven over the years to be of fundamental importance in a wide variety of areas of mathematics and applications. Many of these applications involve planar transformations that are quasiconformal inside a given region except possibly for some exceptional set of points inside the region. The study of this exceptional set leads to the notion of removability, central to this research project and closely related to fundamental questions in complex analysis, dynamical systems, probability and related areas. Another focus of this project is on the study of certain families of quasiconformal mappings called holomorphic motions. The principal investigator will study how quantities such as dimension and area change under holomorphic motions, leading to a better understanding of the geometric properties of quasiconformal mappings. The project also provides opportunities for the training and mentoring of early career researchers, including graduate students. In addition, the principal investigator will continue to be involved in a science and mathematics outreach program for local high school students.

Two strands of research comprise the planned work. The first component involves the study of conformal removability. Motivated by the long-standing Koebe uniformization conjecture, the principal investigator will investigate the relationship between removability and the rigidity of circle domains. This part of the project also involves the study of conformal welding, a correspondence between planar Jordan curves and functions on the circle. Recent years have witnessed a renewal of interest in conformal welding along with new generalizations and variants, notably in the theory of random surfaces and in connection with applications to computer vision and numerical pattern recognition. The second component of the project concerns holomorphic motions. The principal investigator will study the variation of several notions of dimension under holomorphic motions. A new approach to this topic by the principal investigator and his collaborators using inf-harmonic functions has already yielded a unified treatment of several celebrated theorems about quasiconformal mappings, and many more fruitful connections are anticipated as progress continues to be made towards a better understanding of holomorphic motions. This part of the project also involves the relationship between global quasiconformal dimension and conformal dimension.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350356","Dynamics of Nonlinear and Disordered Systems","DMS","ANALYSIS PROGRAM","06/01/2024","04/02/2024","Wilhelm Schlag","CT","Yale University","Continuing Grant","Marian Bocea","05/31/2027","$149,265.00","","wilhelm.schlag@yale.edu","150 MUNSON ST","NEW HAVEN","CT","065113572","2037854689","MPS","128100","","$0.00","Observations of solitary waves that maintain their shape and velocity during their propagation were recorded around 200 years ago. First by Bidone in Turin in 1826, and then famously by Russell in 1834 who followed a hump of water moving at constant speed along a channel for several miles. Today these objects are known as solitons. Lying at the intersection of mathematics and physics, they have been studied rigorously since the 1960s. For completely integrable wave equations, many properties of solitons are known, such as their elastic collisions, their stability properties, as well as their role as building blocks in the long-time description of waves. The latter is particularly important, as it for example predicts how waves carrying information decompose into quantifiable units. In quantum physics, quantum chemistry, and material science, these mathematical tools allow for a better understanding of the movement of electrons in various media. This project aims to develop the mathematical foundations which support these areas in applied science, which are of great importance to industry and society at large. The project provides research training opportunities for graduate students.

The project?s goal is to establish both new results and new techniques in nonlinear evolution partial differential equations on the one hand, and the spectral theory of disordered systems on the other hand. The long-range scattering theory developed by Luhrmann and the Principal Investigator (PI) achieved the first results on potentials which exhibit a threshold resonance in the context of topological solitons. This work is motivated by the fundamental question about asymptotic kink stability for the phi-4 model. Asymptotic stability of Ginzburg-Landau vortices in their own equivariance class is not understood. The linearized problem involves a non-selfadjoint matrix operator, and the PI has begun to work on its spectral theory. With collaborators, the PI will engage on research on bubbling for the harmonic map heat flow and attempt to combine the recent paper on continuous-in-time bubbling with a suitable modulation theory. The third area relevant to this project is the spectral theory of disordered systems. More specifically, the PI will continue his work on quasiperiodic symplectic cocycles which arise in several models in condensed matter physics such as in graphene and on non-perturbative methods to analyze them.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2349865","Analysis and Dynamics in Several Complex Variables","DMS","ANALYSIS PROGRAM","06/01/2024","03/21/2024","Xianghong Gong","WI","University of Wisconsin-Madison","Standard Grant","Jeremy Tyson","05/31/2027","$333,182.00","","gong@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","128100","","$0.00","This award supports research at the interface of several complex variables, differential geometry, and dynamical systems. Complex analysis studies the behavior and regularity of functions defined on and taking values in spaces of complex numbers. It remains an indispensable tool across many domains in the sciences, engineering, and economics. This project considers the smoothness of transformations on a domain defined by complex valued functions when the domain is deformed. Using integral formulas, the PI will study how invariants of a domain vary when the underlying structure of the domain changes. Another component of the project involves the study of resonance. The PI will use small divisors that measure non-resonance to classify singularities of the complex structure arising in linear approximations of curved manifolds. The project will involve collaboration with researchers in an early career stage and will support the training of graduate students.

Motivated by recent counterexamples showing that smooth families of domains may be equivalent by a discontinuous family of biholomorphisms, the PI will study the existence of families of biholomorphisms between families of domains using biholomorphism groups and other analytic tools such as Bergman metrics. The PI will construct a global homotopy formula with good estimates for suitable domains in a complex manifold. One of the goals is to construct a global formula in cases when a local homotopy formula fails to exist. The PI will use such global homotopy formulas to investigate the stability of holomorphic embeddings of domains with strongly pseudoconvex or concave boundary in a complex manifold, when the complex structure on the domains is deformed. The PI will use this approach to investigate stability of global Cauchy-Riemann structures on Cauchy-Riemann manifolds of higher codimension. The project seeks a holomorphic classification of neighborhoods of embeddings of a compact complex manifold in complex manifolds via the Levi-form and curvature of the normal bundle. In addition, the PI will study the classification of Cauchy-Riemann singularities for real manifolds using methods from several complex variables and small-divisor conditions in dynamical systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350351","Unique continuation and the regularity of elliptic PDEs and generalized minimal submanifolds","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","06/01/2024","03/27/2024","Zihui Zhao","MD","Johns Hopkins University","Standard Grant","Jeremy Tyson","05/31/2027","$253,734.00","","zhaozh@jhu.edu","3400 N CHARLES ST","BALTIMORE","MD","212182608","4439971898","MPS","126500, 128100","5920, 5936, 5946, 5950","$0.00","This award supports research on the regularity of solutions to elliptic partial differential equations and regularity of generalized minimal submanifolds. Elliptic differential equations govern the equilibrium configurations of various physical phenomena, for instance, those arising from minimization problems for natural energy functionals. Examples include the shape of free-hanging bridges, the shape of soap bubbles, and the sound of drums. Elliptic differential equations are also used to quantify the degree to which physical objects are bent or distorted, with far-reaching implications and applications in geometry and topology. The proposed research focuses on the regularity of solutions to such equations. Questions to be addressed include the following: Do non-smooth points (singularities) exist? How large can the set of singularities be? What is the behavior of the solution near a singularity? Is it possible to perturb the underlying environment in order to eliminate the singularity? The project will also provide opportunities for the professional development of graduate students, both via individual mentoring and via the organization of a directed learning seminar on geometric analysis and geometric measure theory.

The mathematical objectives of the project are twofold. First, the principal investigator will study unique continuation for solutions to elliptic partial differential equations, with a focus on quantitative estimates on the size and structure of the singular set of these solutions. A second topic for consideration is the regularity theory for generalized minimal submanifolds (a generalized notion of smooth submanifolds which arise as critical points for the area functional under local deformations). In particular, the principal investigator will study branch singular points in the interior as well as at the boundary of a generalized minimal submanifold, under an area-minimizing or stability assumption. Research on the latter topic, which can be viewed as a non-linear analogue of quantitative unique continuation for elliptic equations, requires the integration of ideas from geometric measure theory, partial differential equations and geometric analysis.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350263","Diffusion in Kinetic Equations","DMS","ANALYSIS PROGRAM","07/01/2024","03/27/2024","Luis Silvestre","IL","University of Chicago","Standard Grant","Marian Bocea","06/30/2027","$363,887.00","","luis@math.uchicago.edu","5801 S ELLIS AVE","CHICAGO","IL","606375418","7737028669","MPS","128100","","$0.00","Kinetic equations model the evolution of densities of a large system of interactive particles. They may be used, for example, to study the evolution of a gas or a plasma. The Principal Investigator (PI) is interested in the study of the Boltzmann and Landau equations, for systems of particles that repel each other by power-law potentials. These equations exhibit a regularization effect. An outstanding open problem is to understand if a singularity could emerge from the natural flow of the equation, or if the regularization effects actually dominate the evolution and keep the solutions smooth. The PI mentors graduate students and postdocs in research on the topics of this project.

This project aims at developing tools in the analysis of nonlocal equations, parabolic equations and hypoelliptic theory targeted to their applications in kinetic equations. The Boltzmann collision operator acts as a nonlinear diffusive operator of fractional order. It can be studied in the framework of parabolic integro-differential equations. The Landau equation is a model from statistical mechanics used to describe the dynamics of plasma. It can be obtained as a limit case of the Boltzmann equation when grazing collisions prevail. It is a second order, nonlinear, parabolic equation. The project connects different areas of mathematics and mathematical physics, relating recent progress in nonlinear integro-differential equations with the classical Boltzmann equation from statistical mechanics. Kinetic equations involve a nonlinear diffusive operator with respect to velocity, combined with a transport equation with respect to space. The regularization effect in all variables requires ideas from hypoelliptic theory. For the Boltzmann equation in the case of very soft potentials, as well as for the Landau equation with Coulomb potentials, the diffusive part of the equations is not strong enough to prevent the solution from blowing up in theory. In that case, new ideas are needed to properly understand the regularization effects of the equation.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2400008","A description of surface dynamics","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Enrique Pujals","NY","CUNY Graduate School University Center","Standard Grant","Jeremy Tyson","06/30/2026","$249,103.00","","epujals@gc.cuny.edu","365 5TH AVE STE 8113","NEW YORK","NY","100164309","2128177526","MPS","128100","5913, 5918","$0.00","This project seeks to understand the mechanisms that underlie the transition of a dynamical system from an ordered state to a random (chaotic) state. In other words, the aim is to understand the processes through which a system's behavior evolves from periodicity toward chaos, as one or more governing parameters are varied. A related goal is to identify the primary bifurcation responsible for qualitative changes exhibited by a dynamical system. While such comprehension has previously been attained for low-dimensional dynamical systems, this project introduces a novel approach to transcend the low-dimensional limitation. The project will offer new conceptual ideas and approaches to provide fresh perspectives on advances in mathematics and science. Additionally, the project will facilitate the training of graduate students directly engaged in the research, and will afford educational opportunities to undergraduate students through the organization of a summer school presenting topics in mathematics, including topics related to dynamical systems.

The theory of one-dimensional dynamical systems successfully explains the depth and complexity of chaotic phenomena in concert with a description of the dynamics of typical orbits for typical maps. Its remarkable universality properties supplement this understanding with powerful geometric tools. In the two-dimensional setting, the range of possible dynamical scenarios that can emerge is at present only partially understood, and a general framework for those new phenomena that do not occur for one-dimensional dynamics remains to be developed. In prior work supported by the NSF, the principal investigator introduced a large open class of two-dimensional dynamical systems, including the classical Henon family without the restriction of large area contraction, that is amenable to obtaining results as in the one-dimensional case. Moreover, major progress was reached to understand the transition from zero entropy to positive entropy using renormalization schemes. The present project has several components. First, existing renormalization schemes will be adapted to the positive entropy realm. Next, initial steps towards a characterization of dissipative diffeomorphisms in more general contexts will be addressed. Finally, the principal investigator will seek to develop the theory of differentiable renormalization without an a priori assumption of proximity to the one-dimensional setting. These results will open the door to a global description of dissipative diffeomorphisms and their behavior under perturbation, bringing both new tools and new perspectives to smooth dynamical systems theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350481","Complex Analysis and Random Geometry","DMS","ANALYSIS PROGRAM","06/15/2024","04/01/2024","Steffen Rohde","WA","University of Washington","Standard Grant","Jeremy Tyson","05/31/2027","$299,834.00","","rohde@math.washington.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","128100","5918, 5946, 5955","$0.00","The project explores probabilistic and deterministic aspects of self-similar geometry. Self-similar sets are characterized by the property that they look the same at different scales. Such sets arise in the study of dynamical systems, for instance, in complex dynamics and the study of the Mandelbrot set. On the other hand, in probability theory and statistical physics one often encounters stochastically self-similar sets. Such objects only have the same statistical properties at different scales. There are surprising analogies between the probabilistic theory and its deterministic counterpart. The research supported by this award explores these analogies and addresses foundational questions regarding self-similar objects, using methods from complex analysis. The project also provides opportunities for the training and mentoring of junior researchers, including graduate students and postdoctoral researchers. The PI will contribute to the dissemination of mathematical knowledge through the organization of conferences, workshops, and summer schools.

Research to be conducted under this award involves the geometry of conformally self-similar structures, both in stochastic and deterministic settings. Julia sets for the iteration of complex mappings illustrate the latter setting, while the former includes topics such as Schramm-Loewner evolution. The project aims to answer fundamental regularity questions for conformally self-similar objects, including Jordan curves of finite Loewner energy. A new parametrization of the Teichmueller spaces of punctured spheres will also be studied. Additional motivation for the project arises from the interaction between the deterministic and stochastic frameworks, notably, the transfer of methods and results between these two areas. For instance, the concept of conformal mating of polynomials in complex dynamics bears close similarity to Sheffield's mating of trees construction for random spheres. The PI?s research uses methods developed in complex dynamics to provide analytic constructions for random structures. Conversely, insights from the probabilistic theory translate to new research avenues in complex dynamics. Conformal welding is a tool of central importance in both theories, and the proposal aims to resolve several fundamental questions regarding Weil-Petersson curves, welding of Liouville Quantum Gravity discs, and Werner's conformal restriction measure on Jordan curves.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424015","Oscillatory Integrals and Falconer's Conjecture","DMS","ANALYSIS PROGRAM","03/01/2024","03/12/2024","Hong Wang","NY","New York University","Standard Grant","Marian Bocea","08/31/2024","$72,178.00","","hongwang@math.ucla.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","128100","","$0.00","The project is on the restriction theory in Fourier analysis. This field is concerns functions with Fourier transform (frequencies) supported (non-zero at most) on some curved objects such as a sphere or a cone. Such functions appear naturally in several areas of science and mathematics: in the study of Schrödinger equations, wave equations and number theory. For instance, a solution to the linear wave equation can be represented as a function with Fourier transform supported on a cone. Investigating these functions allows one to understand how waves evolve in time. In number theory, one can count the number of integer solutions to some Diophantine equations (polynomial equations with integer coefficients) by estimating such functions. Namely, if the corresponding functions are concentrated, then one expects the Diophantine equation to have many integer solutions. And an upper bound on the number of solutions can be given in terms of how spread out the functions are. This project will be focused on how the curvature of the Fourier support prevents the functions from being concentrated.

The work will be concentrated on oscillatory integrals and related to Falconer's conjecture. The latter is an unsolved question concerning the sets of Euclidean distances between points in compact d-dimensional spaces. The projects on oscillatory integrals concern the restriction conjecture, the Hormander operator, and decoupling questions. For the restriction conjecture, Stein's restriction conjecture will be studied in higher dimensions and in dimension three. For the Hörmander operator the Bochner-Riesz conjecture will be investigated by considering it as a Hörmander operator not satisfying Bourgain's ""generic failure"" condition. Work will be done on the dimension of radial projections with applications surrounding Falconer's conjecture.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401113","Conference: 2024 Riviere-Fabes Symposium","DMS","ANALYSIS PROGRAM","04/01/2024","02/27/2024","Daniel Spirn","MN","University of Minnesota-Twin Cities","Standard Grant","Marian Bocea","03/31/2025","$35,340.00","Ru-yu Lai, Markus Keel","spirn@math.umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","128100","7556","$0.00","This award supports the participation of graduate students and postdoctoral researchers in the ""2024 Riviere-Fabes Symposium on Analysis and PDE"" which is scheduled for April 19-21, 2024 at the University of Minnesota. The award gives early-career researchers and researchers without other sources of funding a chance to participate in the conference. In this way, the award supports the communication of state-of-the-art mathematical techniques and promotes the development of future generations of scientists working in important, cross-disciplinary fields.

The symposium focuses on recent developments in mathematical analysis, this year especially in areas involving harmonic analysis, fluid dynamics, partial differential equations, and statistical mechanics. More information can be found on the symposium web page https://cse.umn.edu/math/riviere-fabes.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Combinatorics/Awards-Combinatorics-2024.csv b/Combinatorics/Awards-Combinatorics-2024.csv index a0fd440..61026e4 100644 --- a/Combinatorics/Awards-Combinatorics-2024.csv +++ b/Combinatorics/Awards-Combinatorics-2024.csv @@ -1,10 +1,13 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2417981","Conference: New Trends in Geometry, Combinatorics and Mathematical Physics","DMS","ALGEBRA,NUMBER THEORY,AND COM, Combinatorics","08/01/2024","07/26/2024","Natalia Rojkovskaia","KS","Kansas State University","Standard Grant","James Matthew Douglass","07/31/2025","$17,500.00","","rozhkovs@math.ksu.edu","1601 VATTIER STREET","MANHATTAN","KS","665062504","7855326804","MPS","126400, 797000","7556, 9150","$0.00","The project supports travel of the US-based mathematicians to the international conference New Trends in Geometry, Combinatorics and Mathematical Physics, that will be take place October 21-25, 2024 at the CNRS center la Vieille Perrotine - Oleron, France. The goal of the project is to provide opportunities for early-career, US-based researchers and to boost the visibility and impact of US-based research. Early-career participants will benefit by acquiring new scientific knowledge from international experts and building long-term professional connections. Ultimately, participation of US-based researchers in the conference will have a positive impact on research projects conducted in the United States.

The scientific foci of the conference are differential geometry and algebraic combinatorics, with applications to mathematical physics. More specifically, applications of cluster algebras in integrable systems and mathematical physics. These applications will be a main topic of the conference, along with interactions between cluster algebras and complex geometry. Further applications of cluster algebras in physics will also be highlighted. Participants from a wide variety of backgrounds will serve to boost the exchange of methods, applications and new ideas, and will form foundations for continuing collaborations. This project is jointly funded by the Algebra and Number Theory and the Combinatorics programs. The conference website is https://indico.math.cnrs.fr/event/11259/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413439","Conference: The 9th International Symposium on Riordan Arrays and Related Topics","DMS","Combinatorics","06/01/2024","05/21/2024","Dennis Davenport","DC","Howard University","Standard Grant","Stefaan De Winter","05/31/2025","$15,000.00","Louis Shapiro","dennis.davenport@howard.edu","2400 6TH ST NW","WASHINGTON","DC","200590002","2028064759","MPS","797000","7556","$0.00","This award supports participation in the 9th International Symposium on Riordan Arrays and Related Topics (9RART), scheduled to occur at Howard University in Washington, D.C. from June 3rd to June 5th. Notably, there is a significant historical tie to this event, as the original paper on the Riordan group was authored by four mathematicians from Howard University in 1991. Since then, eight international conferences have taken place, but this is the first to be held at Howard University. The primary objective of the symposium is to foster collaboration and networking among researchers interested in Riordan arrays and associated subjects. It seeks to catalyze fresh research directions, offer platforms for emerging scholars to showcase their work, and serve as an international nexus for academic exchange and cooperation. Additionally, it aims to broaden the community of mathematicians engaged in Riordan array research.

The symposium features two distinguished international scholars specializing in enumerative combinatorics, who deliver hour-long colloquium-style lectures on their respective fields of expertise. These lectures provide comprehensive overviews of current research trends and suggest potential avenues for future exploration. Furthermore, the event hosts four keynote speakers recognized for their contributions to Riordan arrays. Additionally, there are scheduled several 30-minute presentations and a poster session showcasing student research. The conference website is : https://riordanarray.org/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2400268","Conference: CombinaTexas 2024-2026","DMS","Combinatorics","03/01/2024","02/23/2024","Chun-Hung Liu","TX","Texas A&M University","Continuing Grant","Stefaan De Winter","02/28/2027","$13,320.00","Huafei Yan, Jacob White, Laura Matusevich","chliu@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","797000","7556","$0.00","The CombinaTexas 2024 conference will be held at Texas A&M University, College Station, TX, on March 23-24, 2024. The conference will feature five fifty-minute plenary lectures and a number of contributed talks in various areas of Combinatorics and Graph Theory. The aim of the CombinaTexas series is to enhance communication among mathematicians in Texas and surrounding states, promote research activities of the local combinatorics community, and provide a platform for the presentation and discussion of the latest developments in the broad field of combinatorics. Ever since Texas A&M University hosted the first conference in 2000, it has been held almost every year at an institution in the South Central United States. CombinaTexas 2024 is the 20th conference in this series. The CombinaTexas conference series will be continuously held in 2025 and 2026 supported by this award.

The topics of the CombinaTexas Series include all branches of Combinatorics, Graph Theory, and their connections to Algebra, Geometry, Probability Theory, and Computer Science. In 2024 the confirmed plenary speakers are Boris Bukh (Carnegie Mellon University), Sam Hopkins (Howard University), Jeremy Martin (University of Kansas), Jessica Striker (North Dakota State University), and Fan Wei (Duke University). They will cover topics in Algebraic Combinatorics, Extremal Combinatorics, Discrete Geometry, Graph Theory and their interaction with Algebraic Geometry, Commutative Algebra, and Computer Science. About 70 participants are anticipated, with an estimated 20 contributed talks in parallel sessions. More information about the conference will be available at the webpage https://www.math.tamu.edu/conferences/combinatexas/""

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348843","Combinatorial Representation Theory of Quantum Groups and Coinvariant Algebras","DMS","Combinatorics","07/01/2024","03/25/2024","Joshua Swanson","CA","University of Southern California","Standard Grant","Stefaan De Winter","06/30/2027","$180,000.00","","swansonj@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","90033","2137407762","MPS","797000","","$0.00","Combinatorics has been described as the nanotechnology of mathematics. It is concerned with counting discrete objects, which naturally arise in many applications. As one example, software development frequently requires choosing between different algorithms to solve a problem. Combinatorics allows one to count the number of steps each candidate algorithm takes and then choose the best solution. In this way, combinatorics provides a set of basic tools and a collection of argument prototypes that guide the solution of problems throughout STEM. One of the virtues of combinatorics research is that it provides students with concrete opportunities to develop problem-solving, software development, and other key skills.

Algebraic combinatorics, more specifically, focuses on the combinatorial essence of highly structured and often advanced problems coming from topology, representation theory, particle physics, and other areas. Such problems are frequently reduced in some fashion to an intricate combinatorial analysis. One such algebraic problem is to understand quantum groups. These remarkable structures arose around 1980 from connections with integrable lattice models in quantum mechanics, and some of the technically deepest theories in pure mathematics and physics are in this area. One of the main focuses of the present project is to further develop certain combinatorial diagrams called web bases. These combinatorial objects encode the representation category of quantum groups and allow for efficient computations with powerful topological quantum invariants. They connect a remarkably diverse collection of topics, including total positivity, alternating sign matrices, plane partitions, crystal bases, dynamical algebraic combinatorics, and the geometry of the affine Grassmannian. Students will be involved in the research project.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2429145","Conference: Binghamton University Graduate Combinatorics, Algebra, and Topology Conference (BUGCAT Conference) 2024,2025,2026","DMS","ALGEBRA,NUMBER THEORY,AND COM, Combinatorics","09/15/2024","07/16/2024","Alexander Borisov","NY","SUNY at Binghamton","Continuing Grant","Andrew Pollington","08/31/2027","$28,000.00","","borisov@math.binghamton.edu","4400 VESTAL PKWY E","BINGHAMTON","NY","139024400","6077776136","MPS","126400, 797000","7556","$0.00","This award supports the BUGCAT Conference (Binghamton University Graduate Combinatorics, Algebra, and Topology Conference) 2024 which will take place at the Binghamton University campus on October 26-27, 2024 and also tosupport the conference in the fall of 2025 and 2026. This conference has been running since 2008, with support from NSF in many years, including the last three in-person conferences, in 2019, 2022, and 2023. Continuing NSF support will allow to keep the conference at a current level of more than 100 registered participants, three hour-long keynote presentations, and 40-45 contributed talks of 20-25 minutes in length. The three keynote speakers are professional mathematicians, while most of the other participants are graduate students, with some postdocs and undergraduates.

The conference is run by a rotating committee of graduate students, with general oversight and guidance from the P.I. and some other faculty members. This helps to maintain a friendly and inclusive atmosphere, to facilitate free scientific interactions at the level appropriate for the beginning researchers at various stages of their mathematical development. This also gives the graduate student organizers experience in running a larger conference, and helps them appreciate what is involved in this, when they go give talks at conferences elsewhere. The organizers make efforts to encourage diversity, both by virtue of the varied backgrounds of the organizing committee members, and by the selection of the keynote speakers, without sacrificing the scientific level of the conference. The permanent conference website with the 2023 information, and some previous years' documents, can be found here: https://seminars.math.binghamton.edu/BUGCAT/index.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2404924","Conference: Summer School on Cluster Algebras and Related Topics","DMS","Combinatorics","06/15/2024","06/03/2024","Ralf Schiffler","CT","University of Connecticut","Standard Grant","Stefaan De Winter","11/30/2025","$47,996.00","Emily Gunawan","schiffler@math.uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","797000","7556","$0.00","The Cluster Algebra Summer School takes place at the University of Connecticut June 17-21, 2024. It is aimed at graduate and advanced undergraduate students, and it comprises four mini-courses on different recent developments in the theory of cluster algebras and related topics. This theory is a relatively young branch of mathematics. The initial motivation was to gain an understanding of certain positivity properties in representation theory, a branch of modern algebra. The theory quickly developed deep connections to a variety of disciplines in mathematics and physics, and it is a highly active research area. Cluster algebras are commutative rings equipped with a combinatorial structure that groups its elements into certain subsets, called clusters, which are related to each other via an intricate apparatus called mutation. This structure turns out to be very natural, in the sense that it is present in a large number of mathematical designs.

The four mini-courses are on the following topics. (1) Cluster structures on Richardson varieties and their categorification, which focuses on a relation between representation theory and cluster algebras in the setting of algebras arising from Grassmannian varieties. (2) Cluster algebras and Legendrian links, a mini-course on a connection between cluster algebras and symplectic geometry, especially the contact structure on positive braids. (3) Maximal almost rigid modules, a new type of modules over gentle algebras that correspond bijectively to triangulations of surfaces. (4) Cluster algebras and knot theory, which is on a fundamental relation to knots and links that gives new insights into both areas. All courses are on recent advances in the field and are taught by researchers who are directly involved in these developments. This summer school will help to prepare a diverse group of junior mathematicians to work in this important field. The url for the website of the school is https://egunawan.github.io/cass24/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409861","Conference: An Undergraduate Research Program in Combinatorics","DMS","Combinatorics","06/15/2024","06/03/2024","Joseph Gallian","MN","University of Minnesota Duluth","Continuing Grant","Stefaan De Winter","05/31/2026","$49,109.00","","jgallian@d.umn.edu","1035 UNIVERSITY DR # 133","DULUTH","MN","558123031","2187267582","MPS","797000","7556","$0.00","This award partially supports two meetings of the Undergraduate Research Program in Combinatorics at the University of Minnesota Duluth. The first meeting will be held June 9 - August 1, 2024. In particular, the award supports two graduate assistants at the summer undergraduate research program during the 2024 and 2025 summer. These graduate assistants will assist the PI and co-director of the program. The graduate assistants will be engaged in all aspects of the program: finding suitable problems, acting as mentors and role models, interacting mathematically and socially with participants and visitors, holding practice sessions for presentations, arranging social activities, reading manuscripts, providing advice about graduate schools and fellowships, writing evaluations of the participants' research that the directors of the program use for letters of recommendation. They will likely continue their mentorship activities after the program is over: such as being a coauthor with participants on papers written after the summer program.


The Undergraduate Research Program in Combinatorics will contribute to the advancement of combinatorics by resolving conjectures and answering questions in the literature of interest to well-established people in the field. New methods and concepts and novel applications and examples will be introduced. Some papers will provide deeper insights and better ways to think about concepts. The most significant impact the Duluth programs in 2024 and 2025 will have is the training of future generations of mathematicians who will foster undergraduate and graduate research when they become professionals.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2404924","Conference: Summer School on Cluster Algebras and Related Topics","DMS","Combinatorics","06/15/2024","06/03/2024","Ralf Schiffler","CT","University of Connecticut","Standard Grant","Stefaan De Winter","11/30/2025","$47,996.00","Emily Gunawan","schiffler@math.uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","797000","7556","$0.00","The Cluster Algebra Summer School takes place at the University of Connecticut June 17-21, 2024. It is aimed at graduate and advanced undergraduate students, and it comprises four mini-courses on different recent developments in the theory of cluster algebras and related topics. This theory is a relatively young branch of mathematics. The initial motivation was to gain an understanding of certain positivity properties in representation theory, a branch of modern algebra. The theory quickly developed deep connections to a variety of disciplines in mathematics and physics, and it is a highly active research area. Cluster algebras are commutative rings equipped with a combinatorial structure that groups its elements into certain subsets, called clusters, which are related to each other via an intricate apparatus called mutation. This structure turns out to be very natural, in the sense that it is present in a large number of mathematical designs.

The four mini-courses are on the following topics. (1) Cluster structures on Richardson varieties and their categorification, which focuses on a relation between representation theory and cluster algebras in the setting of algebras arising from Grassmannian varieties. (2) Cluster algebras and Legendrian links, a mini-course on a connection between cluster algebras and symplectic geometry, especially the contact structure on positive braids. (3) Maximal almost rigid modules, a new type of modules over gentle algebras that correspond bijectively to triangulations of surfaces. (4) Cluster algebras and knot theory, which is on a fundamental relation to knots and links that gives new insights into both areas. All courses are on recent advances in the field and are taught by researchers who are directly involved in these developments. This summer school will help to prepare a diverse group of junior mathematicians to work in this important field. The url for the website of the school is https://egunawan.github.io/cass24/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2344639","Conference: Conference on Enumerative and Algebraic Combinatorics","DMS","Combinatorics","02/15/2024","02/08/2024","Vincent Vatter","FL","University of Florida","Standard Grant","Stefaan De Winter","01/31/2025","$22,356.00","Andrew Vince, Miklos Bona, Zachary Hamaker","vatter@ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","797000","7556","$0.00","The Conference on Enumerative and Algebraic Combinatorics will take place at the University of Florida in Gainesville, Florida, February 25-27, 2024. The conference will feature 25 invited and contributed talks by leading researchers in the field as well as a poster session. By bringing together those working in both the Enumerative and Algebraic Combinatorics communities, attending researchers will have ample opportunity to learn about recent developments and develop new mathematics.

The aims of the conference are to present outstanding recent developments in both enumerative and algebraic combinatorics, with a particular focus on their overlap. Specific topics will include standard Young tableaux, permutations, partially ordered sets, symmetric functions, lattice paths, and compositions, all of which are amenable to both enumerative and algebraic study. For more information see the conference web page: https://combinatorics.math.ufl.edu/conferences/sagan2024/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348799","Positive Geometry","DMS","Combinatorics","06/01/2024","05/22/2024","Thomas Lam","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Stefaan De Winter","05/31/2027","$215,974.00","","tfylam@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","797000","","$0.00","The aim of this project is to develop ""positive geometry"". Positive geometry was first conceived of in the study of fundamental questions in particle physics: the calculation of scattering amplitudes that determine how elementary particles, such as electrons and photons, interact. Positive geometries are shapes (for example, higher dimensional versions of cubes and pyramids) whose structure reflects the behavior of particle interaction. In this project, the PI will develop the mathematical foundations of positive geometry which will in turn be applied to physical questions. The project will involve both undergraduate and graduate students.

Positive geometries are semi-algebraic spaces equipped with a differential form, the ""canonical form"", whose polar structure reflects the facial structure of the geometry. Examples of positive geometries include convex polytopes, positive parts of toric varieties, totally nonnegative flag varieties, and conjecturally Grassmann polytopes and amplituhedra. This project aims to study the combinatorics, topology, and geometry of positive geometries in analogy with the theory of convex polytopes. The project will find new positive geometries and new formulae for canonical forms, and apply this to the theory of scattering amplitudes in physics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2413439","Conference: The 9th International Symposium on Riordan Arrays and Related Topics","DMS","Combinatorics","06/01/2024","05/21/2024","Dennis Davenport","DC","Howard University","Standard Grant","Stefaan De Winter","05/31/2025","$15,000.00","Louis Shapiro","dennis.davenport@howard.edu","2400 6TH ST NW","WASHINGTON","DC","200590002","2028064759","MPS","797000","7556","$0.00","This award supports participation in the 9th International Symposium on Riordan Arrays and Related Topics (9RART), scheduled to occur at Howard University in Washington, D.C. from June 3rd to June 5th. Notably, there is a significant historical tie to this event, as the original paper on the Riordan group was authored by four mathematicians from Howard University in 1991. Since then, eight international conferences have taken place, but this is the first to be held at Howard University. The primary objective of the symposium is to foster collaboration and networking among researchers interested in Riordan arrays and associated subjects. It seeks to catalyze fresh research directions, offer platforms for emerging scholars to showcase their work, and serve as an international nexus for academic exchange and cooperation. Additionally, it aims to broaden the community of mathematicians engaged in Riordan array research.

The symposium features two distinguished international scholars specializing in enumerative combinatorics, who deliver hour-long colloquium-style lectures on their respective fields of expertise. These lectures provide comprehensive overviews of current research trends and suggest potential avenues for future exploration. Furthermore, the event hosts four keynote speakers recognized for their contributions to Riordan arrays. Additionally, there are scheduled several 30-minute presentations and a poster session showcasing student research. The conference website is : https://riordanarray.org/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408960","Conference: A Celebration of Algebraic Combinatorics","DMS","Combinatorics","06/01/2024","05/14/2024","Lauren Williams","MA","Harvard University","Standard Grant","Stefaan De Winter","11/30/2025","$49,500.00","","williams@math.harvard.edu","1033 MASSACHUSETTS AVE STE 3","CAMBRIDGE","MA","021385366","6174955501","MPS","797000","7556","$0.00","The conference ``A celebration of algebraic combinatorics'' takes place on June 3-7, 2024, at the Harvard Geological lecture hall at Harvard University. It covers many aspects of combinatorics, a field which was extensively developed by Richard Stanley through his work in algebraic, topological, geometric, and enumerative combinatorics. The conference presents a chance to bring together both experts in the field and early career mathematicians to learn about the latest developments in the field.

The talks at the conference cover a range of topics, ranging from total positivity, symmetric functions, Schubert calculus, poset topology, polytopes, to cluster algebras, log-concavity, the dimer model, and connections with probability. Besides the talks, there are plans to have an open problem session. The website for the conference can be found at https://www.math.harvard.edu/event/math-conference-honoring-richard-p-stanley/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408985","Conference: Mid-Atlantic Algebra, Geometry, and Combinatorics Workshop","DMS","Combinatorics","07/01/2024","05/15/2024","Nicola Tarasca","VA","Virginia Commonwealth University","Continuing Grant","Stefaan De Winter","06/30/2027","$11,368.00","Joel Lewis, Ying Anna Pun","tarascan@vcu.edu","910 WEST FRANKLIN ST","RICHMOND","VA","232849005","8048286772","MPS","797000","7556","$0.00","This award supports the next three editions of the Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) workshop, tentatively scheduled for October 12?13, 2024 at George Washington University, May 30?31, 2025 at CUNY Graduate Center, and May 29?30, 2026 at Virginia Commonwealth University. This conference series aims to bring together senior researchers and junior mathematicians in order to promote collaborations and regional interactions, while highlighting recent developments in algebraic combinatorics, algebraic geometry, representation theory, and other related fields. Each meeting will consist of four invited talks, a poster session for early-career participants, and a panel discussion on career advice, all while allowing for plenty of unstructured time for building mathematical connections.

The goals of MAAGC include helping researchers learn about cutting-edge developments and forge meaningful research collaborations and professional connections throughout the Mid-Atlantic region. The workshops are designed to strengthen and connect the scientific community in algebraic combinatorics and related areas, by facilitating positive interactions among undergraduate and graduate students, postdocs, and faculty at small colleges as well as research universities throughout the region. For more information, please visit the MAAGC website: http://maagc.info

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2411850","Conference: Dynamical and Statistical Combinatorics","DMS","Combinatorics","06/01/2024","05/13/2024","David Speyer","MI","Regents of the University of Michigan - Ann Arbor","Standard Grant","Stefaan De Winter","05/31/2025","$49,000.00","Gregg Musiker, Thomas Roby","speyer@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","797000","7556","$0.00","This award supports the upcoming conference ?Statistical and Dynamical Combinatorics,? taking place at MIT from June 26th to June 29th, 2024. Participants will include a broad and diverse spectrum of mathematicians including distinguished leaders, junior researchers and graduate students. Statistical and dynamical combinatorics has emerged as a topic of intensive research interest, studying different ways in which objects can be moved around and associated numbers that track different aspects of this movement. Mathematical tools from both probability and combinatorics play a key role in analyzing these situations, and there is a strong need for the two communities to come together to work on them.

Topics will include the following highly active areas: (1) Large scale randomness, (2) Markov processes, and (3) Dynamical algebraic combinatorics. All of these areas involve the use of statistics associated with combinatorial objects, each of which often admits multiple equivalent descriptions. Translating between the various forms in which these statistics and objects appear is one of the highlights of the subject. The conference website can be found at https://dept.math.lsa.umich.edu/~speyer/JIM/ .

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -15,8 +18,6 @@ "2348676","A Polytopal View of Classical Polynomials","DMS","Combinatorics","07/01/2024","03/25/2024","Karola Meszaros","NY","Cornell University","Standard Grant","Stefaan De Winter","06/30/2027","$329,999.00","","karola@math.cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","797000","","$0.00","Knot theory is the mathematical study of knots and links. A knot is a single tangled string with the ends tied; a link consists of several knots tangled together. Knot theory has wide applications in the natural sciences, such as in the study of DNA. A basic difficult question of knot theory is how to tell if two links are different: can one be deformed to the other without untying the ends of the strings? Associating polynomials to links is one way to tackle this problem. The aim of this project is to study polynomials in knot theory and other classical branches of mathematics by associating polytopes to them. Polytopes are geometric objects in arbitrary dimensions with flat sides. The study of 3-dimensional polytopes dates back to ancient times. The project also involves mentoring of graduate students as well as outreach to middle and high school students.

The support of a polynomial is the set of exponent vectors of its monomials appearing with nonzero coefficients. The Newton polytope of a polynomial is the smallest integer polytope containing its support. A polynomial has a saturated Newton polytope if every integer point in its Newton polytope is in its support. These notions extend to other bases besides the monomial basis. The goals of this project are (1) the study of saturation properties of classical multivariate polynomials with respect to various bases, such as the monomial and Schubert bases; (2) the study of the integer polytopes they give rise to; and (3) their applications to outstanding conjectures. An illustrative example of this approach is the recent progress by Hafner, Mészáros and Vidinas on Fox?s conjecture from 1962, which states that the absolute values of the coefficients of the Alexander polynomial of an alternating link form a trapezoidal sequence. There are many combinatorial models for the Alexander polynomial which can be used to define combinatorial multivariate Alexander polynomials. For one such model, the support of an associated combinatorial multivariate Alexander polynomial of a special alternating link is the set of integer points in a generalized permutahedron. Such polytopal results, together with the theory of Lorentzian polynomials developed by Brändén and Huh, enabled the proof of log-concavity, and thus trapezoidal property, of the original Alexander polynomial in the case of special alternating links.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2416063","Conference: Research School: Bridges between Algebra and Combinatorics","DMS","Combinatorics","05/01/2024","02/27/2024","Rafael Santiago Gonzalez De Leon","IL","Loyola University of Chicago","Standard Grant","Stefaan De Winter","04/30/2025","$27,000.00","","rgonzalezdleon@luc.edu","820 N MICHIGAN AVE","CHICAGO","IL","606112147","7735082471","MPS","797000","7556","$0.00","This award supports the participation of US-based students and early career mathematicians in the summer research School ""VIII Encuentro Colombiano de Combinatoria: Bridges between Algebra and Combinatorics (ECCO 2024)"" which will be held at Universidad del Cauca in Popayán, Colombia on June 17-28 2024. The series ""Encuentro Colombiano de Combinatoria"" was established in 2003 and has grown to become a staple event in the international combinatorial community. One of the main goals of the school is to foster close interactions between mathematicians at all levels of the career, including the speakers and instructors of the mini-courses. Great value is given to establishing professional connections, mentoring, and community building. The other important pillar of ECCO is to have a strong scientific program where participants learn directly from the experts about the most recent questions and developments in the areas of geometric, algebraic, and enumerative combinatorics.

The scientific program in this school is composed of four mini-courses with exercise sessions, two plenary talks, fifteen contributed talks, two poster sessions, two Sage Math sessions, two open problem sessions, and two professional panels. This school will focus on recent developments of algebraic and combinatorial tools inspired in geometry which have permitted answering combinatorial questions where purely combinatorial techniques might have fallen short in the past. Further details on the program will be posted on the website of the school https://ecco2024.combinatoria.co/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2416639","Conference: Triangle Lectures in Combinatorics","DMS","Combinatorics","03/15/2024","02/26/2024","Clifford Smyth","NC","University of North Carolina Greensboro","Continuing Grant","Stefaan De Winter","02/28/2027","$16,666.00","Fan Wei, Laura Colmenarejo Hernando, Gabor Pataki, Sean English","cdsmyth@uncg.edu","1000 SPRING GARDEN ST","GREENSBORO","NC","274125068","3363345878","MPS","797000","7556","$0.00","The 24th Triangle Lectures in Combinatorics (TLC) will be held on March 23, 2024 on the campus of UNC Greensboro, in Greensboro, North Carolina. It will feature four speakers who are nationally recognized figures in combinatorics and closely related fields. The intellectual merit of the conference includes the dissemination of some of the most significant recent developments in combinatorics to the research community of the Southeastern United States and the fostering of research interactions among participants, leading to new research results. The conference also promotes the teaching and training of graduate students by exposing them to the perspectives of leading researchers as well as the broadening participation of underrepresented groups in mathematical research.

Future editions of the TLC will take place once per semester at different locations near the Triangle Research area. Further details, speakers, titles, and abstracts are posted on the conference website https://wp.math.ncsu.edu/tlc/ as they become available.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2400268","Conference: CombinaTexas 2024-2026","DMS","Combinatorics","03/01/2024","02/23/2024","Chun-Hung Liu","TX","Texas A&M University","Continuing Grant","Stefaan De Winter","02/28/2027","$13,320.00","Huafei Yan, Jacob White, Laura Matusevich","chliu@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","797000","7556","$0.00","The CombinaTexas 2024 conference will be held at Texas A&M University, College Station, TX, on March 23-24, 2024. The conference will feature five fifty-minute plenary lectures and a number of contributed talks in various areas of Combinatorics and Graph Theory. The aim of the CombinaTexas series is to enhance communication among mathematicians in Texas and surrounding states, promote research activities of the local combinatorics community, and provide a platform for the presentation and discussion of the latest developments in the broad field of combinatorics. Ever since Texas A&M University hosted the first conference in 2000, it has been held almost every year at an institution in the South Central United States. CombinaTexas 2024 is the 20th conference in this series. The CombinaTexas conference series will be continuously held in 2025 and 2026 supported by this award.

The topics of the CombinaTexas Series include all branches of Combinatorics, Graph Theory, and their connections to Algebra, Geometry, Probability Theory, and Computer Science. In 2024 the confirmed plenary speakers are Boris Bukh (Carnegie Mellon University), Sam Hopkins (Howard University), Jeremy Martin (University of Kansas), Jessica Striker (North Dakota State University), and Fan Wei (Duke University). They will cover topics in Algebraic Combinatorics, Extremal Combinatorics, Discrete Geometry, Graph Theory and their interaction with Algebraic Geometry, Commutative Algebra, and Computer Science. About 70 participants are anticipated, with an estimated 20 contributed talks in parallel sessions. More information about the conference will be available at the webpage https://www.math.tamu.edu/conferences/combinatexas/""

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348843","Combinatorial Representation Theory of Quantum Groups and Coinvariant Algebras","DMS","Combinatorics","07/01/2024","03/25/2024","Joshua Swanson","CA","University of Southern California","Standard Grant","Stefaan De Winter","06/30/2027","$180,000.00","","swansonj@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","900890701","2137407762","MPS","797000","","$0.00","Combinatorics has been described as the nanotechnology of mathematics. It is concerned with counting discrete objects, which naturally arise in many applications. As one example, software development frequently requires choosing between different algorithms to solve a problem. Combinatorics allows one to count the number of steps each candidate algorithm takes and then choose the best solution. In this way, combinatorics provides a set of basic tools and a collection of argument prototypes that guide the solution of problems throughout STEM. One of the virtues of combinatorics research is that it provides students with concrete opportunities to develop problem-solving, software development, and other key skills.

Algebraic combinatorics, more specifically, focuses on the combinatorial essence of highly structured and often advanced problems coming from topology, representation theory, particle physics, and other areas. Such problems are frequently reduced in some fashion to an intricate combinatorial analysis. One such algebraic problem is to understand quantum groups. These remarkable structures arose around 1980 from connections with integrable lattice models in quantum mechanics, and some of the technically deepest theories in pure mathematics and physics are in this area. One of the main focuses of the present project is to further develop certain combinatorial diagrams called web bases. These combinatorial objects encode the representation category of quantum groups and allow for efficient computations with powerful topological quantum invariants. They connect a remarkably diverse collection of topics, including total positivity, alternating sign matrices, plane partitions, crystal bases, dynamical algebraic combinatorics, and the geometry of the affine Grassmannian. Students will be involved in the research project.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349004","Conference: 9th Lake Michigan Workshop on Combinatorics and Graph Theory","DMS","Combinatorics","03/01/2024","02/26/2024","Andrzej Dudek","MI","Western Michigan University","Standard Grant","Stefaan De Winter","02/28/2025","$21,930.00","Patrick Bennett","andrzej.dudek@wmich.edu","1903 W MICHIGAN AVE","KALAMAZOO","MI","490085200","2693878298","MPS","797000","7556","$0.00","The 9th Lake Michigan Workshop on Combinatorics and Graph Theory will be held at Western Michigan University on April 13-14, 2024. The workshop will benefit graduate students and junior researchers in the field of discrete mathematics working at institutions in the Great Lakes area. It will be built around three sets of two tutorial lectures, focusing on state-of-the-art techniques and results that the speakers feel are underrepresented in typical graduate sequences and on emerging techniques on which the speakers are particularly qualified to expound. There will also be short talks by students and younger faculty members. There will be ample unscheduled time during the weekend, allowing new research collaborations to commence and active collaborations to be continued. Junior participants will establish valuable connections with more senior colleagues and receive guidance from them in a relaxed and informal environment. The tutorial speakers for the 2024 workshop are confirmed to be David Conlon (California Institute of Technology), Wes Pegden (Carnegie Mellon University), and Liana Yepremyan (Emory University).

The topics that will be addressed include homomorphism inequalities between graph densities, probability spaces driven by geometric constraints, and graph colorings, among others. The conference website is https://sites.google.com/wmich.edu/dudek/9th-lake-michigan-workshop

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2334815","Conference: 2024 19th Annual Graduate Students Combinatorics Conference","DMS","Combinatorics","02/01/2024","01/23/2024","Prasad Tetali","PA","Carnegie-Mellon University","Standard Grant","Stefaan De Winter","01/31/2025","$25,000.00","","ptetali@andrew.cmu.edu","5000 FORBES AVE","PITTSBURGH","PA","152133815","4122688746","MPS","797000","7556","$0.00","The 19th Annual Graduate Student Combinatorics Conference (GSCC) will be held from March 15-17, 2024, at Carnegie Mellon University in Pittsburgh, PA. The GSCC is organized by and for graduate students, and includes many subfields of combinatorics, including algebraic, topological, additive, and probabilistic combinatorics. The goal of GSCC is to provide a welcoming environment for graduate students to present their research, learn about the research of others, and meet and collaborate with other students in their field. Carnegie Mellon is well-known for its strength in combinatorics and the applications of combinatorics to computer science. Through a conference for graduate students, the hope is to provide support and encouragement to the next generation of researchers in this thriving subject, as such the aim is to make it accessible and inclusive to a broad spectrum of students.

The main feature of the GSCC is that graduate student attendees are invited to present 25-minute talks on their research, which will run in parallel sessions. There will be four plenary speakers, who are all distinguished professors within different subfields of combinatorics: Jane Pu Gao (Waterloo), Thomas Lam (Michigan), Igor Pak (UCLA), and Michael Young (Carnegie Mellon). Conference registration (free) will open by January, as will applications for travel support. More information for the GSCC is available at sites.google.com/view/GSCC2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348525","Conference: Combinatorial Algebra Meets Algebraic Combinatorics","DMS","Combinatorics","02/15/2024","02/08/2024","Alejandro Morales","MA","University of Massachusetts Amherst","Standard Grant","Stefaan De Winter","01/31/2025","$14,317.00","","ahmorales@math.amherst.edu","101 COMMONWEALTH AVE","AMHERST","MA","010039252","4135450698","MPS","797000","7556","$0.00","The 21st Annual Combinatorial Algebra meets Algebraic Combinatorics (CAAC) conference is scheduled to be held at the Université du Québec à Montréal from Friday, January 26, 2024, to Sunday, January 28, 2024. Since its inception in 2004, the CAAC meeting has annually provided a unique platform for the dynamic interaction between combinatorial algebra and algebraic combinatorics. Emphasizing inclusivity, the conference has traditionally fostered a supportive environment for graduate students, postdoctoral fellows, and early career researchers to engage with established mathematicians, present their work, explore new research directions, and establish collaborative relationships.

Over the years, CAAC conferences have gained popularity, attracting a growing number of participants and contributing significantly to the mathematical community. The upcoming CAAC 2024 conference aims to continue this tradition by featuring four invited 50-minute lectures, contributed talks by graduate students and postdoctoral fellows, software demonstrations, and a poster session. Recognizing the importance of inclusivity, all talks will be streamed online, enabling broader participation from mathematicians unable to attend in person. The conference also seeks funding to support participants from the United States, fostering collaboration, knowledge dissemination, and the advancement of students and postdoctoral fellows in the fields of algebraic combinatorics and combinatorial algebra. Further details and updates about CAAC 2024 can be found on the conference website: https://sites.google.com/view/caac2024/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Probability/Awards-Probability-2024.csv b/Probability/Awards-Probability-2024.csv index fe655a9..0062d85 100644 --- a/Probability/Awards-Probability-2024.csv +++ b/Probability/Awards-Probability-2024.csv @@ -1,7 +1,10 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" "2441646","Permutations in Random Geometry","DMS","PROBABILITY","08/01/2024","07/25/2024","Jacopo Borga","MA","Massachusetts Institute of Technology","Continuing Grant","Elizabeth Wilmer","05/31/2027","$43,582.00","","jborga@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126300","","$0.00","This project lies at the intersection of probability theory, combinatorics, and mathematical physics. Its primary objective is to uncover novel connections between two currently active research domains that have developed independently until recently: random permutations and random geometry. The emerging interplay between permutons (limits of random permutations) and random geometric objects arising in quantum physics and statistical mechanics (such as Schramm?Loewner evolution curves and Liouville quantum gravity surfaces) will play a fundamental role in generating significant advancements in both fields. This will involve formulating novel theories for universal random permutons and random directed metrics, expanding existing ones, and effectively resolving long-standing problems on meanders and meandric systems.

The three main objectives of this research project are, first, to investigate the problem of the longest increasing subsequence of random permutations from a novel angle, which involves linking it to directed metrics in planar maps. The goal is to construct a 'quantum version' of the universal Kardar-Parisi-Zhang geometry, i.e., the directed landscape. Second, to study the geometry of random meanders and broader statistical physics models involving crossing fully packed loops on planar maps. The objective is to tackle the long-standing open problem of determining the scaling limit of random uniform meanders and meandric permutations. Third to establish connections between the limits of d-dimensional permutations and new scale-invariant d-dimensional random geometries introduced in the physical literature. The aim is to begin developing a novel d-dimensional theory of random geometries and permutons. The project offers opportunities for education and outreach to high school and undergraduate students, as well as mentoring of undergraduate and Ph.D. students.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348024","Permutations in Random Geometry","DMS","PROBABILITY","06/01/2024","05/22/2024","Jacopo Borga","CA","Stanford University","Continuing Grant","Elizabeth Wilmer","08/31/2024","$43,582.00","","jborga@mit.edu","450 JANE STANFORD WAY","STANFORD","CA","943052004","6507232300","MPS","126300","","$0.00","This project lies at the intersection of probability theory, combinatorics, and mathematical physics. Its primary objective is to uncover novel connections between two currently active research domains that have developed independently until recently: random permutations and random geometry. The emerging interplay between permutons (limits of random permutations) and random geometric objects arising in quantum physics and statistical mechanics (such as Schramm?Loewner evolution curves and Liouville quantum gravity surfaces) will play a fundamental role in generating significant advancements in both fields. This will involve formulating novel theories for universal random permutons and random directed metrics, expanding existing ones, and effectively resolving long-standing problems on meanders and meandric systems.

The three main objectives of this research project are, first, to investigate the problem of the longest increasing subsequence of random permutations from a novel angle, which involves linking it to directed metrics in planar maps. The goal is to construct a 'quantum version' of the universal Kardar-Parisi-Zhang geometry, i.e., the directed landscape. Second, to study the geometry of random meanders and broader statistical physics models involving crossing fully packed loops on planar maps. The objective is to tackle the long-standing open problem of determining the scaling limit of random uniform meanders and meandric permutations. Third to establish connections between the limits of d-dimensional permutations and new scale-invariant d-dimensional random geometries introduced in the physical literature. The aim is to begin developing a novel d-dimensional theory of random geometries and permutons. The project offers opportunities for education and outreach to high school and undergraduate students, as well as mentoring of undergraduate and Ph.D. students.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2432024","Conference: Advances in probability theory and interacting particle systems","DMS","PROBABILITY","08/01/2024","07/26/2024","Kevin Yang","MA","Harvard University","Standard Grant","Tomek Bartoszynski","07/31/2025","$37,500.00","Paul Bourgade","kevinyang@math.harvard.edu","1033 MASSACHUSETTS AVE STE 3","CAMBRIDGE","MA","021385366","6174955501","MPS","126300","7556","$0.00","This award supports the conference ""Advances in probability theory and interacting particle systems"" that will be held from the 26th-28th of August, 2024, at Harvard University. The conference has 21 confirmed speakers in very active and fundamental areas at the intersection of probability, analysis, and mathematical physics. The main aim is the rigorous study of universal phenomena for particle systems; to explain how random microscopic systems display predictable and statistically universal collective macroscopic behaviors. Large deviations are often key to understanding such problems, especially in large dimensions. Many problems remain in explaining how initial conditions and the details of the microscopic models govern the pre-stationary behavior. Many different approaches in this area will be represented at the conference, including spin-glasses, stochastic PDEs, and random walks in random environments. It is expected that this gathering will lead to cross-fertilization between these approaches, and inspire and inform a new generation of researchers.

Many of the complex systems which will be discussed in this conference aim to describe real world phenomena and results proved for the mathematical models provide predictions applicable to the real systems. A key aspect of the conference proposal is centered on general methods for hydrodynamic limits and fluctuations of particle systems, in fixed or diverging dimensions. In the past, recent progress and the inclusion of new methods has shed light on many of the important questions related to the above. These include the understanding of p-spin models, a proof of the cutoff phenomena for the statistical physics models, fine asymptotics of mixing and cover times for general models, universality in random matrix theory. However, many of the original questions and conjectures remain open. Besides physical applications, complex systems (e.g., spin glasses, growth processes and random matrices) have found many applications in computer science, machine learning, data science, bioinformatics, chemistry, and even areas like ecology and earth science.

The website for this conference is: https://www.math.harvard.edu/event/math-conference-honoring-srinivasa-varadhan/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348096","Multiscale analysis of infinite-dimensional stochastic systems","DMS","PROBABILITY","09/01/2024","07/24/2024","Sandra Cerrai","MD","University of Maryland, College Park","Standard Grant","Elizabeth Wilmer","08/31/2027","$300,000.00","","cerrai@math.umd.edu","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","126300","","$0.00","When studying complex systems, having a simplified description is crucial. Often, this simplification comes from focusing on a select few factors; however, factors that initially seem insignificant can be critical over longer time scales. Thus, a deep understanding of interactions across scales is essential for more effective models of complex systems. This project will address issues in the asymptotic behavior of infinite-dimensional systems that are governed by stochastic partial differential equations (SPDEs) with multiple scales, focusing on SPDEs with conservation laws?a field that remains largely unexplored for systems of infinite dimensions. The planned work will bridge significant gaps in theory and introduce new approaches to the analysis of these multiscale systems. Graduate students and postdocs will participate in the research, and the awardee will develop graduate courses and contribute to the broader mathematical community through lectures, organization of events, and editorial service.

Central to this research is the analysis of the Smoluchowski-Kramers diffusion approximation for stochastic systems with an infinite number of degrees of freedom. We aim to prove the validity of the small-mass limit for stochastic damped geometric wave equations, initially concentrating on stochastic wave maps in one dimension and expanding to more complex systems with state-dependent friction. Both non-local and local friction coefficients will be explored, studying their implications on the trajectories over finite time intervals and on stationary solutions. Further, the project plans to develop an infinite-dimensional version of the classical Friedlin-Wentcell averaging theory for random perturbations of PDEs with conservation laws. This includes constructing SPDEs that live on the level sets of specific functional, establishing the existence invariant measures for these processes, and proving their unique ergodicity and averaging limits. Through these endeavors, the proposal aims to understand better the long-term effects of small stochastic and deterministic perturbations on complex systems. By achieving a deeper understanding of these interactions, the research not only contributes to the fundamental theories in mathematical physics and applied mathematics but also provides robust tools for addressing similar phenomena in various scientific disciplines.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2331449","Conference: Northeast Probability Seminar 2023-2025","DMS","PROBABILITY","02/15/2024","02/15/2024","Jay Rosen","NY","CUNY College of Staten Island","Continuing Grant","Elizabeth Wilmer","01/31/2027","$32,444.00","Ivan Corwin, Yuri Bakhtin, Elena Kosygina, Victor de la Pena","jrosen30@optimum.net","2800 VICTORY BLVD","STATEN ISLAND","NY","103146609","7189822254","MPS","126300","7556","$0.00","The Northeast Probability Seminar is a series that has run for over twenty years. This award will support the continuation of these meetings through 2023, 2024, and 2025. The 2023 meeting is scheduled to take place on November 16-17 at New York University. The 2024 meeting is planned for the City University of New York, and the 2025 meeting is planned for Columbia University. The steering committee includes faculty from all these institutions and several others in and near New York City. These meetings have four plenary lectures, two on Thursday morning and two on Friday morning. Thursday and Friday afternoons are set aside for sessions where 25 junior participants will have the chance to give ten-minute presentations with questions of their recent work.

The Northeast Probability Seminar gives researchers in a dense geographic area an opportunity to exchange fresh ideas and discuss new theories in a highly active area of mathematical research with many interdisciplinary applications. It also provides junior researchers with an opportunity to network with each other and with senior mathematicians. Regional meetings like this one are especially important because they provide an opportunity to establish new collaborations.

The Seminar Web site: https://probability.commons.gc.cuny.edu/22nd-northeast-probability-seminar/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348024","Permutations in Random Geometry","DMS","PROBABILITY","06/01/2024","05/22/2024","Jacopo Borga","CA","Stanford University","Continuing Grant","Elizabeth Wilmer","08/31/2024","$43,582.00","","jborga@mit.edu","450 JANE STANFORD WAY","STANFORD","CA","943052004","6507232300","MPS","126300","","$0.00","This project lies at the intersection of probability theory, combinatorics, and mathematical physics. Its primary objective is to uncover novel connections between two currently active research domains that have developed independently until recently: random permutations and random geometry. The emerging interplay between permutons (limits of random permutations) and random geometric objects arising in quantum physics and statistical mechanics (such as Schramm?Loewner evolution curves and Liouville quantum gravity surfaces) will play a fundamental role in generating significant advancements in both fields. This will involve formulating novel theories for universal random permutons and random directed metrics, expanding existing ones, and effectively resolving long-standing problems on meanders and meandric systems.

The three main objectives of this research project are, first, to investigate the problem of the longest increasing subsequence of random permutations from a novel angle, which involves linking it to directed metrics in planar maps. The goal is to construct a 'quantum version' of the universal Kardar-Parisi-Zhang geometry, i.e., the directed landscape. Second, to study the geometry of random meanders and broader statistical physics models involving crossing fully packed loops on planar maps. The objective is to tackle the long-standing open problem of determining the scaling limit of random uniform meanders and meandric permutations. Third to establish connections between the limits of d-dimensional permutations and new scale-invariant d-dimensional random geometries introduced in the physical literature. The aim is to begin developing a novel d-dimensional theory of random geometries and permutons. The project offers opportunities for education and outreach to high school and undergraduate students, as well as mentoring of undergraduate and Ph.D. students.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2336788","CAREER: Analytic and High-dimensional Methods in Probability","DMS","PROBABILITY","09/01/2024","07/09/2024","Marcus Michelen","IL","University of Illinois at Chicago","Continuing Grant","Elizabeth Wilmer","08/31/2029","$7,709.00","","michelen@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126300","1045","$0.00","This project focuses on the mathematical area of probability theory, the study of random structures. Random structures are ubiquitous throughout the sciences for their use as models as well as their use in the design of algorithms. The main focus of this project is on random structures in high dimensions, meaning random structures with many degrees of freedom. Some examples are random matrices, random sphere packings and random polynomials. Each of these classes of models has direct application in various other scientific fields such as data science, statistical physics and theoretical computer science. The project includes workshops for early-career researchers and graduate students, with an aim of bringing together disparate mathematical subfields.

The project consists of three components, with specific problems chosen with the aim of developing new techniques in high-dimensional probability and the use of analytic approaches in probability theory. The first component of the project concerns universality properties of random polynomials along with their use in optimization and algorithmic problems. The second component focuses on the structure of random sphere packings using connections to more combinatorial objects such as independent sets. The third component studies the non-asymptotic theory of random matrices with a focus on extremal behavior such as understanding the behavior of the least singular value in models without independent entries.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400081","Conference: Seminar on Stochastic Processes 2024","DMS","PROBABILITY","08/01/2024","07/16/2024","Guodong Pang","TX","William Marsh Rice University","Standard Grant","Elizabeth Wilmer","01/31/2025","$50,000.00","Marek Kimmel, Katherine Ensor, Frederi Viens","gdpang@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126300","7556","$0.00","This award supports the 2024 edition of the Seminar on Stochastic Processes, held March 13-16, 2024 at Rice University. This annual meeting has had tremendous impact on the probability community since its inception in 1981, both in North America and internationally. The conference brings together a diverse group of accomplished and early-career researchers and graduate students working in the field of probability and stochastic processes. There are five invited speakers, delivering three plenary lectures and two distinguished plenary lectures known as the ?SSP Founders lecture? and the ?IMS Medallion lecture?, and one tutorial speaker. There are two poster sessions with brief introductory talks, two open problem discussion sessions and a panel session on career development. The conference provides all the participants an opportunity to interact and discuss recent advances in probability theory and stochastic processes, and their applications. As such, the conference represents an important networking opportunity for the many dozens of early-career researchers in attendance and it will enhance the careers of the next generation of researchers in stochastic processes.

The scientific committee has chosen invited speakers who represent a wide breadth of research areas in probability and stochastic processes, including stochastic analysis, stochastic partial differential equations, backward stochastic differential equations, discrete probability, mathematical finance, stochastic geometry, and mathematical physics. The topics also cover a wide range of application areas including biology, data science, physics and epidemiology. Recent research work by other participants is presented at poster sessions. The open problem sessions provide opportunities for discussions about emerging and challenging topics in probability and stochastic processes and the formation of future collaborations. https://ssp2024.rice.edu/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400246","Free Probability, Stochastic Differential Equations, and the Large-N Limit","DMS","PROBABILITY, ANALYSIS PROGRAM","08/01/2024","07/18/2024","Todd Kemp","CA","University of California-San Diego","Standard Grant","Elizabeth Wilmer","07/31/2027","$295,000.00","","tkemp@math.ucsd.edu","9500 GILMAN DR","LA JOLLA","CA","920930021","8585344896","MPS","126300, 128100","079Z","$0.00","In much of physical science, two competing factors determine the behavior of systems: deterministic laws of nature, and random ""noise"". Physical laws are usually described mathematically by differential equations. Over the last half century, a comprehensive theory of differential equations with random noise, called stochastic differential equations, has been developed and is very well-understood in many regimes. One area where foundational work is still needed is understanding how the behavior of systems described by stochastic differential equations scales as the dimension, i.e. the number of features in the system, grows. This project aims to provide a broad theoretical framework and a general scaling limit theory for high-dimensional stochastic differential equations. This theory will have significant applications to research fields as diverse as deep learning and neural networks, neurobiology (understanding learning structures in the brains of insects and other animals), the design of broadband wireless networks, and theoretical physics (quantum field theory). The award will also support the training of graduate student researchers the dissemination of the research at conferences and workshops around the US and the world.

The principal research goals of this award are to study noncommutative stochastic calculus, developing a broad analytic foundation for the subject, and to prove general scaling limit theorems about the solutions of matrix stochastic differential equations (SDEs) as the matrix size grows. Noncommutative stochastic calculus has been developed in several quarters since the 1980s, but key analytic features of the classical theory have been missed owing to the noncommutativity - often, the methods are combinatorial, and function classes are restricted to polynomials or analytic functions. Current work has developed a new approach to noncommutative stochastic calculus, using noncommutative function theory which mirrors the classical martingale theoretic approach. This yields a general theory of noncommutative quadratic variation and an Ito formula which extends all previously known Ito formulations in free probability. This project will use these tools to study the large-N limits of NxN matrix SDEs, proving a general scaling limit for their solutions as described by noncommutative SDEs in free probability. The outline of this approach for self-adjoint processes is now clear, and the technical difficulties should be approachable with methods described above. A further goal is to extend such scaling limits to the non-self-adjoint setting using Brown measure.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2346915","Stochastic partial differential equations: the critical dimension and invariant measures","DMS","PROBABILITY","09/01/2024","07/16/2024","Alexander Dunlap","NC","Duke University","Continuing Grant","Elizabeth Wilmer","08/31/2027","$57,427.00","","dunlap@math.duke.edu","2200 W MAIN ST","DURHAM","NC","277054640","9196843030","MPS","126300","","$0.00","Stochastic partial differential equations (SPDEs) are models of space-time systems subject to random effects. They are especially useful in studying systems in which the randomness is rapidly decorrelating in space and/or time, meaning that different parts of the system are subject to independent random noise. Mathematical studies of such systems are often concentrated on how this small-scale randomness manifests in larger-scale properties of the system. The present project is aimed at studying two aspects of the theory of SPDEs. The first aspect concerns SPDEs in critical dimensions. These SPDEs have a scale-invariance that puts them just beyond the scope of many general techniques but also gives them a symmetry that can be leveraged for computations. The second aspect is to study the long-time behavior of SPDEs on unbounded domains. This involves questions about the relationship between ""long-time"" and ""large-space"" effects in random systems. The awardee also plans to engage in mentoring and exposition to broaden the use and understanding of probabilistic techniques.

One goal of the present project is to work towards a general theory of SPDEs in the critical dimension. The study of stochastic heat equations in dimension two has yielded a rich set of phenomena, and the awardee plans to develop ways to understand these phenomena for larger classes of equations, such as stochastic heat and Hamilton?Jacobi equations with more general nonlinearities. The awardee also plans to further develop the understanding of critical-dimension/critical-temperature problems such as the Critical Stochastic Heat Flow. Another goal is to work towards qualitative understanding of SPDE invariant measures that do not admit explicit descriptions, and to use this understanding to study additive functionals of these processes.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -11,13 +14,11 @@ "2348045","Renormalization, dynamics, and spontaneous symmetry breaking","DMS","PROBABILITY","07/15/2024","07/10/2024","Roland Bauerschmidt","NY","New York University","Continuing Grant","Elizabeth Wilmer","06/30/2027","$84,297.00","","rb5650@nyu.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","126300","","$0.00","The renormalization group method is a cornerstone of modern theoretical physics, explaining a vast range of central phenomena from areas spanning from elementary particle to solid state physics and beyond. The main idea is the analysis of an effective description of a theory at different length scales, leading to a dynamics as the scale varies---the renormalization group dynamics. The mathematics of the renormalization group however is only well understood in very few cases. One of the main goals of this project is to develop mathematical methods and examples of the renormalization group in different contexts. Graduate students wills be mentored as part of the project; the awardee will present courses on relevant material and make their lecture notes available, and also participate in outreach programs for K12 students.

The main focus of this proposal is on the use of the renormalization group method in two contexts, the small and large scale properties of stochastic dynamics of statistical field theories, and the mathematics of spontaneously broken continuous symmetries, in particular in the example of the OSp(1|2) non-linear sigma model. In a complementary direction, some examples of integrable quantum field theories will be explored as well.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2338062","CAREER: Statistical Inference on Random Graphs and Hypergraphs: Geometry, Combinatorics, and Computation","DMS","PROBABILITY, STATISTICS","07/15/2024","07/09/2024","Cheng Mao","GA","Georgia Tech Research Corporation","Continuing Grant","Yong Zeng","06/30/2029","$90,000.00","","cmao35@gatech.edu","926 DALNEY ST NW","ATLANTA","GA","303186395","4048944819","MPS","126300, 126900","079Z, 1045","$0.00","Over the past few decades, the study of complex networks has evolved into an important and dynamic field of research due to the ubiquity of relational data. Statistics plays an increasingly significant role in network analysis because it provides a toolbox for extracting information from noisy network data. Statistical inferential methods have been successfully applied to analyze a broad range of real-world networks, including social, biological, and technological networks. The overall objective of this research is to further advance the theory and methodology for statistical inference with network data. By modeling large-scale networks as random graphs, this research will develop novel algorithmic techniques and analytic tools for inferential tasks on networks. Furthermore, this project will provide research opportunities to undergraduate and graduate students with diverse backgrounds, broadening their participation in interdisciplinary research through summer programs. By integrating research topics with teaching, the PI will also develop innovative statistics curricula that foster students' interest in data science.

The research will focus on the following aspects of statistical inference on random graphs. First, to analyze networks with node attributes, the project will study a class of random geometric graphs, as well as associated detection and recovery problems. Second, a major computational challenge in network analysis lies in the recovery of hidden combinatorial structures. The project will address a variety of such combinatorial structural learning problems, such as geometric graph matching and vertex ordering in nonparametric models. Third, while many real-world networks are hypergraphs, the tools and results are relatively limited, and this project will fill the gap by developing new models and methods for analyzing random hypergraphs. For each of these problems, the research will follow a principled approach to characterize the information-theoretic and computational limits. The project will also develop and implement novel efficient algorithms with provable guarantees, including combinatorial methods based on subgraph counts and improved spectral methods. In summary, the research will substantially forward the development of statistical methods for random graphs, leading to long-term advances in our understanding of network data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2422936","Conference: Stochastic PDEs in Seoul 2024","DMS","PROBABILITY","07/15/2024","07/08/2024","Carl Mueller","NY","University of Rochester","Standard Grant","Elizabeth Wilmer","06/30/2025","$39,728.00","","carl0000mueller@gmail.com","910 GENESEE ST","ROCHESTER","NY","146113847","5852754031","MPS","126300","7556","$0.00","This is a proposal for support of US participation in a forthcoming international workshop on stochastic partial differential equations, ""Stochastic PDEs in Seoul 2024"", scheduled to be held in Korea Institute for Advanced Studies (KIAS, S. Korea) on August 12-16, 2024. The organizers are Professors Nam-Gyu Kang (KIAS, S. Korea), Kunwoo Kim (POSTECH, S. Korea), Davar Khoshnevisan (University of Utah, U.S.A.), and Carl Mueller (University of Rochester, U.S.A.). This 5-day workshop intends to bring together leading researchers and highly promising early career mathematicians from across the globe to exchange ideas on some of the cutting-edge questions and topics in Stochastic Partial Differential Equations, a central topic in modern probability theory.

The organizers anticipate approximately 20 plenary speakers, and additional participants to take part in discussions on and around the main theme of the workshop. The workshop will be structured so that, in addition to sharing latest developments in their research, participants will have ample opportunities to closely interact, with the ultimate aim of generating new ideas. The principal speakers are expected to come from across the globe, and be leading figures in scientific areas within the scope of the workshop. Nearly half of the speakers are expected to represent the United States, and they are expected to be at various career stages. This proposal is designed to make it possible so that those speakers and some of their graduate-student trainees and postdoctoral scholars can attend and participate. Conference URL: https://sites.google.com/view/spde2024

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2336788","CAREER: Analytic and High-dimensional Methods in Probability","DMS","PROBABILITY","09/01/2024","07/09/2024","Marcus Michelen","IL","University of Illinois at Chicago","Continuing Grant","Elizabeth Wilmer","08/31/2029","$7,709.00","","michelen@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126300","1045","$0.00","This project focuses on the mathematical area of probability theory, the study of random structures. Random structures are ubiquitous throughout the sciences for their use as models as well as their use in the design of algorithms. The main focus of this project is on random structures in high dimensions, meaning random structures with many degrees of freedom. Some examples are random matrices, random sphere packings and random polynomials. Each of these classes of models has direct application in various other scientific fields such as data science, statistical physics and theoretical computer science. The project includes workshops for early-career researchers and graduate students, with an aim of bringing together disparate mathematical subfields.

The project consists of three components, with specific problems chosen with the aim of developing new techniques in high-dimensional probability and the use of analytic approaches in probability theory. The first component of the project concerns universality properties of random polynomials along with their use in optimization and algorithmic problems. The second component focuses on the structure of random sphere packings using connections to more combinatorial objects such as independent sets. The third component studies the non-asymptotic theory of random matrices with a focus on extremal behavior such as understanding the behavior of the least singular value in models without independent entries.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348118","Conference: Recent progress in stochastic analysis and its applications","DMS","PROBABILITY","06/01/2024","05/17/2024","Shuwen Lou","IL","Loyola University of Chicago","Standard Grant","Elizabeth Wilmer","05/31/2025","$49,248.00","Krzysztof Burdzy, Jason Swanson, Wai Fan","slou1@luc.edu","820 N MICHIGAN AVE","CHICAGO","IL","606112147","7735082471","MPS","126300","7556","$0.00","This award will support the conference ""Recent Progress in Stochastic Analysis and its Applications?, which will take place at Loyola University Chicago on July 15?19, 2024. This conference will bring together leading experts in probability to highlight exciting recent progress and open problems that have the potential to profoundly impact stochastic analysis and its applications, which include other areas of mathematics, and science and engineering fields. The gathering will seek to foster inclusivity by actively engaging junior participants and researchers from traditionally underrepresented groups.

While central to probability theory, stochastic analysis transcends theoretical boundaries, forging crucial links with various scientific and engineering domains. This conference will highlight four important subareas: Dirichlet form theory and applications, heat kernels and their estimates, stochastic partial differential equations, and interacting particle systems and percolation theory. The conference website is: https://sites.google.com/view/rpsaa2024/home

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348164","Long time dynamics and genealogies of stochastic reaction-diffusion systems","DMS","PROBABILITY","07/01/2024","03/20/2024","Wai Fan","IN","Indiana University","Continuing Grant","Elizabeth Wilmer","06/30/2027","$110,047.00","","louisfan@unc.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","126300","","$0.00","Stochastic models of reaction-diffusion type are crucial for modeling spatial interactions and randomness in dynamical systems across numerous scientific disciplines. Despite their utility, these models are mathematically challenging, due to issues including high dimensionality and nonlinear interactions. This project will address these challenges by focusing on the critical role of space in influencing population dynamics, which is pivotal for questions in ecology, evolutionary biology, and virology. The outcomes of this project may provide insights that improve management of ecosystems and treatments for viral infections. The research will also contribute to the development of novel mathematical methods and promote the participation of a diverse group of student researchers.

Our specific focus is on a class of stochastic partial differential equations (SPDEs) where space is modeled as a general metric graph, allowing for a detailed examination of spatial effects on population dynamics. This approach not only addresses the theoretical challenges but also bridges the gap with microscopic particle models. PI will explore several key phenomena, including traveling wavefronts, the asymptotic speed of stochastic waves, and genealogies in expanding populations. By integrating innovative techniques from various branches of mathematics including probability and spectral graph theory, this project aims to significantly advance the understanding of SPDEs on metric spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2419167","Conference: Conference on New Developments in Probability","DMS","PROBABILITY","06/15/2024","06/06/2024","Tai Melcher","VA","University of Virginia Main Campus","Standard Grant","Elizabeth Wilmer","08/31/2025","$43,766.00","Jing Wang","melcher@virginia.edu","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126300","7556","$0.00","This award provides support for US-based researchers to attend the Conference on New Developments in Probability (CNDP) at the Centre de Recherches Mathématiques (CRM) at Université de Montréal September 26-28, 2024. This meeting is the third CNDP, a conference series jointly organized with Women in Probability. This conference has two main goals. The first is to bring together leading experts, researchers, and scholars to explore the latest advancements in the field of probability theory and to share cutting-edge research. The second goal is to provide a platform for early career researchers in probability theory to present their work in an environment which cultivates collaboration. Probability is the backbone of many mathematical disciplines, providing the language and tools for reasoning about uncertain outcomes and making predictions based on available information, with applications in diverse fields of science, engineering, and economics. Over the years, this area has witnessed remarkable growth, with novel methodologies, techniques, and applications that transform our understanding of uncertainty and randomness. The conference is expected to have a lasting impact on the academic community of researchers in probability theory, and to foster a collaborative environment that encourages the exchange of ideas and knowledge among experts.

The 2024 Conference on New Developments in Probability seeks to highlight recent breakthroughs in the field of probability, in particular, advancements in the areas of stochastic processes and random matrices, interacting particle systems, statistical inference and machine learning, random graphs and networks, high-dimensional probability, and stochastic analysis. This meeting will contribute to advancing the field of probability through diverse perspectives and innovative ideas, fostering the exchange of ideas and opportunities for collaboration. The conference will feature research presentations from speakers representing a range of career stages. This includes short talks by early career participants (postdocs and graduate students) who will receive advising and feedback on delivering research presentations, providing them with invaluable networking opportunities and mentorship experiences. There will be emphasis on both theoretical foundations and practical applications, leading to new research directions and interdisciplinary collaborations. The CNDP also seeks to highlight the contributions of researchers from underrepresented groups in probability, increasing their visibility within the academic community, which will lead to more opportunities for collaborations, grants, and academic positions, ultimately empowering them to progress in their careers. More details can be found at the conference website http://womeninprobability.org/CNDP.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350478","Conference: Finger Lakes Probability Seminar","DMS","PROBABILITY","06/01/2024","05/30/2024","Sevak Mkrtchyan","NY","University of Rochester","Continuing Grant","Elizabeth Wilmer","05/31/2028","$7,838.00","Carl Mueller","sevak.mkrtchyan@rochester.edu","910 GENESEE ST","ROCHESTER","NY","146113847","5852754031","MPS","126300","7556","$0.00","This award will support the annual Finger Lakes Probability Seminar in the years 2025-2028 at four universities in the Finger Lakes region of NY according to the following schedule:
April 18-19, 2025 at University of Rochester
April 17-18, 2026 at Syracuse University
April 16-17, 2027 at Cornell University
April 21-22, 2028 at SUNY Binghamton

The conference will bring together researchers in probability from the Finger Lakes region. It will facilitate communication, exchange of ideas, and introduction to new research directions. Each meeting will have talks given by 3 invited speakers and several sessions of contributed talks. It will give an opportunity for graduate students and young researchers to enlarge their professional network and present their research.
Information about the conferences will be available on the conference website: https://people.math.rochester.edu/faculty/cmlr/Finger-Lakes/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347954","Structured Randomness: Random Matrices and Geometry","DMS","PROBABILITY","06/01/2024","05/29/2024","Ramon Van Handel","NJ","Princeton University","Continuing Grant","Elizabeth Wilmer","05/31/2027","$152,144.00","","rvan@princeton.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","126300","","$0.00","Many complex problems in mathematics exhibit both random features and non-random structures. While different structures are often studied on a case-by-case basis, this project aims to develop general mathematical tools to explain the interplay between randomness and the underlying structure. The focus of the project is on two distinct areas, random matrix theory and metric geometry, where recent advances provide powerful new tools to understand essentially arbitrarily structured models. Such technology makes it possible to study a range of problems that are outside the reach of traditional methods, with applications both in pure mathematics and in areas such as data science and computer science. Graduate and undergraduate student researchers will participate in the project, there will be outreach to schools including middle-school math festivals, and substantial pedagogical materials will be developed and disseminated.

Concretely, the project has two main themes. The first theme aims to develop a broadly applicable toolbox to investigate arbitrarily structured random matrices. The guiding principle behind this toolbox is that the behavior of structured random matrices can be modelled by the behavior of deterministic operators whose spectra are explicitly computable, building on recent advances in this area. The second theme aims to develop probabilistic methods that are motivated by the study of embeddings of metric spaces in normed spaces. Both topics leverage connections between probability theory, operator theory, functional analysis, and metric geometry. While the two themes are independent and involve different mathematical ideas, what they have in common is that they aim to develop general principles and tools to study structured problems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2331449","Conference: Northeast Probability Seminar 2023-2025","DMS","PROBABILITY","02/15/2024","02/15/2024","Jay Rosen","NY","CUNY College of Staten Island","Continuing Grant","Elizabeth Wilmer","01/31/2027","$32,444.00","Victor de la Pena, Elena Kosygina, Yuri Bakhtin, Ivan Corwin","jrosen30@optimum.net","2800 VICTORY BLVD","STATEN ISLAND","NY","103146609","7189822254","MPS","126300","7556","$0.00","The Northeast Probability Seminar is a series that has run for over twenty years. This award will support the continuation of these meetings through 2023, 2024, and 2025. The 2023 meeting is scheduled to take place on November 16-17 at New York University. The 2024 meeting is planned for the City University of New York, and the 2025 meeting is planned for Columbia University. The steering committee includes faculty from all these institutions and several others in and near New York City. These meetings have four plenary lectures, two on Thursday morning and two on Friday morning. Thursday and Friday afternoons are set aside for sessions where 25 junior participants will have the chance to give ten-minute presentations with questions of their recent work.

The Northeast Probability Seminar gives researchers in a dense geographic area an opportunity to exchange fresh ideas and discuss new theories in a highly active area of mathematical research with many interdisciplinary applications. It also provides junior researchers with an opportunity to network with each other and with senior mathematicians. Regional meetings like this one are especially important because they provide an opportunity to establish new collaborations.

The Seminar Web site: https://probability.commons.gc.cuny.edu/22nd-northeast-probability-seminar/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347885","Probabilistic Models with Boundary: Symmetries and Asymptotics","DMS","PROBABILITY","06/01/2024","05/22/2024","Jimmy He","MA","Massachusetts Institute of Technology","Continuing Grant","Elizabeth Wilmer","05/31/2027","$57,049.00","","jimmyhe@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126300","","$0.00","A major goal of modern probability is to understand the macroscopic behavior of large random systems. This project studies a class of random growth models taking place in different geometric settings and will develop new tools effective for these structures; the aim is to understand the behavior of these systems and the impact of the underlying geometry on this behavior. These systems, for example, might be used to model the growth of cancer along a wall or a cylinder.

The extensive algebraic structure underlying integrable or exactly solvable models without boundary has been successfully used to study a variety of probabilistic questions for these models. Many of these models are expected to exhibit universality, meaning that the behavior studied should occur in a wide variety of other models. However, once non-trivial boundary conditions are imposed, our understanding is incomplete. The proposal aims to develop a better understanding of the algebraic structures involved once boundary conditions are imposed and to use this structure to attack probabilistic problems. In particular, the work aims to find new hidden symmetries for these models and to establish asymptotic results via new exact formulas for models with boundary. Undergraduate students will participate in the research, continuing the awardee's record of student mentorship, and the work will be disseminated at seminars and conferences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400605","Conference: PIMS-CRM Summer School 2024 in Probability","DMS","PROBABILITY","07/01/2024","05/16/2024","Christopher Hoffman","WA","University of Washington","Standard Grant","Elizabeth Wilmer","06/30/2025","$49,800.00","Dana Addario-Berry","hoffman@math.washington.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","126300","7556","$0.00","The 2024 CRM-PIMS Summer School in Probability will take place at the Centre de Recherches Mathématiques in Montreal, Canada from July 1 to 26, 2024. This summer school will be aimed at graduate students who are in a Ph.D. program in mathematics. The summer school will also have attendees who have recently obtained their degrees. During this conference the attendees will study current areas of research in probability. They will also study how these topics relate to research in optimization and data science. This award support the participation of American citizens, permanent residents and students at US universities in the summer school.

The summer school will consist two main courses and three week-long mini courses. One of the main courses is ""Random matrix theory of high-dimensional optimization"". This will be taught by Elliot Paquette. The other main course is ""Random walks and branching random walks: old and new perspectives"". This course will be taught by Perla Sousi. Each course will consist of 16 lectures as well as problem sessions.The three mini-courses are: 1. Probabilistic techniques in number theory, taught by Emma Bailey 2. Permutations in random geometry, taught by Jacopo Borga 3. Condensation phenomena in random trees, taught by Igor Kortchemski. These will each consist of three or four lectures. In addition we will have opportunities for the attendees to talk about their research. The website for the school is https://secure.math.ubc.ca/Links/ssprob24/index.php

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337122","Conference: The 2024 Summer School on Random Matrices","DMS","PROBABILITY","05/15/2024","05/13/2024","Jinho Baik","MI","Regents of the University of Michigan - Ann Arbor","Standard Grant","Elizabeth Wilmer","04/30/2025","$49,050.00","Rajesh Nadakuditi, Andrei Prokhorov","baik@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126300","7556","$0.00","Random matrices are arrays of random numbers. Such objects arise from physics, statistics, and electrical engineering when considering quantum systems or large data sets. Random matrix theory is an active area of research in mathematics, science, and engineering due to its wide range of applications. New techniques for random matrix theory are currently undergoing rapid progress. The 2024 Summer School on Random Matrices, which will take place at the University of Michigan from June 17-28, 2024, is intended to provide starting graduate students with the opportunity to learn new techniques different from their own backgrounds. This summer school is the fourth one, following the successful ones in 2016, 2018, and 2022.

Four speakers will deliver lectures on various aspects of random matrix theory, such as high-dimensional optimization problems, potential theory for random matrices, and applications of random matrix theory in data science and statistics. There will be intensive group problem sessions. The website for the summer school is https://sites.google.com/umich.edu/rmtschool/home
?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Statistics/Awards-Statistics-2024.csv b/Statistics/Awards-Statistics-2024.csv index d23a697..0187c58 100644 --- a/Statistics/Awards-Statistics-2024.csv +++ b/Statistics/Awards-Statistics-2024.csv @@ -1,12 +1,24 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" "2413243","A Statistical Foundation of In-Context Learning and Chain-of-Thought Prompting with Large Language Models","DMS","STATISTICS","08/01/2024","07/24/2024","Zhuoran Yang","CT","Yale University","Continuing Grant","Tapabrata Maiti","07/31/2027","$80,882.00","","zhuoran.yang@yale.edu","150 MUNSON ST","NEW HAVEN","CT","065113572","2037854689","MPS","126900","1269","$0.00","Large Language Models (LLMs) like GPT-4 have transformed natural language processing and related fields by demonstrating unprecedented capabilities in interpreting human instructions and completing complex reasoning tasks. Representing a paradigm shift in statistical machine learning, these models are trained on extensive text corpora and can perform novel tasks without modifications to their parameters. This project seeks to develop a comprehensive theoretical framework to understand mainstream methods used with deployed LLMs through a statistical lens. The anticipated broader impacts of this research include enriching educational curricula at participating institutions and providing significant training opportunities for both graduate and undergraduate students. Moreover, the project's outcomes are expected to enhance high-impact applications in sectors such as robotics and transportation systems, thereby improving the practical deployment of LLMs in complex decision-making scenarios.

Specifically, this research explores the statistical foundations of various prompting methods utilized in LLMs, including in-context learning (ICL) and chain-of-thought (CoT) prompting. The study is organized around three main thrusts: first, deciphering how LLMs perform ICL and CoT as forms of implicit Bayesian inference and understanding how transformer architectures' attention mechanisms approximately encode these Bayesian estimators. Second, the project will develop algorithms to analyze the statistical errors?incurred during pre-training and prompting stages ?associated with these prompting-based estimators. The third thrust aims to apply this theoretical framework to real-world applications like robotic control and autonomous driving, formulating principled methods that utilize pre-trained LLMs for complex decision-making. By establishing a robust statistical foundation for prompting-based methodologies, this research aims to advance the field of prompt engineering and contribute to the development of principled methods for using LLMs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413721","New Directions in Bayesian Heterogeneous Data Integration: Methods, Theory and Applications","DMS","STATISTICS","07/01/2024","06/17/2024","Sharmistha Guha","TX","Texas A&M University","Continuing Grant","Tapabrata Maiti","06/30/2027","$49,899.00","","sharmistha@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126900","1269","$0.00","As the scientific community is moving into a data-driven era, there is an unprecedented opportunity for the integrative analysis of network and functional data from multiple sources to uncover important scientific insights which might be missing when these data sources are analyzed in isolation. To this end, this project plans to transform the current landscape of integrating network and functional data, leveraging their combined strength for scientific advancements through the development of innovative hierarchical Bayesian statistical models. The proposed work holds transformative promise in vital scientific domains, such as cognitive and motor aging, and neurodegenerative diseases. It will enhance scientific collaborations with neuroscientists using multi-source image data for targeted investigations of key brain regions significant in the study of motor and cognitive aging. Moreover, the proposed research will facilitate the prediction of images, traditionally acquired via costly imaging modalities, utilizing images from more cost-effective alternatives, which is poised to bring about transformative changes in the healthcare economy. The open-source software and educational materials created will be maintained and accessible to a wider audience of statisticians and domain experts. This accessibility is anticipated to foster widespread adoption of these techniques among statisticians and domain scientists. The PI's involvement in conference presentations, specialized course development, curriculum expansion, graduate student mentoring, undergraduate research engagement with a focus on under-represented backgrounds, and provision of short courses will enhance dissemination efforts and encourage diverse utilization of the developed methods.

The proposed project aims to address the urgent need for principled statistical approaches to seamlessly merge information from diverse sources, including modern network and functional data. It challenges the prevailing trend of analyzing individual data sources, which inherently limits the potential for uncovering innovative scientific insights that could arise from integrating multiple sources. Hierarchical Bayesian models are an effective way to capture the complex structures in network and functional data. These models naturally share information among heterogeneous objects, providing comprehensive uncertainty in inference through science-driven joint posterior distributions. Despite the potential advantages of Bayesian perspectives, their widespread adoption is hindered by the lack of theoretical guarantees, computational challenges, and difficulties in specifying robust priors for high-dimensional problems. This proposal will address these limitations by integrating network and functional data, leveraging their combined strength for scientific advancements through the development of innovative hierarchical Bayesian models. Specifically, the project will develop a semi-parametric joint regression framework with network and functional responses, deep network regression with multiple network responses, and Bayesian interpretable deep neural network regression with functional response on network and functional predictors. Besides offering a novel toolbox for multi-source object data integration, the proposed approach will advance the emerging field of interpretable deep learning for object regression by formulating novel and interpretable deep neural networks that combine predictive power with statistical model interpretability. The project will develop Bayesian asymptotic results to guarantee accurate parametric and predictive inference from these models as a function of network and functional features and sample size, an unexplored domain in the Bayesian integration of multi-object data. The proposed methodology will significantly enhance the seamless integration of multimodal neuroimaging data, leading to principled inferences and deeper comprehension of brain structure and function in the study of Alzheimer's disease and aging.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2412746","New nonparametric theory and methods for censored data","DMS","STATISTICS","10/01/2024","04/23/2024","Bin Nan","CA","University of California-Irvine","Standard Grant","Jun Zhu","09/30/2027","$300,000.00","","nanb@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126900","079Z","$0.00","Estimating the survival time distribution given a set of predictors is of great importance in biomedical research and epidemiological studies, where the survival time is often censored, thus unobserved, due to dropouts or limited follow-up time. To obtain robust results, making weak model assumptions is desirable. This project focuses on two sets of tools without making assumptions about the functional form of any effect of a predictor on the survival time: one is a classical approach based on spline basis expansion, and the other is a modern approach based on deep neural networks. For the spline method, the project aims to develop a generally applicable distributional theory for the estimates of unknown functions in several widely used survival models, which is needed for making proper statistical inference but still lacking in the current literature. Furthermore, the deep neural network approach makes the weakest possible assumption and is the most flexible estimating method for an unknown multivariate function. The project considers deep neural networks with a full likelihood-based loss function for censored survival data and more general types of predictors that can randomly vary with time. The project aims to investigate both the numerical implementation and the theory for the estimation precision. This work will foster interdisciplinary research with epidemiologists, nephrologists, neurologists, and other scientists working on real scientific studies, and contribute to the well-being of human beings and the scientific community in a significant way through its versatile real-life applications, thus create an impact in and beyond statistical periphery.

Spline basis expansion is a commonly used approach for approximating an unknown smooth function, hence widely applied in estimating functional parameters. It is too often, however, that the approximation is treated as ?exact? in practice so to treat a nonparametric estimation problem as a parametric one because the asymptotic distributional theory for the spline estimation is lacking for models beyond the nonparametric linear model. The project takes advantages of recent developments in the random matrix theory to tackle the distributional theoretical problem of spline estimates in a broad range of commonly used statistical models in censored data analysis. The most general nonparametric problem is to estimate the conditional distribution other than, for example, the conditional mean or median. With the conditional distribution at hand, prediction becomes a choice of a particular characteristic of the conditional distribution and a prediction interval can be easily obtained. The project focuses on full likelihood-based loss functions characterized by the conditional hazard function and applies either deep neural networks or deep operator networks for the estimation of the conditional distribution function given functional covariates. In survival analysis, the functional covariates can be time-varying covariates that affect the hazard function in an arbitrarily way, for which no estimating method exists in the literature. Convergence rates of considered neural network methods with functional inputs will be established.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413671","Travel: Junior travel support for the 2024 World Meeting of the International Society for Bayesian Analysis","DMS","STATISTICS","05/01/2024","04/19/2024","Sinead Williamson","TX","University of Texas at Austin","Standard Grant","Tapabrata Maiti","10/31/2024","$20,000.00","","sinead.williamson@mccombs.utexas.edu","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","126900","","$0.00","This grant will fund 25 travel awards for US-based junior researchers attending the 2024 ISBA (International Society for Bayesian Analysis) World Meeting, to be held in Venice, Italy from 1-7 July 2024. The meeting's website is https://www.unive.it/web/en/2208/home. The ISBA World Meetings are the largest conferences in Bayesian statistics, attracting attendees from all around the world. The travel awards, averaging $800 per person, will partially offset the cost of travelling to Venice from the US, helping PhD students and other junior researchers to participate in the meeting. The selection committee will prioritize funding female researchers and members of minority groups underrepresented in the field.

The 2024 ISBA World Meeting will feature keynote talks, invited and contributed talks, poster sessions, and short courses, selected to showcase cutting-edge research in Bayesian statistics. Attendance at the meeting will offer attendees a chance to learn about emerging research topics in Bayesian statistics. In addition, the scientific committee has selected as part of the program multiple talks and posters by junior researchers. This offers junior researchers an opportunity to share their research with an international audience of Bayesian statisticians.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413954","The Design and Analysis of Experiments under the K-Nearest-Neighbors Interference Model","DMS","OFFICE OF MULTIDISCIPLINARY AC, STATISTICS","08/01/2024","07/26/2024","Michael Higgins","KS","Kansas State University","Standard Grant","Yong Zeng","07/31/2027","$200,000.00","Perla Reyes","mikehiggins83@gmail.com","1601 VATTIER STREET","MANHATTAN","KS","665062504","7855326804","MPS","125300, 126900","075Z, 079Z, 9150","$0.00","Traditional methods for estimating causal effects from experimental data often assume that an intervention only affects the unit receiving the intervention and does not impact the behavior of any other unit in the experiment. However, experimental settings where this condition fails to hold are increasingly common. For example, in an experiment on a social media network, an individual receiving an intervention may engage with other users on the network, thereby impacting the other users' responses. When this occurs, we say that the experiment exhibits treatment interference. This project investigates a new model of treatment interference- the K-nearest neighbors interference model (KNNIM)-in which a unit's response may be affected by the intervention given to its 'K' closest connections. Notably, this model allows for interventions given to closer connections of a unit to have a greater impact on that unit's response. This project also provides research training opportunities for graduate students.

The project will derive estimators for useful causal estimands, in particular, nearest neighbor treatment effects, which quantify the amount of influence that neighboring units have on a unit's response under KNNIM and relaxations of this model. Tests for determining whether these relaxed models are plausible will also be developed. Furthermore, the project will derive effective experimental designs for improved estimation of and inference of treatment effects under KNNIM. Finally, borrowing approaches for detecting communities in networks, this project will develop methods for simultaneously determining the correct KNNIM interference structure-i.e., the correct value of 'K'- and estimating treatment effects under repeated experimentation on the same set of units.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413885","Data-adaptive multivariate inference with finite sample guarantees","DMS","STATISTICS","08/01/2024","07/25/2024","Guenther Walther","CA","Stanford University","Standard Grant","Yong Zeng","07/31/2027","$300,000.00","","Walther@stat.stanford.edu","450 JANE STANFORD WAY","STANFORD","CA","943052004","6507232300","MPS","126900","079Z","$0.00","Working with complex data requires a good data structure in order to efficiently organize these data in a computer. The research project will show that a certain popular data structure also has surprising and advantageous statistical properties. It will be shown how these properties can be used to give performance guarantees for a number of statistical procedures and that these guarantees lead to optimal statistical inference. In particular, the project will show how these properties can be used to overcome a problem that affects many multivariate statistical analyses and which is known as the `curse of dimensionality' or `empty space phenomenon'. The research project will also involve mentoring undergraduate students in the context of summer research projects and provide research training opportunities for graduate students.

k-d trees are space-partitioning binary trees that are popular in computer science because of their computational efficiency. This project will show that k-d trees also have advantageous stochastic properties that can be used to effectively address a number of challenging statistical problems. In particular, the research will show how the data-adaptive multiresolution partitions generated by a k-d tree can be used to avoid the `curse of dimensionality' or `empty space phenomenon' that afflicts many multivariate statistical procedures. It will also show that the resulting inference comes with finite sample guarantees and that it satisfies certain optimality properties. The to-be-developed methodology will be used to address a number of important problems, such as inference about a multivariate log-concave distribution. Finding the maximum likelihood estimator for such a distribution is computationally very expensive, even for low-dimensional observations. The research will show how the data-adaptive partition can be used to compute a confidence band for a log-concave density in a fast way, and it will establish statistical optimality properties for these bands.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413516","Measuring extremal dependence of functional data","DMS","STATISTICS","08/01/2024","07/25/2024","Mihyun Kim","WV","West Virginia University Research Corporation","Standard Grant","Yulia Gel","07/31/2027","$115,000.00","","mihyun.kim@mail.wvu.edu","886 CHESTNUT RIDGE ROAD","MORGANTOWN","WV","265052742","3042933998","MPS","126900","9150","$0.00","With the increasing availability of high-resolution data, curve-type data have emerged in various fields. Examples include daily precipitation curves, daily pollution level patterns, and intraday stock return curves. As highly fluctuating patterns in these curves become increasingly common due to the growing impact of extreme events, such as unusual weather or financial downturns, it is crucial to effectively analyze and predict these extreme patterns for risk management across all domains. Currently, there is a notable lack of appropriate statistical tools for analyzing extremal behavior in such data, primarily due to its complexity. To address this critical gap, this project aims to develop innovative methodologies for accurate modeling and quantifying extremal patterns in curve-type data. The outcomes of the project have a potential to enhance preparedness for natural disasters and to advances risk assessment in the financial sector. For instance, the tools developed can forecast the likelihood of simultaneous extreme precipitation patterns in different locations, thereby aiding in developing more efficient risk mitigation strategies for natural disasters like flash floods. This capability is crucial in regions with diverse topographies, such as West Virginia, where mountainous terrain with numerous creeks and rivers is susceptible to flash floods during intense rainfall, as seen in the rare 2016 event that caused significant damage and loss of life. The risk assessment tools are adaptable beyond West Virginia, benefiting other states facing similar challenges in managing extreme weather events. Additionally, these tools can help financial institutions manage risk exposure by determining the likelihood of concurrent extreme losses in intraday return patterns across different sectors. Given that millions of Americans have savings in retirement plans, accurately quantifying the risk of catastrophic financial losses is essential. By providing precise measurements of risks associated with extreme market conditions, this project supports national efforts to safeguard economic security. Furthermore, it will contribute to workforce development by training undergraduate and graduate students in statistics and mathematics research.

This project introduces a new framework for analyzing and modeling extremal behavior in functional data. The research agenda aims to develop statistical tools for quantifying extremal dependence in paired functional samples and to create statistical hypothesis tests for the independence of heavy-tailed functional time series. Specifically, this project will develop a novel tool?the extremal correlation coefficient?to measure how likely extreme curves exhibit similar patterns simultaneously. For instance, it can answer questions such as: how likely is it for location A to experience heavy precipitation patterns similar to those observed in location B on the same day? Or, during a stock market crisis, do returns of different sectors exhibit similar extreme daily trajectories? Additionally, based on the extremal correlation coefficient, the project will propose a new autocorrelation function and a portmanteau white noise test tailored for heavy-tailed functional time series. Currently, no method exists to detect serial dependence structures in such functional time series. These tools will evaluate the serial correlation of heavy-tailed functional time series and validate the independence of the model residuals. By leveraging the mathematical theory of regularly varying measures for functional objects, the project aims to ensure the asymptotic properties of the proposed estimator for the extremal correlation coefficient and establish theoretical results for the portmanteau white noise test.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412573","Statistical and Computational Guarantees of Estimation of Generative Models and Optimal Transport","DMS","OFFICE OF MULTIDISCIPLINARY AC, STATISTICS","08/01/2024","07/24/2024","Huibin Zhou","CT","Yale University","Standard Grant","Yulia Gel","07/31/2027","$225,000.00","","huibin.zhou@yale.edu","150 MUNSON ST","NEW HAVEN","CT","065113572","2037854689","MPS","125300, 126900","075Z, 1269, 6856","$0.00","Generative machine learning models are currently revolutionizing the artificial intelligence (AI) community with their significant capabilities in creating innovative images and text. At its heart, generative AI fundamentally addresses a high dimensional density estimation problem. Alternatively, it can be perceived as a transport problem, transforming a simple and known distribution/noise into a complex and unknown distribution. Despite the development of numerous successful algorithms, the literature lacks statistical guarantees to theoretically underpin these algorithms, and concerns about the environmental impact due to extensive computations continue to persist. Among these models, score-based diffusion models are currently replacing the generative adversarial neural nets and at the forefront in terms of popularity and efficacy. However, the score training process can be exceedingly slow and energy intensive. To address this, the investigator will study the more computationally and energetically efficient rectified flow algorithm and its variants which turn the high-dimensional density estimation to an iterative regression problem, and this iterative regression leads to an optimal transport. The research will advance the understanding of the success of models in generative AI. The intrinsic connections to be explored among those models will help convert statistical guarantees from one generative model to another, and lead to novel and improved algorithms, which would eventually advance the state of art of generative AI.

The investigator aims to study the statistical and computational assurances of rectified flow and diffusion models and explore two connections among those models: score matching and solving ordinary/stochastic differential equation, with an intriguing linkage to nonparametric empirical Bayes. The following questions will be addressed: 1) can we show that the iterative rectified flow obtains density and transport estimation optimally in just one step of regression? 2) how fast does the iterative regression of rectified flow converge to the optimal transport? 3) can we propose an improved algorithm over the rectified flow for a better statistical and computational guarantee? 4) what are the statistical and computational guarantees of diffusion models? 5) can we improve the denoising diffusion probabilistic models by an iterative algorithm to obtain the optimal transport? In addition, the project will explore applications of generative models and optimal transport to neuroscience and autism spectrum disorder. Research results from this proposal will be disseminated through articles, workshops, and interdisciplinary seminar series. It will integrate research and education by teaching monograph courses and organizing workshops and seminars to enhance the career development of the next generations of statisticians and data scientists, including a particular focus on the underrepresented groups in mathematical sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413953","Collaborative Research: Statistical Inference for High Dimensional and High Frequency Data: Contiguity, Matrix Decompositions, Uncertainty Quantification","DMS","STATISTICS","07/01/2024","06/21/2024","Lan Zhang","IL","University of Illinois at Chicago","Standard Grant","Jun Zhu","06/30/2027","$155,372.00","","lanzhang@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126900","","$0.00","To pursue the promise of the big data revolution, the current project is concerned with a particular form of such data, high dimensional high frequency data (HD2), where series of high-dimensional observations can see new data updates in fractions of milliseconds. With technological advances in data collection, HD2 data occurs in medicine (from neuroscience to patient care), finance and economics, geosciences (such as earthquake data), marine science (fishing and shipping), and, of course, in internet data. This research project focuses on how to extract information from HD2 data, and how to turn this data into knowledge. As part of the process, the project develops cutting-edge mathematics and statistical methodology to uncover the dependence structure governing HD2 data. It interfaces with concepts of artificial intelligence. In addition to developing a general theory, the project is concerned with applications to financial data, including risk management, forecasting, and portfolio management. More precise estimators, with improved margins of error, will be useful in all these areas of finance. The results are of interest to main-street investors, regulators and policymakers, and the results are entirely in the public domain. The project will also provide research training opportunities for students.

In more detail, the project will focus on four linked questions for HD2 data: contiguity, matrix decompositions, uncertainty quantification, and the estimation of spot quantities. The investigators will extend their contiguity theory to the common case where observations have noise, which also permits the use of longer local intervals. Under a contiguous probability, the structure of the observations is often more accessible (frequently Gaussian) in local neighborhoods, facilitating statistical analysis. This is achieved without altering the underlying models. Because the effect of the probability change is quite transparent, this approach also enables more direct uncertainty quantification. To model HD2 data, the investigators will explore time-varying matrix decompositions, including the development of a singular value decomposition (SVD) for high frequency data, as a more direct path to a factor model. Both SVD and principal component analysis (PCA) benefit from contiguity, which eases both the time-varying construction, and uncertainty quantification. The latter is of particular importance not only to set standard errors, but also to determine the trade-offs involved in estimation under longitudinal variation: for example, how many minutes or days are required to estimate a covariance matrix, or singular vectors? The investigators also plan to develop volatility matrices for the drift part of a financial process, and their PCAs. The work on matrix decompositions will also benefit from projected results on spot estimation, which also ties in with contiguity. It is expected that the consequences of the contiguity and the HD2 inference will be transformational, leading to more efficient estimators and better prediction, and that this approach will form a new paradigm for high frequency data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413715","Wasserstein guided nonparametric Bayes","DMS","STATISTICS","07/01/2024","05/30/2024","Debdeep Pati","TX","Texas A&M University","Standard Grant","Tapabrata Maiti","06/30/2027","$299,669.00","Anirban Bhattacharya","debdeep@stat.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126900","1269","$0.00","Stochastic generative models are a cornerstone of applied statistical modeling and inference. A generative model is an abstraction, and often a simplification, of a data generating mechanism using probabilistic tools, where specific features of interest regarding the generating mechanism are encapsulated into parameters of the generative model. Bayesian statistical inference is a popular statistical paradigm for combining such generative models for data with prior information about model parameters in a principled fashion to perform statistical inference on the unknown parameters. Some of the salient aspects behind the tremendous growth in popularity of Bayesian inference include principled incorporation of domain information, an in-built penalty for model complexity allowing automatic model selection, and facilitating borrowing of information across different domains via hierarchical modeling. However, being inherently model-based, Bayesian statistics is intrinsically susceptible to departures from the postulated generative model. Through this project, the investigators will explore and develop new statistical methodology for performing Bayesian inference allowing flexible departures from the generative model under consideration. A major focus will be the user-friendliness of the proposed approaches, circumventing the need for a user to explicitly build probabilistic models of increasing richness. The research will be disseminated through articles at prominent avenues and research presentations. Additionally, software packages for the methods developed will be made available publicly. The investigators are committed to enhancing the pedagogical component of the proposal through advising students and developing graduate and undergraduate topic courses.

Flexible nonparametric Bayesian methods have gained in popularity to address perceived issues of traditional Bayesian modeling regarding model-misspecification. The last thirty years have seen a proliferation of such methods, both in mainstream statistics as well as the machine learning community, as we continue to encounter increasing levels of complexities in modern datasets. However, nonparametric Bayesian methods can be challenging to implement as well as interpret. Furthermore, in many applications, the targets of interest are quite simple and it is essentially futile to model all aspects of the data. The fundamental aim of the proposed research is to develop a flexible Bayesian non-parametric approach that retains the generative modeling aspect of traditional parametric Bayesian modeling while avoiding a complete probabilistic specification of the data generating mechanism as typically performed in nonparametric Bayesian modeling. This will be performed by defining a modified likelihood function, leveraging ideas from the empirical likelihood literature as well as optimal transport theory, that centers around a user-specified parametric family of densities. An automated calibration procedure will be developed to control the extent of centering around the parametric model. The investigators will offer a firm theoretical underpinning of the proposed procedure and develop computationally efficient algorithms to carry out inferential tasks. The developed methods will be applied to scientific learning problems in neuroscience and nuclear physics to allow departures from existing scientific models in situations where their operating characteristics are less understood.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2409876","Conference: The 9th Workshop on Biostatistics and Bioinformatics","DMS","STATISTICS","05/01/2024","04/10/2024","Yichuan Zhao","GA","Georgia State University Research Foundation, Inc.","Standard Grant","Tapabrata Maiti","04/30/2025","$10,000.00","","yichuan@gsu.edu","58 EDGEWOOD AVE NE","ATLANTA","GA","303032921","4044133570","MPS","126900","7556","$0.00","The 9th Workshop on Biostatistics and Bioinformatics will be held at Georgia State University, May 03-05, 2024. It will provide a platform for senior researchers, junior researchers, and graduate students to discuss the latest advances and challenges in the field. The main objective of the workshop is to address emerging challenges in applications of AI, causal inference, and statistical genomics data analysis. The workshop will feature a keynote speaker, leading experts and young researchers, and it provides an invaluable opportunity for graduate students and young researchers to gain experience giving poster presentations. To present posters will help them to receive feedback from experts in the field, and engage in discussions with fellow attendees. The workshop will provide a distinctive opportunity for collaboration, discussion, and dissemination of ideas. In addition, the workshop places special emphasis on supporting young people, underrepresented individuals, and women through financial supports, aiming to cultivate an inclusive environment. Through the integration of interactive sessions, networking opportunities, and a commitment to the diversity, the workshop can enhance its overall impact.


The workshop aims to push the boundaries of biostatistics and bioinformatics through collaborative efforts among various universities. The workshop maintains a very strong program, which includes one keynote speech by a renowned statistician, invited talks by established and emerging experts, poster presentations from junior researchers and graduate students. The workshop will also offer a short course ""Tutorial on Deep Learning and Generative AI"" and five Best Student Poster Awards will be announced during the award ceremony. Special effort is dedicated to forging connections with historically black universities in the Metro Atlanta area, by inviting underrepresented individuals to participate in the workshop. We expect that the workshop will attract a significant number of participants from underrepresented groups. Travel support is available for junior researchers, graduate students, and underrepresented people by promoting the inclusivity and diversity within the workshop. More information about the workshop can be found at the website: https://math.gsu.edu/yichuan/2024Workshop/index.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413043","Collaborative Research: Accounting for geolocation error in point pattern analysis","DMS","STATISTICS","08/01/2024","07/24/2024","Scott Cook","TX","Texas A&M University","Standard Grant","Jun Zhu","07/31/2027","$50,000.00","","sjcook@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126900","","$0.00","Researchers in the social sciences increasingly utilize event data sets when studying crime, protests, and terrorism. These data sets provide information on each incident, including where it occurred, who was involved, what the consequences were, etc. Unfortunately, the recorded location of incidents in these data sets are often inaccurate, due to limitations in the available information from which they are drawn (ex. incomplete media reports). Left unaddressed, these geolocation errors impair one?s ability to effectively learn about the underlying process of interest from these data. For example, geolocation errors may cause researchers to infer spatial patterns from these data that would not be found with the correct locations. In this research, investigators will develop statistical methods to better account for geolocation errors in these kinds of data. The statistical methods developed will then be applied to data on political violence, demonstrating their importance for improved understanding of real-world problems. The multidisciplinary project will also provide training for the next generation of researchers at the intersection of statistics and the social sciences. This collaborative project includes support and mentorship for graduate students.

Spatial point processes are a natural approach for modeling event data. However, geolocation errors produce two distinct, but related, problems for these methods: i) duplicate event locations, and ii) inaccurate spatial coordinate information. In this project, investigators will address both issues, developing a computationally efficient statistical inference method to account for geolocation error in spatial point pattern data within the Log-Gaussian Cox Process framework. Various geolocation error structures will be considered, including nonstationary errors, to better reflect complex real-world applications. The project will include research on both the finite-sample performance and asymptotic behavior of the estimators from the developed inference methods. These methods will be used to analyze real-world political violence data from various sources.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413042","Collaborative Research: Accounting for geolocation error in point pattern analysis","DMS","STATISTICS","08/01/2024","07/24/2024","Mikyoung Jun","TX","University of Houston","Standard Grant","Jun Zhu","07/31/2027","$149,947.00","","mjun@central.uh.edu","4300 MARTIN LUTHER KING BLVD","HOUSTON","TX","772043067","7137435773","MPS","126900","","$0.00","Researchers in the social sciences increasingly utilize event data sets when studying crime, protests, and terrorism. These data sets provide information on each incident, including where it occurred, who was involved, what the consequences were, etc. Unfortunately, the recorded location of incidents in these data sets are often inaccurate, due to limitations in the available information from which they are drawn (ex. incomplete media reports). Left unaddressed, these geolocation errors impair one?s ability to effectively learn about the underlying process of interest from these data. For example, geolocation errors may cause researchers to infer spatial patterns from these data that would not be found with the correct locations. In this research, investigators will develop statistical methods to better account for geolocation errors in these kinds of data. The statistical methods developed will then be applied to data on political violence, demonstrating their importance for improved understanding of real-world problems. The multidisciplinary project will also provide training for the next generation of researchers at the intersection of statistics and the social sciences. This collaborative project includes support and mentorship for graduate students.

Spatial point processes are a natural approach for modeling event data. However, geolocation errors produce two distinct, but related, problems for these methods: i) duplicate event locations, and ii) inaccurate spatial coordinate information. In this project, investigators will address both issues, developing a computationally efficient statistical inference method to account for geolocation error in spatial point pattern data within the Log-Gaussian Cox Process framework. Various geolocation error structures will be considered, including nonstationary errors, to better reflect complex real-world applications. The project will include research on both the finite-sample performance and asymptotic behavior of the estimators from the developed inference methods. These methods will be used to analyze real-world political violence data from various sources.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413404","Collaborative Research: Statistical Optimal Transport: Foundation, Computation and Applications","DMS","STATISTICS","07/01/2024","06/18/2024","Xiaohui Chen","CA","University of Southern California","Standard Grant","Yong Zeng","06/30/2027","$180,000.00","","xiaohuic@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","90033","2137407762","MPS","126900","079Z","$0.00","Comparing probability models is a fundamental task in almost every data-enabled problem, and Optimal Transport (OT) offers a powerful and versatile framework to do so. Recent years have witnessed a rapid development of computational OT, which has expanded applications of OT to statistics, including clustering, generative modeling, domain adaptation, distribution-to-distribution regression, dimension reduction, and sampling. Still, understanding the fundamental strengths and limitations of OT as a statistical tool is much to be desired. This research project aims to fill this important gap by advancing statistical analysis (estimation and inference) and practical approximation of two fundamental notions (average and quantiles) in statistics and machine learning, demonstrated through modern applications for measure-valued data. The project also provides research training opportunities for graduate students.

The award contains three main research projects. The first project will develop a new regularized formulation of the Wasserstein barycenter based on the multi-marginal OT and conduct an in-depth statistical analysis, encompassing sample complexity, limiting distributions, and bootstrap consistency. The second project will establish asymptotic distribution and bootstrap consistency results for linear functionals of OT maps and will study sharp asymptotics for entropically regularized OT maps when regularization parameters tend to zero. Building on the first two projects, the third project explores applications of the OT methodology to two important statistical tasks: dimension reduction and vector quantile regression. The research agenda will develop a novel and computationally efficient principal component method for measure-valued data and a statistically valid duality-based estimator for quantile regression with multivariate responses. The three projects will produce novel technical tools integrated from OT theory, empirical process theory, and partial differential equations, which are essential for OT-based inferential methods and will inspire new applications of OT to measure-valued and multivariate data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413553","Collaborative Research: Statistical Network Integration","DMS","STATISTICS","07/01/2024","06/17/2024","Jesús Arroyo","TX","Texas A&M University","Continuing Grant","Yulia Gel","06/30/2027","$37,118.00","","jarroyo@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126900","1269","$0.00","This project pursues the contemporary problem of statistical network integration facing scientists, practitioners, and theoreticians. The study of networks and graph-structured data has received growing attention in recent years, motivated by investigations of complex systems throughout the biological and social sciences. Models and methods have been developed to analyze network data objects, often focused on single networks or homogeneous data settings, yet modern available data are increasingly heterogeneous, multi-sample, and multi-modal. Consequently, there is a growing need to leverage data arising from different sources that result in multiple network observations with attributes. This project will develop statistically principled data integration methodologies for neuroimaging studies, which routinely collect multiple subject data across different groups (strains, conditions, edge groups), modalities (functional and diffusion MRI), and brain covariate information (phenotypes, healthy status, gene expression data from brain tissue). The investigators will offer interdisciplinary mentoring opportunities to students participating in the research project and co-teach a workshop based on the proposed research.

The goals of this project are to establish flexible, parsimonious latent space models for network integration and to develop efficient, theoretically justified inference procedures for such models. More specifically, this project will develop latent space models to disentangle common and individual local and global latent features in samples of networks, propose efficient spectral matrix-based methods for data integration, provide high-dimensional structured penalties for dimensionality reduction and regularization in network data, and develop cross-validation methods for multiple network data integration. New theoretical developments spanning concentration inequalities, eigenvector perturbation analysis, and distributional asymptotic results will elucidate the advantages and limitations of these methods in terms of signal aggregation, heterogeneity, and flexibility. Applications of these methodologies to the analysis of multi-subject brain network data will be studied. Emphasis will be on interpretability, computation, and theoretical justification.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413549","Bayesian Joint Model for High Dimensional Health Data","DMS","STATISTICS","08/01/2024","07/24/2024","Sanjib Basu","IL","University of Illinois at Chicago","Continuing Grant","Jun Zhu","07/31/2027","$131,615.00","Jiehuan Sun","sbasu@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126900","","$0.00","The associations between longitudinal processes and time-to-event outcome are of interest in many scientific studies. Scientific and technological advances now routinely provide high-dimensional data measured from a large number of longitudinal processes. Clinical studies involving targeted group of patients now often track rich collection of health-related information that are collected at each patient visit, and more importantly, curated in the Electronic Health Record (EHR) systems. Such health data may include clinical information, and a large set of biomarkers from omics, blood draws or similar approaches. For example, advanced stage non-small cell lung cancer patients usually undergo blood draws and CT scans at each visit from which varying set of features and markers are measured. The goal of this research is to develop improved models for utilizing information from these longitudinal measurements to associate with and predict the outcome of interest, which, in many such studies is a time-to-event, such as progression or survival. The overall objective of this project is to develop novel Bayesian high-dimensional joint models for analysis of such complex data. This project will also aim to develop efficient Bayesian computation approaches for these complex models and make them available in publicly available software with detailed documentation. The project will also provide research training opportunities for students.

This research project will develop statistical joint model methodologies that include high-dimensional longitudinal processes, time-to-event outcome(s) and association models connecting the two. Advances in technology have made data on high-dimensional longitudinal processes increasingly available, but most existing joint models only consider one or a few longitudinal processes and cannot efficiently handle a large number of longitudinal processes. The project will develop efficient Bayesian nonparametric joint models for analyzing such complex high-dimensional data. These models will allow capturing the inherent complexities of the longitudinal processes by flexibly modeling their nonlinear trajectories. This project will explore different approaches to model the complex associations among the longitudinal processes and the time-to-event of interest.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413265","Theory for the Practice of Deep Learning: Insights into Autoencoder, LLM Fine-Tuning, and Transfer Learning","DMS","OFFICE OF MULTIDISCIPLINARY AC, STATISTICS","08/01/2024","07/24/2024","Bin Yu","CA","University of California-Berkeley","Standard Grant","Tapabrata Maiti","07/31/2027","$299,756.00","","binyu@stat.berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","125300, 126900","075Z, 1269","$0.00","AI entered a new and accelerated phase with the public rollout in Nov. 2022, of the generative AI large language model (LLM) ChatGPT, which is a transformer deep learning (DL) model with 1.5 billion parameters trained on 570GB of data. The potential impact of ChatGPT and other chatbots in scientific research, teaching, medicine, government, business, and society at large is enormous. Currently, the dominant empirical paradigm for solving tasks using deep learning is to first pretrain massive models in an unsupervised manner on large data corpora and then fine-tune them on specific tasks of interest. For example, the standard practice for pretraining modern LLMs like ChatGPT is to train models to predict the next token on datasets scraped from the internet, which allows the model to learn meaningful and general representations about language. Although models learn extensively about language during the pre-training phase, they are typically not immediately useful for tasks of interest, and transfer learning must be applied by fine-tuning on a specific downstream task, such as coding, math, chat-botting, etc. There are many important questions about this fine-tuning process, such as how the hyperparameters should be set and when different algorithms can be expected to generalize well. In this project, a theoretical study will be taken to address different aspects of finetuning and transfer learning with the aim of producing practically relevant guidance for improving efficiency and generalization performance for these settings. This project includes financial support and mentorship for graduate students.

Concretely, the proposed research will focus on the following two directions: developing methods that help choose the learning rate and rank in a near-optimal manner for a popular finetuning method known as Low Rank Adapters (LoRA). Insights from the large width scaling theory of neural networks will be used to guide how to select hyperparameters appropriately. Successful methods have the potential to greatly reduce the computing cost of hyperparameter tuning when finetuning large models. The second thrust involves studying transfer learning in the context of over-parametrized linear regression. The setting in over-parametrized linear regression is rich enough to provide conceptual insights into modern deep learning yet simplified enough for a rigorous mathematical study of generalization performance. Building upon previous works analyzing in-distribution generalization performance in over-parametrized linear regression and using similar random matrix theoretic tools, extensions will be made to the out-of-distribution transfer learning setting. By rigorously characterizing how transfer learning affects generalization, intuition will be provided for practitioners seeking to predict how various shifts will affect the performance of their models.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2335569","Collaborative Research: Planning: FIRE-PLAN:High-Spatiotemporal-Resolution Sensing and Digital Twin to Advance Wildland Fire Science","DMS","S&CC: Smart & Connected Commun, STATISTICS, HDBE-Humans, Disasters, and th, Cross-BIO Activities, EPCN-Energy-Power-Ctrl-Netwrks","01/01/2024","08/09/2023","Xiaolin Hu","GA","Georgia State University Research Foundation, Inc.","Standard Grant","Yulia Gel","12/31/2025","$52,000.00","","xhu@cs.gsu.edu","58 EDGEWOOD AVE NE","ATLANTA","GA","303032921","4044133570","MPS","033Y00, 126900, 163800, 727500, 760700","019E, 042E, 042Z, 132Z, 5294, 7275, 9150","$0.00","The number of catastrophic wildfires in the United States has been steadily increasing in recent decades, which generate casualties, large loss of properties, and dramatic environmental changes. However, it is difficult to make accurate predictions of wildland fire spread in real time for firefighters and emergency response teams. Although many fire spread models have been developed, one of the biggest challenges in their operational use is the lack of ground truth fire data at high spatiotemporal resolutions, which are indispensable for model evaluation and improvements. The objective of this planning project is to bring together wildland fire science researchers, fire sensing and data science experts, and diverse stakeholders to develop standards and requirements for high-spatiotemporal-resolution wildland fire sensing and digital twin construction. An organizing committee will be formed from wildland fire science, engineering, and stake holder communities including fire ecology and behavior modeling, pollution monitoring, robotics, cyber physical systems (CPS), wildfire fighting, indigenous cultural burns, and prescribed fires. A series of physical and remote workshops will be held focusing on themes such as open fire data for wildland fire modeling validation, digital twins for prescribed fires, and safe and efficient wildland fire data collection.

Research tasks of this planning project include: 1) identification of key high-spatiotemporal-resolution fire metrics and data representations to support fire model validation and fire operations, 2) proposition of sensing strategies and algorithms for fire sensing and suppression robots and cyber physical systems that can support safe and efficient collection of desired high-resolution fire data, 3) development and evaluation of data assimilation and digital twin construction using high-resolution data to advance fire behavior modeling, coupled fire-atmosphere modeling, and smoke modeling, and 4) prototype and initial fire data ecosystem demonstration including collection of cultural burn data and establishment of GeoFireData, a benchmark fire data sharing and digital twin website, which can support different fire operation types such as fire spread model validation and controlled burn planning. The special attention will be devoted to interdisciplinary training of the next generation of scientists working with wildfire risks at the interface of computational sciences, engineering, ecology, and data sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2339241","CAREER: Learning stochastic spatiotemporal dynamics in single-molecule genetics","DMS","Cellular Dynamics and Function, STATISTICS, MATHEMATICAL BIOLOGY","07/01/2024","01/29/2024","Christopher Miles","CA","University of California-Irvine","Continuing Grant","Amina Eladdadi","06/30/2029","$239,517.00","","cemiles@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","111400, 126900, 733400","068Z, 079Z, 1045, 7465, 8038","$0.00","The ability to measure which genes are expressed in cells has revolutionized our understanding of biological systems. Discoveries range from pinpointing what makes different cell types unique (e.g., a skin vs. brain cell) to how diseases emerge from genetic mutations. This gene expression data is now a ubiquitously used tool in every cell biologist?s toolbox. However, the mathematical theories for reliably extracting insight from this data have lagged behind the amazing progress of the techniques for harvesting it. This CAREER project will develop key theoretical foundations for analyzing imaging data of gene expression. The advances span theory to practice, including developing mathematical models and machine-learning approaches that will be used with data from experimental collaborators. Altogether, the project aims to create a new gold standard of techniques in studying spatial imaging data of gene expression and enable revelation of new biological and biomedical insights. In addition, this proposed research will incorporate interdisciplinary graduate students and local community college undergraduates to train the next generation of scientists in the ever-evolving intersection of data science, biology, and mathematics. Alongside research activities, the project will create mentorship networks for supporting first-generation student scientists in pursuit of diversifying the STEM workforce.

The supported research is a comprehensive program for studying single-molecule gene expression spatial patterns through the lens of stochastic reaction-diffusion models. The key aim is to generalize mathematical connections between these models and their observation as spatial point processes. The new theory will incorporate factors necessary to describe spatial gene expression at subcellular and multicellular scales including various reactions, spatial movements, and geometric effects. This project will also establish the statistical theory of inference on the resulting inverse problem of inferring stochastic rates from only snapshots of individual particle positions. Investigations into parameter identifiability, optimal experimental design, and model selection will ensure robust and reliable inference. In complement to the developed theory, this project will implement and benchmark cutting-edge approaches for efficiently performing large-scale statistical inference, including variational Bayesian Monte Carlo and physics-informed neural networks. The culmination of this work will be packaged into open-source software that infers interpretable biophysical parameters from multi-gene tissue-scale datasets.

This CAREER Award is co-funded by the Mathematical Biology and Statistics Programs at the Division of Mathematical Sciences and the Cellular Dynamics & Function Cluster in the Division of Molecular & Cellular Biosciences, BIO Directorate.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2347284","Conference: Design and Analysis of Experiments 2024","DMS","STATISTICS","02/01/2024","12/06/2023","John Morgan","VA","Virginia Polytechnic Institute and State University","Standard Grant","Tapabrata Maiti","01/31/2025","$18,000.00","Xinwei Deng, Anne Driscoll","jpmorgan@vt.edu","300 TURNER ST NW","BLACKSBURG","VA","240603359","5402315281","MPS","126900","7556","$0.00","The Design and Analysis of Experiments Conference 2024 (DAE 2024) will meet May 15-17, 2024 on the campus of Virginia Tech in Blacksburg, VA. It will bring together researchers from across the United States and beyond, and from both academia and industry, to focus on advancing the statistical techniques for experimentation that empower knowledge discovery. It will provide a forum for interaction, discussion, and exchange of ideas on novel research for designing effective experiments, and for analyzing the data that they produce. The aim of the conference is to increase the efficacy of data collection in areas as wide-ranging as autonomous driving, drug development, environmental monitoring, infectious disease dynamics, cybersecurity, and manufacturing, among many others, and so accelerate the pace of innovation in all of these domains. DAE 2024 will emphasize inclusion and mentoring of young researchers and minorities, and in so doing will be a cog in the development of the next generation of statistical experts in the techniques of experimental design.

Designed experimentation and the corresponding techniques for analysis are integral to the process of scientific discovery, be it in engineering, medicine, commerce, manufacturing, or indeed in any of the vast range of human activities where continuing knowledge acquisition is a requirement for advancement and success. Driven by these needs, developments are rapidly taking place in experimental design and analysis research, in both traditional and emerging areas of applications. As new areas of application arise, correspondingly new computational tools are enabling the development of better designs for data collection in complex problems. Technical sessions of DAE 2024 will include leading experts addressing Covering Arrays and Combinatorial Testing; Online Experimentation; Sequential Design, Active Learning, and Bayesian Optimization; Design Issues in Uncertainty Quantification; Orthogonal Arrays and Related Designs; Causal Inference and Experimental Design; Design Challenges in Transportation; and more. Additional features will include roundtable discussions, mentoring sessions for junior researchers, and poster sessions highlighting advancements in addition to those covered in the technical sessions. Further details about the conference may be found at https://sites.google.com/view/dae2024/dae-2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412661","Self-Normalized Inference for High-Dimensional Time Series","DMS","STATISTICS","08/01/2024","07/19/2024","Ting Zhang","GA","University of Georgia Research Foundation Inc","Standard Grant","Jun Zhu","07/31/2027","$175,000.00","","tingzhang@uga.edu","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126900","","$0.00","The project aims to initiate a new paradigm for statistical inference of high-dimensional time series. High-dimensional time series refer to a sequence of large dimensional data collected over time, and examples include large panel data in economics, functional magnetic resonance imaging data in neuroscience, stock price data for a large set of companies in finance, cellular usage data over time for a large number of users in telecommunication, high-resolution spatio-temporal data in climate science, and many others. An intrinsic feature of high-dimensional time series data is the temporal dependence among high-dimensional data vectors collected at different time points, while many existing results on high-dimensional data analysis require such vectors to be independent of each other. By allowing dependence to exist not only among different components of the data vector at any given time point but also among data vectors collected at different time points, the project results are expected to lead to a new paradigm for statistical inference and uncertainty quantification of high-dimensional time series. In addition, the project products are expected to be transformative and useful in a wide range of applications to provide the practitioners with a powerful and convenient statistical toolbox for scientific discoveries involving the analysis of high-dimensional time series data. The research developed is expected to be integrated into the undergraduate and graduate education and equip the students with advanced yet accessible statistical tools for analyzing high-dimensional time series data.

The project involves the development of a new paradigm to quantify the accumulative uncertainty of self-normalized statistics over an increasing dimension, and a number of its guided statistical inference problems and real applications. Self-normalization refers to the technique of using recursive estimators to pivotalize the asymptotic distribution of the statistic of interest, which has enjoyed considerable development in the low-dimensional setting. Its extension to the high-dimensional setting, however, can be a nontrivial challenge and directly applying self-normalization to high-dimensional objects can lead to singularities or substantial size distortions. A major gap that prevented self-normalized statistics from prevailing in high-dimensional time series analysis is their non-standard limiting distribution which has been mostly tabulated through numerical approximations. To address this, the project seeks a new approach in connection with harmonic analysis to provide an analytical characterization on how the uncertainty of self-normalized distributions accumulates over an increasing dimension. The results then would guide the development of various statistical methods and their asymptotic theory for self-normalized inference of high-dimensional time series. These include, for example, self-normalized high-dimensional feature selection, simultaneous uncertainty quantification of high-dimensional objects, and extensions to general quantities such as the median, variance, quantiles, autocovariances, ratio statistics, and others.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413294","Objective and reliable methods for inference from modern omics data","DMS","STATISTICS","09/01/2024","07/19/2024","Aaron Molstad","MN","University of Minnesota-Twin Cities","Standard Grant","Jun Zhu","08/31/2027","$150,000.00","","amolstad@umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","126900","","$0.00","Modern ?omics? (e.g., transcriptomics or proteomics) studies often generate data using single-cell or spatially-resolved sequencing technologies. These technologies enable researchers to study, for example, the spatial variation of gene expression across cells or tissues, offering a high-resolution perspective of complex biological dynamics. This perspective allows researchers to better understand disease mechanisms and can lead to the development of novel treatments. However, the data generated by these technologies are high-dimensional and dependent, which can complicate statistical inference. Existing inferential methods are often subjective or unreliable, either requiring user input that may bias or invalidate results, or requiring rigid model assumptions that are frequently violated in practice. This project will address these issues by developing statistical methods that do not rely on user input, and work reliably in more general settings than existing methods. The new methods will be theoretically justified and equipped with fast computational algorithms. Software implementing these methods will be made publicly available, enabling their wide use in academia and industry. The project will also provide training opportunities for both graduate and undergraduate students.

This project develops new statistical methods for inference with high-dimensional dependent data, motivated by challenges in analyzing single-cell and spatially-resolved sequencing data. Specific challenges include the failure of traditional inferential methods when the parameter is at or near the boundary of the parameter space; the need to both generate and test hypotheses from the same data without inflating Type I error rates; and insufficient model flexibility and scalability. The investigator will address each of these issues directly by (i) developing a new test procedure that resolves a well-known challenge of constructing confidence regions for variance components (or functions thereof) near zero; (ii) providing a unified approach for valid post-clustering inference with high-dimensional data from a broad class of distributions; and (iii) developing a general class of penalized mixture models that accommodates multiple latent sources of heterogeneity. The methodological developments in this project lay the groundwork for more general methods addressing more broad challenges in inference near the boundary of the parameter space, post-selection inference, and modeling heterogeneous high-dimensional data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2426575","A Consensus Study on Frontiers of Statistics in Science and Engineering: 2035 and Beyond","DMS","STATISTICS, IUSE, Climate & Large-Scale Dynamics, Networking Technology and Syst, Ecosystem Science, Comm & Information Foundations, ECR-EDU Core Research, DMREF","09/01/2024","07/19/2024","Michelle Schwalbe","DC","National Academy of Sciences","Continuing Grant","Yong Zeng","08/31/2026","$400,000.00","","mschwalbe@nas.edu","2101 CONSTITUTION AVE NW","WASHINGTON","DC","204180007","2023342254","MPS","126900, 199800, 574000, 736300, 738100, 779700, 798000, 829200","054Z, 094Z, 095Z, 1269, 4444, 7556, 8400","$0.00","This project intends to explore the vitality of research in the field of statistics and consider the future of the discipline. The study will highlight the significance of recent discoveries, the rate of progress at the frontiers of statistics, and emerging trends and fields, as well as address the developments in the realm of deep learning, artificial intelligence, and data science, as well as the statistical questions that motivate this growth. Additionally, the role of statistics in the interactions between mathematics, engineering, and computer science will be examined. The report will also illustrate the importance of statistics in key research domains, such as public health and medicine, and materials science, as well as the impact of research and training in the statistical sciences on science and engineering. This study aims to foster a forward-looking discussion about the state of the statistical sciences and emerging opportunities for the discipline and its stakeholders, including applications relevant to industry and technology, innovation and economic competitiveness, the internet, health and well-being, national security, and other areas of national interest. NSA and NIH also contribute to the study.

The National Academies will assemble an interdisciplinary ad hoc committee to produce a forward-looking assessment of the current state of the statistical sciences and emerging opportunities for the discipline and its stakeholders as they look ahead to 2035 and beyond. The study may make recommendations to funding agencies on how to adjust and expand their portfolios of activities and partnerships to understand the evolution of the field and strengthen the impact of the discipline. Specifically, the study will assess: The state of research in the statistical sciences, examining aspects such as the significance of recent developments and highlighting current and emerging trends, challenges, and directions. It will further assess statistical research in allied fields, and interactions between the statistical sciences and the mathematical, computational, engineering, materials science, and related fields such as biostatistics, probability, machine learning, artificial intelligence, and data science. The study will also examine the statistical needs to support scientific and technological advances, including the importance of statistical sciences and the strength of interdisciplinary collaborations. The role of statistical sciences in key research domains for American competitiveness, such as manufacturing, materials science, blockchain, biomedical and biological sciences, public health, medicine, health equity, geosciences, environmental health and science, astronomy, and energy applications. Finally, the study will also assess statistical education, training, and workforce development.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -23,31 +35,27 @@ "2412853","Statistical Learning and Inference for Network Data with Positive and Negative Edges","DMS","STATISTICS","07/01/2024","06/25/2024","Weijing Tang","PA","Carnegie-Mellon University","Continuing Grant","Yulia Gel","06/30/2027","$85,179.00","","weijingt@andrew.cmu.edu","5000 FORBES AVE","PITTSBURGH","PA","152133815","4122688746","MPS","126900","1269, 7794","$0.00","Networks, representing relationships or interactions between subjects in complex systems, are ubiquitous across diverse engineering and scientific disciplines. However, real-world relationships often go beyond simple presence or absence, which poses challenges and necessitates the development of advanced methods. This project focuses on an important class of heterogeneous networks -- ?signed networks?, where relationships can be positive (for example, friendship, alliance, and mutualism) or negative (for example, enmity, disputes, and competition). Such signed relationships are prevalent and exhibit substantially different and unique interaction patterns. This project aims to provide a comprehensive investigation on signed networks through statistical model-based learning and inference, pushing the frontier of our understanding of the role of negative edges in real-world complex systems. The research outcome will stimulate interdisciplinary research and make significant contributions in a broad range of scientific domains, including political science, biochemistry, medicine, genetics, ecology, and business and marketing. The project will support and train STEM workforce members by providing research training opportunities for undergraduate and graduate students.

This project will develop novel statistical methodologies and theories for analyzing signed networks, focusing on the integration of negative relationships in three core problems: (a) understanding the formation mechanism of signed networks guided by fundamental social theories; (b) detecting communities in signed networks by leveraging unique patterns; and (c) learning informative and interpretable embeddings for signed networks to assist downstream analysis. For the first problem, the investigator will provide a valid statistical inference method under novel nonparametric graphon models for signed networks and study real-world evidence of conceptual theories to understand its formation mechanism. For the second problem, new fast community detection methods will be developed under a novel stochastic block model with a hierarchical structure for signed networks, with associated theory emphasizing the positive impacts of negative relationships. Finally, the project will tackle the problem of embedding learning by developing a general latent space framework. The developed methods, algorithms, and theories in this project will be applicable to various practical problems across different domains.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337882","CAREER: Perturbation Methods for Quantifying Uncertainties in Machine Learning Models","DMS","STATISTICS","07/01/2024","06/25/2024","Snigdha Panigrahi","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Yulia Gel","06/30/2029","$85,389.00","","psnigdha@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126900","1045","$0.00","In applied machine learning and statistics, it is common practice to search through many different models before estimating a best model: one that is simple to explain, while still providing good predictive performance. Over the past decade, several methods have emerged which first estimate a model from a range of choices, and then fit the estimated model to extract useful trends and predict future outcomes. However, predictive accuracy, on its own, has limited explanatory value and point estimators with high uncertainties may lead to poor replicability down the line. Yet, most such models, supervised or unsupervised, lack uncertainties for the related estimators. This project introduces a new class of perturbation methods to quantify uncertainties in machine learning models, with various applications in regression, classification, and dimension reduction. The research plans have three main goals. The first goal is to develop methods that can be used with different types of data and are not limited to specific models. The second goal is to ensure that the methods can be scaled and applied to decentralized datasets on multiple machines. The last goal is to create versatile methods that can be used with different estimation techniques. An overarching goal is to allow researchers to apply these techniques to various data types and forms, without being constrained by unrealistic assumptions or limited methods for model estimation. The project's educational and outreach plans are closely tied to its research plans. The project will help the PI conduct summer training programs with K-12 outreach, develop new curricula, and broaden participation of underrepresented groups in the field.

This project aims to develop methods for attaching uncertainties to the outputs of model estimation methods. The research agenda is structured into three main aims. In the first aim, the project will introduce distribution-free methods that can quantify uncertainties in a flexible class of semiparametric models. In the second aim, the project will develop distributed methods that use decentralized data from a cluster of nodes to quantify uncertainties in an estimated model. These methods will need only basic, aggregated statistics from each node and will be accompanied by communication-efficient algorithms. In the third aim, the project will focus on developing perturbation methods as a versatile approach for uncertainty quantification that can be used in a wide range of model estimation algorithms, both supervised and unsupervised. To achieve these aims, the project will use perturbation to exploit a link between the geometric properties of estimators and their underlying probability, and will employ an integrated approach using mathematical statistics, probability theory and optimization. Throughout the project and after its completion, the methodology and open-source software will be applied to improve biomedical decision-making and replication in health studies.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413552","Collaborative Research: Statistical Network Integration","DMS","STATISTICS","07/01/2024","06/17/2024","Joshua Cape","WI","University of Wisconsin-Madison","Continuing Grant","Yulia Gel","06/30/2027","$37,235.00","","jrcape@wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","126900","1269","$0.00","This project pursues the contemporary problem of statistical network integration facing scientists, practitioners, and theoreticians. The study of networks and graph-structured data has received growing attention in recent years, motivated by investigations of complex systems throughout the biological and social sciences. Models and methods have been developed to analyze network data objects, often focused on single networks or homogeneous data settings, yet modern available data are increasingly heterogeneous, multi-sample, and multi-modal. Consequently, there is a growing need to leverage data arising from different sources that result in multiple network observations with attributes. This project will develop statistically principled data integration methodologies for neuroimaging studies, which routinely collect multiple subject data across different groups (strains, conditions, edge groups), modalities (functional and diffusion MRI), and brain covariate information (phenotypes, healthy status, gene expression data from brain tissue). The investigators will offer interdisciplinary mentoring opportunities to students participating in the research project and co-teach a workshop based on the proposed research.

The goals of this project are to establish flexible, parsimonious latent space models for network integration and to develop efficient, theoretically justified inference procedures for such models. More specifically, this project will develop latent space models to disentangle common and individual local and global latent features in samples of networks, propose efficient spectral matrix-based methods for data integration, provide high-dimensional structured penalties for dimensionality reduction and regularization in network data, and develop cross-validation methods for multiple network data integration. New theoretical developments spanning concentration inequalities, eigenvector perturbation analysis, and distributional asymptotic results will elucidate the advantages and limitations of these methods in terms of signal aggregation, heterogeneity, and flexibility. Applications of these methodologies to the analysis of multi-subject brain network data will be studied. Emphasis will be on interpretability, computation, and theoretical justification.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2413953","Collaborative Research: Statistical Inference for High Dimensional and High Frequency Data: Contiguity, Matrix Decompositions, Uncertainty Quantification","DMS","STATISTICS","07/01/2024","06/21/2024","Lan Zhang","IL","University of Illinois at Chicago","Standard Grant","Jun Zhu","06/30/2027","$155,372.00","","lanzhang@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126900","","$0.00","To pursue the promise of the big data revolution, the current project is concerned with a particular form of such data, high dimensional high frequency data (HD2), where series of high-dimensional observations can see new data updates in fractions of milliseconds. With technological advances in data collection, HD2 data occurs in medicine (from neuroscience to patient care), finance and economics, geosciences (such as earthquake data), marine science (fishing and shipping), and, of course, in internet data. This research project focuses on how to extract information from HD2 data, and how to turn this data into knowledge. As part of the process, the project develops cutting-edge mathematics and statistical methodology to uncover the dependence structure governing HD2 data. It interfaces with concepts of artificial intelligence. In addition to developing a general theory, the project is concerned with applications to financial data, including risk management, forecasting, and portfolio management. More precise estimators, with improved margins of error, will be useful in all these areas of finance. The results are of interest to main-street investors, regulators and policymakers, and the results are entirely in the public domain. The project will also provide research training opportunities for students.

In more detail, the project will focus on four linked questions for HD2 data: contiguity, matrix decompositions, uncertainty quantification, and the estimation of spot quantities. The investigators will extend their contiguity theory to the common case where observations have noise, which also permits the use of longer local intervals. Under a contiguous probability, the structure of the observations is often more accessible (frequently Gaussian) in local neighborhoods, facilitating statistical analysis. This is achieved without altering the underlying models. Because the effect of the probability change is quite transparent, this approach also enables more direct uncertainty quantification. To model HD2 data, the investigators will explore time-varying matrix decompositions, including the development of a singular value decomposition (SVD) for high frequency data, as a more direct path to a factor model. Both SVD and principal component analysis (PCA) benefit from contiguity, which eases both the time-varying construction, and uncertainty quantification. The latter is of particular importance not only to set standard errors, but also to determine the trade-offs involved in estimation under longitudinal variation: for example, how many minutes or days are required to estimate a covariance matrix, or singular vectors? The investigators also plan to develop volatility matrices for the drift part of a financial process, and their PCAs. The work on matrix decompositions will also benefit from projected results on spot estimation, which also ties in with contiguity. It is expected that the consequences of the contiguity and the HD2 inference will be transformational, leading to more efficient estimators and better prediction, and that this approach will form a new paradigm for high frequency data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413301","Next-Generation Functional Data Analysis via Machine Learning","DMS","STATISTICS","07/01/2024","06/21/2024","Guanqun Cao","MI","Michigan State University","Standard Grant","Yulia Gel","06/30/2027","$170,000.00","","caoguanq@msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","126900","079Z, 1269","$0.00","Classical functional data refer to curves or functions, i.e., the data for each variable are viewed as smooth curves, surfaces, or hypersurfaces evaluated at a finite subset of some interval in one-, two- or three-dimensional Euclidean spaces (for example, some period of time, some range of pixels or voxels, and so on). The independent and identically distributed functional data are sometimes referred to as first-generation functional data. Modern studies from a variety of fields record multiple functional observations according to either multivariate, high-dimensional, multilevel, or time series designs. Such data are called next-generation functional data. This project will elevate the focus on developing machine learning (ML) and artificial intelligence-based methodologies tailored for the next-generation of functional data analysis (FDA). The project will bridge the gap between theoretical knowledge and practical application in ML and FDA. While there have been efforts to integrate ML into the FDA field, these initiatives have predominantly concentrated on handling relatively straightforward formats of functional data. In addition, multiple student research training opportunities will be offered, and high-performance statistics software packages will be developed. These packages will enable researchers from various disciplines to investigate complex relationships that exist among modern functional data.

The widespread utilization of resilient digital devices has led to a notable increase of dependent, high-dimensional, and multi-way functional data. Consequently, the existing toolkit?s efficiency diminishes when tasked with addressing emerging FDA challenges. The PI will introduce: (i) Deep neural networks-based Lasso for dependent FDA; (ii) Optimal multi-way FDA; and (iii) Transfer learning for FDA, and will develop flexible and intelligent ML based estimators, classifiers, clusters, and investigate their statistical properties including the bounds of the prediction errors, convergence rates and minimax excess risk. The proposed methodology will be particularly useful for modeling complex functional data whose underlying structure cannot be properly captured by the existing statistical methods.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413747","Collaborative Research: NSF MPS/DMS-EPSRC: Stochastic Shape Processes and Inference","DMS","STATISTICS","08/01/2024","06/20/2024","Sebastian Kurtek","OH","Ohio State University","Standard Grant","Yulia Gel","07/31/2027","$199,555.00","","kurtek.1@osu.edu","1960 KENNY RD","COLUMBUS","OH","432101016","6146888735","MPS","126900","1269, 7929","$0.00","The intimate link between form, or shape, and function is ubiquitous in science. In biology, for instance, the shapes of biological components are pivotal in understanding patterns of normal behavior and growth; a notable example is protein shape, which contributes to our understanding of protein function and classification. This project, led by a team of investigators from the USA and the UK, will develop ways of modeling how biological and other shapes change with time, using formal statistical frameworks that capture not only the changes themselves, but how these changes vary across objects and populations. This will enable the study of the link between form and function in all its variability. As example applications, the project will develop models for changes in cell morphology and topology during motility and division, and changes in human posture during various activities, facilitating the exploration of scientific questions such as how and why cell division fails, or how to improve human postures in factory tasks. These are proofs of concept, but the methods themselves will have much wider applicability. This project will thus not only progress the science of shape analysis and the specific applications studied; it will have broader downstream impacts on a range of scientific application domains, providing practitioners with general and useful tools.

While there are several approaches for representing and analyzing static shapes, encompassing curves, surfaces, and complex structures like trees and shape graphs, the statistical modeling and analysis of dynamic shapes has received limited attention. Mathematically, shapes are elements of quotient spaces of nonlinear manifolds, and shape changes can be modeled as stochastic processes, termed shape processes, on these complex spaces. The primary challenges lie in adapting classical modeling concepts to the nonlinear geometry of shape spaces and in developing efficient statistical tools for computation and inference in such very high-dimensional, nonlinear settings. The project consists of three thrust areas, dealing with combinations of discrete and continuous time, and discrete and continuous representations of shape, with a particular emphasis on the issues raised by topology changes. The key idea is to integrate spatiotemporal registration of objects and their evolution into the statistical formulation, rather than treating them as pre-processing steps. This project will specifically add to the current state-of-the-art in topic areas such as stochastic differential equations on shape manifolds, time series models for shapes, shape-based functional data analysis, and modeling and inference on infinite-dimensional shape spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413833","Collaborative Research: Nonparametric Learning in High-Dimensional Survival Analysis for causal inference and sequential decision making","DMS","STATISTICS","07/01/2024","06/18/2024","Shanshan Ding","DE","University of Delaware","Standard Grant","Jun Zhu","06/30/2027","$200,000.00","Wei Qian","sding@udel.edu","220 HULLIHEN HALL","NEWARK","DE","197160099","3028312136","MPS","126900","9150","$0.00","Data with survival outcomes are commonly encountered in real-world applications to capture the time duration until a specific event of interest occurs. Nonparametric learning for high dimensional survival data offers promising avenues in practice because of its ability to capture complex relationships and provide comprehensive insights for diverse problems in medical and business services, where vast covariates and individual metrics are prevalent. This project will significantly advance the methods and theory for nonparametric learning in high-dimensional survival data analysis, with a specific focus on causal inference and sequential decision making problems. The study will be of interest to practitioners in various fields, particularly providing useful methods for medical researchers to discover relevant risk factors, assess causal treatment effects, and utilize personalized treatment strategies in contemporary health sciences. It will also provide useful analytics tools beneficial to financial and related institutions for assessing user credit risks and facilitating informed decisions through personalized services. The theoretical and empirical studies to incorporate complex nonparametric structures in high-dimensional survival analysis, together with their interdisciplinary applications, will create valuable training and research opportunities for graduate and undergraduate students, including those from underrepresented minority groups.

Under flexible nonparametric learning frameworks, new embedding methods and learning algorithms will be developed for high dimensional survival analysis. First, the investigators will develop supervised doubly robust linear embedding and supervised nonlinear manifold learning method for supervised dimension reduction of high dimensional survival data, without imposing stringent model or distributional assumptions. Second, a robust nonparametric learning framework will be established for estimating causal treatment effect for high dimensional survival data that allows the covariate dimension to grow much faster than the sample size. Third, motivated by applications in personalized service, the investigators will develop a new nonparametric multi-stage algorithm for high dimensional censored bandit problems that allows flexibility with potential non-linear decision boundaries with optimal regret guarantees.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2413721","New Directions in Bayesian Heterogeneous Data Integration: Methods, Theory and Applications","DMS","STATISTICS","07/01/2024","06/17/2024","Sharmistha Guha","TX","Texas A&M University","Continuing Grant","Tapabrata Maiti","06/30/2027","$49,899.00","","sharmistha@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126900","1269","$0.00","As the scientific community is moving into a data-driven era, there is an unprecedented opportunity for the integrative analysis of network and functional data from multiple sources to uncover important scientific insights which might be missing when these data sources are analyzed in isolation. To this end, this project plans to transform the current landscape of integrating network and functional data, leveraging their combined strength for scientific advancements through the development of innovative hierarchical Bayesian statistical models. The proposed work holds transformative promise in vital scientific domains, such as cognitive and motor aging, and neurodegenerative diseases. It will enhance scientific collaborations with neuroscientists using multi-source image data for targeted investigations of key brain regions significant in the study of motor and cognitive aging. Moreover, the proposed research will facilitate the prediction of images, traditionally acquired via costly imaging modalities, utilizing images from more cost-effective alternatives, which is poised to bring about transformative changes in the healthcare economy. The open-source software and educational materials created will be maintained and accessible to a wider audience of statisticians and domain experts. This accessibility is anticipated to foster widespread adoption of these techniques among statisticians and domain scientists. The PI's involvement in conference presentations, specialized course development, curriculum expansion, graduate student mentoring, undergraduate research engagement with a focus on under-represented backgrounds, and provision of short courses will enhance dissemination efforts and encourage diverse utilization of the developed methods.

The proposed project aims to address the urgent need for principled statistical approaches to seamlessly merge information from diverse sources, including modern network and functional data. It challenges the prevailing trend of analyzing individual data sources, which inherently limits the potential for uncovering innovative scientific insights that could arise from integrating multiple sources. Hierarchical Bayesian models are an effective way to capture the complex structures in network and functional data. These models naturally share information among heterogeneous objects, providing comprehensive uncertainty in inference through science-driven joint posterior distributions. Despite the potential advantages of Bayesian perspectives, their widespread adoption is hindered by the lack of theoretical guarantees, computational challenges, and difficulties in specifying robust priors for high-dimensional problems. This proposal will address these limitations by integrating network and functional data, leveraging their combined strength for scientific advancements through the development of innovative hierarchical Bayesian models. Specifically, the project will develop a semi-parametric joint regression framework with network and functional responses, deep network regression with multiple network responses, and Bayesian interpretable deep neural network regression with functional response on network and functional predictors. Besides offering a novel toolbox for multi-source object data integration, the proposed approach will advance the emerging field of interpretable deep learning for object regression by formulating novel and interpretable deep neural networks that combine predictive power with statistical model interpretability. The project will develop Bayesian asymptotic results to guarantee accurate parametric and predictive inference from these models as a function of network and functional features and sample size, an unexplored domain in the Bayesian integration of multi-object data. The proposed methodology will significantly enhance the seamless integration of multimodal neuroimaging data, leading to principled inferences and deeper comprehension of brain structure and function in the study of Alzheimer's disease and aging.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412895","Statistical Entropic Optimal Transport: Theory, Methods and Applications","DMS","STATISTICS","07/01/2024","06/17/2024","Gonzalo Mena","PA","Carnegie-Mellon University","Continuing Grant","Yong Zeng","06/30/2027","$62,726.00","","gmena@andrew.cmu.edu","5000 FORBES AVE","PITTSBURGH","PA","152133815","4122688746","MPS","126900","075Z, 079Z","$0.00","Optimal transport provides a sensible mathematical framework to address the fundamental statistical question of how a statistician measures the distance between two distributions based on possibly large high-dimensional datasets. A variation of the original transportation problem featuring an entropic penalization has appeared as a more scalable alternative, fueling a wave of new results and successful applications in domains such as genomics, neuroscience, and economics, to name a few. Despite its practical success and the achieved understanding of some of its fundamental statistical properties, there is still a substantial gap between theory and practice in the entropic optimal transport framework. This project will bridge this gap through new methods grounded in an improved theoretical understanding of entropic optimal transport, potentially generating an innovative set of applications in the life sciences. Graduate students will be trained within the scope of this project.


The core of this project focuses on two intimately related thrusts: first, to develop a foundation for inference in parametric models with entropic optimal transport and to identify the regimes for which this framework is best suited. This includes the problem of model-based clustering in high-dimensional, non-asymptotic regimes and a study of the robustness of entropic-optimal-transport estimators. Second, the PIs will develop statistical applications of entropic optimal transport in Alzheimer?s disease neuropathology and spatial transcriptomics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412832","Collaborative Research: Statistical Modeling and Inference for Object-valued Time Series","DMS","STATISTICS","07/01/2024","06/17/2024","Changbo Zhu","IN","University of Notre Dame","Continuing Grant","Jun Zhu","06/30/2027","$56,755.00","","czhu4@nd.edu","836 GRACE HALL","NOTRE DAME","IN","465566031","5746317432","MPS","126900","","$0.00","Random objects in general metric spaces have become increasingly common in many fields. For example, the intraday return path of a financial asset, the age-at-death distributions, the annual composition of energy sources, social networks, phylogenetic trees, and EEG scans or MRI fiber tracts of patients can all be viewed as random objects in certain metric spaces. For many endeavors in this area, the data being analyzed is collected with a natural ordering, i.e., the data can be viewed as an object-valued time series. Despite its prevalence in many applied problems, statistical analysis for such time series is still in its early development. A fundamental difficulty of developing statistical techniques is that the spaces where these objects live are nonlinear and commonly used algebraic operations are not applicable. This research project aims to develop new models, methodology and theory for the analysis of object-valued time series. Research results from the project will be disseminated to the relevant scientific communities via publications, conference and seminar presentations. The investigators will jointly mentor a Ph.D. student and involve undergraduate students in the research, as well as offering advanced topic courses to introduce the state-of-the-art techniques in object-valued time series analysis.

The project will develop a systematic body of methods and theory on modeling and inference for object-valued time series. Specifically, the investigators propose to (1) develop a new autoregressive model for distributional time series in Wasserstein geometry and a suite of tools for model estimation, selection and diagnostic checking; (2) develop new specification testing procedures for distributional time series in the one-dimensional Euclidean space; and (3) develop new change-point detection methods to detect distribution shifts in a sequence of object-valued time series. The above three projects tackle several important modeling and inference issues in the analysis of object-valued time series, the investigation of which will lead to innovative methodological and theoretical developments, and lay groundwork for this emerging field.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412403","Robust Extensions to Bayesian Regression Trees for Complex Data","DMS","STATISTICS","08/01/2024","06/17/2024","HENGRUI LUO","TX","William Marsh Rice University","Continuing Grant","Tapabrata Maiti","07/31/2027","$58,710.00","","hl180@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126900","","$0.00","This project is designed to extend the capabilities of tree-based models within the context of machine learning. Tree-based models allow for decision-making based on clear, interpretable rules and are widely adopted in diagnostic and learning tasks. This project will develop novel methodologies to enhance their robustness. Specifically, the research will integrate deep learning techniques with tree-based statistical methods to create models capable of processing complex, high-dimensional data from medical imaging, healthcare, and AI sectors. These advancements aim to significantly improve prediction and decision-making processes, enhancing efficiency and accuracy across a broad range of applications. The project also prioritizes inclusivity and education by integrating training components, thereby advancing scientific knowledge and disseminating results through publications and presentations.

The proposed research leverages Bayesian hierarchies and transformation techniques on trees to develop models capable of managing complex transformations of input data. These models will be tailored to improve interpretability, scalability, and robustness, overcoming current limitations in non-parametric machine learning applications. The project will utilize hierarchical layered structures, where outputs from one tree serve as inputs to subsequent trees, forming network architectures that enhance precision in modeling complex data patterns and relationships. Bayesian techniques will be employed to effectively quantify uncertainty and create ensembles, providing reliable predictions essential for critical offline prediction and real-time decision-making processes. This initiative aims to develop pipelines and set benchmarks for the application of tree-based models across diverse scientific and engineering disciplines.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412015","Statistical methods for point-process time series","DMS","STATISTICS","07/01/2024","06/17/2024","Daniel Gervini","WI","University of Wisconsin-Milwaukee","Standard Grant","Jun Zhu","06/30/2027","$149,989.00","","gervini@uwm.edu","3203 N DOWNER AVE # 273","MILWAUKEE","WI","532113188","4142294853","MPS","126900","","$0.00","This research project will develop statistical models and inference methods for the analysis of random point processes. Random point processes are events that occur at random in time or space according to certain patterns; this project will provide methods for the discovery and analysis of such patterns. Examples of events that can be modelled as random point processes include cyberattacks on a computer network, earthquakes, crimes in a city, spikes of neural activity in humans and animals, car crashes in a highway, and many others. Therefore, the methods to be developed under this project will find applications in many fields, such as national security, economy, neuroscience and geosciences, among others. The project will also provide training opportunities for graduate and undergraduate students in the field of Data Science.

This project will specifically develop statistical tools for the analysis of time series of point processes, that is, for point processes that are observed repeatedly over time; for example, when the spatial distribution of crime in a city is observed for several days. These tools will include trend estimation methods, autocorrelation estimation methods, and autoregressive models. Research activities in this project include the development of parameter estimation procedures, their implementation in computer programs, the study of theoretical large sample properties of these methods, the study of small sample properties by simulation, and their application to real-data problems. Other activities in this project include educational activities, such as the supervision of Ph.D. and Master's students, and the development of graduate and undergraduate courses in Statistics and Data Science.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2412628","Collaborative Research: Partial Priors, Regularization, and Valid & Efficient Probabilistic Structure Learning","DMS","STATISTICS","07/01/2024","06/17/2024","Ryan Martin","NC","North Carolina State University","Standard Grant","Yulia Gel","06/30/2027","$160,000.00","","rgmarti3@ncsu.edu","2601 WOLF VILLAGE WAY","RALEIGH","NC","276950001","9195152444","MPS","126900","1269","$0.00","Modern applications of statistics aim to solve complex scientific problems involving high-dimensional unknowns. One feature that these applications often share is that the high-dimensional unknown is believed to satisfy a complexity-limiting, low-dimensional structure. Specifics of the posited low-dimensional structure are mostly unknown, so a statistically interesting and scientifically relevant problem is structure learning, i.e., using data to learn the latent low-dimensional structure. Because structure learning problems are ubiquitous and reliable uncertainty quantification is imperative, results from this project will have an impact across the biomedical, physical, and social sciences. In addition, the project will offer multiple opportunities for career development of new generations of statisticians and data scientists.

Frequentist methods focus on data-driven estimation or selection of a candidate structure, but currently there are no general strategies for reliable uncertainty quantification concerning the unknown structure. Bayesian methods produce a data-dependent probability distribution over the space of structures that can be used for uncertainty quantification, but it comes with no reliability guarantees. A barrier to progress in reliable uncertainty quantification is the oppositely extreme perspectives: frequentists' anathema of modeling structural/parametric uncertainty versus Bayesians' insistence that such uncertainty always be modeled precisely and probabilistically. Overcoming this barrier requires a new perspective falling between these two extremes, and this project will develop a new framework that features a more general and flexible perspective on probability, namely, imprecise probability. Most importantly, this framework will resolve the aforementioned issues by offering new and powerful methods boasting provably reliable uncertainty quantification in structure learning applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412408","Monitoring time series in structured function spaces","DMS","STATISTICS","07/01/2024","06/14/2024","Piotr Kokoszka","CO","Colorado State University","Standard Grant","Yulia Gel","06/30/2027","$292,362.00","","Piotr.Kokoszka@colostate.edu","601 S HOWES ST","FORT COLLINS","CO","805212807","9704916355","MPS","126900","1269","$0.00","This project aims to develop new mathematical theory and statistical tools that will enable monitoring for changes in complex systems, for example global trade networks. Comprehensive databases containing details of trade between almost all countries are available. Detecting in real time a change in the typical pattern of trade and identifying countries where this change takes place is an important problem. This project will provide statistical methods that will allow making decisions about an emergence of an atypical pattern in a complex system in real time with certain theoretical guarantees. The project will also offer multiple interdisciplinary training opportunities for the next generation of statisticians and data scientists.

The methodology that will be developed is related to sequential change point detection, but is different because the in-control state is estimated rather than assumed. This requires new theoretical developments because it deals with complex infinite dimensional systems, whereas existing mathematical tools apply only to finite-dimensional systems. Panels of structured functions will be considered and methods for on-line identification of components undergoing change will be devised. All methods will be inferential with controlled probabilities of type I errors. Some of the key aspects of the project can be summarized in the following points. First, statistical theory leading to change point monitoring schemes in infinite dimensional function spaces will be developed. Second, strong approximations valid in Banach spaces will lead to assumptions not encountered in scalar settings and potentially to different threshold functions. Third, for monitoring of random density functions, the above challenges will be addressed in custom metric spaces. Fourth, since random densities are not observable, the effect of estimation will be incorporated. The new methodology will be applied to viral load measurements, investment portfolios, and global trade data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413952","Collaborative Research: Statistical Inference for High Dimensional and High Frequency Data: Contiguity, Matrix Decompositions, Uncertainty Quantification","DMS","STATISTICS","07/01/2024","06/21/2024","Per Mykland","IL","University of Chicago","Standard Grant","Jun Zhu","06/30/2027","$219,268.00","","mykland@galton.uchicago.edu","5801 S ELLIS AVE","CHICAGO","IL","606375418","7737028669","MPS","126900","","$0.00","To pursue the promise of the big data revolution, the current project is concerned with a particular form of such data, high dimensional high frequency data (HD2), where series of high-dimensional observations can see new data updates in fractions of milliseconds. With technological advances in data collection, HD2 data occurs in medicine (from neuroscience to patient care), finance and economics, geosciences (such as earthquake data), marine science (fishing and shipping), and, of course, in internet data. This research project focuses on how to extract information from HD2 data, and how to turn this data into knowledge. As part of the process, the project develops cutting-edge mathematics and statistical methodology to uncover the dependence structure governing HD2 data. In addition to developing a general theory, the project is concerned with applications to financial data, including risk management, forecasting, and portfolio management. More precise estimators, with improved margins of error, will be useful in all these areas of finance. The results will be of interest to main-street investors, regulators and policymakers, and the results will be entirely in the public domain. The project will also provide research training opportunities for students.

In more detail, the project will focus on four linked questions for HD2 data: contiguity, matrix decompositions, uncertainty quantification, and the estimation of spot quantities. The investigators will extend their contiguity theory to the common case where observations have noise, which also permits the use of longer local intervals. Under a contiguous probability, the structure of the observations is often more accessible (frequently Gaussian) in local neighborhoods, facilitating statistical analysis. This is achieved without altering the underlying models. Because the effect of the probability change is quite transparent, this approach also enables more direct uncertainty quantification. To model HD2 data, the investigators will explore time-varying matrix decompositions, including the development of a singular value decomposition (SVD) for high frequency data, as a more direct path to a factor model. Both SVD and principal component analysis (PCA) benefit from contiguity, which eases both the time-varying construction, and uncertainty quantification. The latter is of particular importance not only to set standard errors, but also to determine the trade-offs involved in estimation under longitudinal variation: for example, how many minutes or days are required to estimate a covariance matrix, or singular vectors? The investigators also plan to develop volatility matrices for the drift part of a financial process, and their PCAs. The work on matrix decompositions will also benefit from projected results on spot estimation, which also ties in with contiguity. It is expected that the consequences of the contiguity and the HD2 inference will be transformational, leading to more efficient estimators and better prediction, and that this approach will form a new paradigm for high frequency data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413748","Collaborative Research: NSF MPS/DMS-EPSRC: Stochastic Shape Processes and Inference","DMS","STATISTICS","08/01/2024","06/20/2024","Anuj Srivastava","FL","Florida State University","Standard Grant","Yulia Gel","07/31/2027","$200,000.00","","anuj@stat.fsu.edu","874 TRADITIONS WAY","TALLAHASSEE","FL","323060001","8506445260","MPS","126900","1269, 7929","$0.00","The intimate link between form, or shape, and function is ubiquitous in science. In biology, for instance, the shapes of biological components are pivotal in understanding patterns of normal behavior and growth; a notable example is protein shape, which contributes to our understanding of protein function and classification. This project, led by a team of investigators from the USA and the UK, will develop ways of modeling how biological and other shapes change with time, using formal statistical frameworks that capture not only the changes themselves, but how these changes vary across objects and populations. This will enable the study of the link between form and function in all its variability. As example applications, the project will develop models for changes in cell morphology and topology during motility and division, and changes in human posture during various activities, facilitating the exploration of scientific questions such as how and why cell division fails, or how to improve human postures in factory tasks. These are proofs of concept, but the methods themselves will have much wider applicability. This project will thus not only progress the science of shape analysis and the specific applications studied; it will have broader downstream impacts on a range of scientific application domains, providing practitioners with general and useful tools.

While there are several approaches for representing and analyzing static shapes, encompassing curves, surfaces, and complex structures like trees and shape graphs, the statistical modeling and analysis of dynamic shapes has received limited attention. Mathematically, shapes are elements of quotient spaces of nonlinear manifolds, and shape changes can be modeled as stochastic processes, termed shape processes, on these complex spaces. The primary challenges lie in adapting classical modeling concepts to the nonlinear geometry of shape spaces and in developing efficient statistical tools for computation and inference in such very high-dimensional, nonlinear settings. The project consists of three thrust areas, dealing with combinations of discrete and continuous time, and discrete and continuous representations of shape, with a particular emphasis on the issues raised by topology changes. The key idea is to integrate spatiotemporal registration of objects and their evolution into the statistical formulation, rather than treating them as pre-processing steps. This project will specifically add to the current state-of-the-art in topic areas such as stochastic differential equations on shape manifolds, time series models for shapes, shape-based functional data analysis, and modeling and inference on infinite-dimensional shape spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2412628","Collaborative Research: Partial Priors, Regularization, and Valid & Efficient Probabilistic Structure Learning","DMS","STATISTICS","07/01/2024","06/17/2024","Ryan Martin","NC","North Carolina State University","Standard Grant","Yulia Gel","06/30/2027","$160,000.00","","rgmarti3@ncsu.edu","2601 WOLF VILLAGE WAY","RALEIGH","NC","276950001","9195152444","MPS","126900","1269","$0.00","Modern applications of statistics aim to solve complex scientific problems involving high-dimensional unknowns. One feature that these applications often share is that the high-dimensional unknown is believed to satisfy a complexity-limiting, low-dimensional structure. Specifics of the posited low-dimensional structure are mostly unknown, so a statistically interesting and scientifically relevant problem is structure learning, i.e., using data to learn the latent low-dimensional structure. Because structure learning problems are ubiquitous and reliable uncertainty quantification is imperative, results from this project will have an impact across the biomedical, physical, and social sciences. In addition, the project will offer multiple opportunities for career development of new generations of statisticians and data scientists.

Frequentist methods focus on data-driven estimation or selection of a candidate structure, but currently there are no general strategies for reliable uncertainty quantification concerning the unknown structure. Bayesian methods produce a data-dependent probability distribution over the space of structures that can be used for uncertainty quantification, but it comes with no reliability guarantees. A barrier to progress in reliable uncertainty quantification is the oppositely extreme perspectives: frequentists' anathema of modeling structural/parametric uncertainty versus Bayesians' insistence that such uncertainty always be modeled precisely and probabilistically. Overcoming this barrier requires a new perspective falling between these two extremes, and this project will develop a new framework that features a more general and flexible perspective on probability, namely, imprecise probability. Most importantly, this framework will resolve the aforementioned issues by offering new and powerful methods boasting provably reliable uncertainty quantification in structure learning applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413864","Statistical Properties of Neural Networks","DMS","STATISTICS","07/01/2024","06/18/2024","Sourav Chatterjee","CA","Stanford University","Standard Grant","Tapabrata Maiti","06/30/2027","$225,000.00","","souravc@stanford.edu","450 JANE STANFORD WAY","STANFORD","CA","943052004","6507232300","MPS","126900","1269","$0.00","Neural networks have revolutionized science and engineering in recent years, but their theoretical properties are still poorly understood. The proposed projects aim to gain a deeper understanding of these theoretical properties, especially the statistical ones. It is a matter of intense debate whether neural networks can ""think"" like humans do, by recognizing logical patterns. The project aims to take a small step towards showing that under ideal conditions, perhaps they can. If successful, this will have impact in a vast range of applications of neural networks. This award includes support and mentoring for graduate students.

In one direction, it is proposed to study features of deep neural networks that distinguish them from classical statistical parametric models. Preliminary results suggest that the lack of identifiability is the differentiating factor. Secondly, it is proposed to investigate the extent to which neural networks may be seen as algorithm approximators, going beyond the classical literature on universal function approximation for neural networks. This perspective may shed light on recent empirical phenomena in neural networks, including the surprising emergent behavior of transformers and large language models.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413834","Collaborative Research: Nonparametric Learning in High-Dimensional Survival Analysis for causal inference and sequential decision making","DMS","STATISTICS","07/01/2024","06/18/2024","Zhezhen Jin","NY","Columbia University","Standard Grant","Jun Zhu","06/30/2027","$100,000.00","","zj7@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126900","","$0.00","Data with survival outcomes are commonly encountered in real-world applications to capture the time duration until a specific event of interest occurs. Nonparametric learning for high dimensional survival data offers promising avenues in practice because of its ability to capture complex relationships and provide comprehensive insights for diverse problems in medical and business services, where vast covariates and individual metrics are prevalent. This project will significantly advance the methods and theory for nonparametric learning in high-dimensional survival data analysis, with a specific focus on causal inference and sequential decision making problems. The study will be of interest to practitioners in various fields, particularly providing useful methods for medical researchers to discover relevant risk factors, assess causal treatment effects, and utilize personalized treatment strategies in contemporary health sciences. It will also provide useful analytics tools beneficial to financial and related institutions for assessing user credit risks and facilitating informed decisions through personalized services. The theoretical and empirical studies to incorporate complex nonparametric structures in high-dimensional survival analysis, together with their interdisciplinary applications, will create valuable training and research opportunities for graduate and undergraduate students, including those from underrepresented minority groups.

Under flexible nonparametric learning frameworks, new embedding methods and learning algorithms will be developed for high dimensional survival analysis. First, the investigators will develop supervised doubly robust linear embedding and supervised nonlinear manifold learning method for supervised dimension reduction of high dimensional survival data, without imposing stringent model or distributional assumptions. Second, a robust nonparametric learning framework will be established for estimating causal treatment effect for high dimensional survival data that allows the covariate dimension to grow much faster than the sample size. Third, motivated by applications in personalized service, the investigators will develop a new nonparametric multi-stage algorithm for high dimensional censored bandit problems that allows flexibility with potential non-linear decision boundaries with optimal regret guarantees.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413405","Collaborative Research: Statistical Optimal Transport: Foundation, Computation and Applications","DMS","STATISTICS","07/01/2024","06/18/2024","Kengo Kato","NY","Cornell University","Standard Grant","Yong Zeng","06/30/2027","$160,000.00","","kk976@cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","126900","079Z","$0.00","Comparing probability models is a fundamental task in almost every data-enabled problem, and Optimal Transport (OT) offers a powerful and versatile framework to do so. Recent years have witnessed a rapid development of computational OT, which has expanded applications of OT to statistics, including clustering, generative modeling, domain adaptation, distribution-to-distribution regression, dimension reduction, and sampling. Still, understanding the fundamental strengths and limitations of OT as a statistical tool is much to be desired. This research project aims to fill this important gap by advancing statistical analysis (estimation and inference) and practical approximation of two fundamental notions (average and quantiles) in statistics and machine learning, demonstrated through modern applications for measure-valued data. The project also provides research training opportunities for graduate students.

The award contains three main research projects. The first project will develop a new regularized formulation of the Wasserstein barycenter based on the multi-marginal OT and conduct an in-depth statistical analysis, encompassing sample complexity, limiting distributions, and bootstrap consistency. The second project will establish asymptotic distribution and bootstrap consistency results for linear functionals of OT maps and will study sharp asymptotics for entropically regularized OT maps when regularization parameters tend to zero. Building on the first two projects, the third project explores applications of the OT methodology to two important statistical tasks: dimension reduction and vector quantile regression. The research agenda will develop a novel and computationally efficient principal component method for measure-valued data and a statistically valid duality-based estimator for quantile regression with multivariate responses. The three projects will produce novel technical tools integrated from OT theory, empirical process theory, and partial differential equations, which are essential for OT-based inferential methods and will inspire new applications of OT to measure-valued and multivariate data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413426","Collaborative Research: Synergies between Steins Identities and Reproducing Kernels: Modern Tools for Nonparametric Statistics","DMS","STATISTICS","07/01/2024","06/17/2024","Krishnakumar Balasubramanian","CA","University of California-Davis","Standard Grant","Yong Zeng","06/30/2027","$169,999.00","","kbala@ucdavis.edu","1850 RESEARCH PARK DR STE 300","DAVIS","CA","956186153","5307547700","MPS","126900","079Z","$0.00","The project aims to conduct comprehensive statistical and computational analyses, with the overarching objective of advancing innovative nonparametric data analysis techniques. The methodologies and theories developed are anticipated to push the boundaries of modern nonparametric statistical inference and find applicability in other statistical domains such as nonparametric latent variable models, time series analysis, and sequential nonparametric multiple testing. This project will enhance the interconnections among statistics, machine learning, and computation and provide training opportunities for postdoctoral fellows, graduate students, and undergraduates.

More specifically, the project covers key problems in nonparametric hypothesis testing, intending to establish a robust framework for goodness-of-fit testing for distributions on non-Euclidean domains with unknown normalization constants. The research also delves into nonparametric variational inference, aiming to create a particle-based algorithmic framework with discrete-time guarantees. Furthermore, the project focuses on nonparametric functional regression, with an emphasis on designing minimax optimal estimators using infinite-dimensional Stein's identities. The study also examines the trade-offs between statistics and computation in all the aforementioned methods. The common thread weaving through these endeavors is the synergy between various versions of Stein's identities and reproducing kernels, contributing substantially to the advancement of models, methods, and theories in contemporary nonparametric statistics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413823","Robust and efficient Bayesian inference for misspecified and underspecified models","DMS","STATISTICS","07/01/2024","06/18/2024","Steven MacEachern","OH","Ohio State University","Standard Grant","Tapabrata Maiti","06/30/2027","$300,000.00","Ju Hee Lee, Hang Joon Kim","snm@stat.osu.edu","1960 KENNY RD","COLUMBUS","OH","432101016","6146888735","MPS","126900","","$0.00","This research project aims to improve data-driven modelling and decision-making. Its focus is on the development of Bayesian methods for low-information settings. Bayesian methods have proven to be tremendously successful in high-information settings where data is of high-quality, the scientific/business background that has generated the data is well-understood, and clear questions are asked. This project will develop a suite of Bayesian methods designed for low-information settings, including those where (i) the data show particular types of deficiencies, such as a preponderance of outlying or ?bad data?, (ii) a limited conceptual understanding of the phenomenon under study leads to a model that leaves a substantial gap between model and reality, producing a misspecified model or a model that is not fully specified, and (iii) when there is a shortage of data, so that the model captures only a very simplified version of reality. The new methods will expand the scope of Bayesian applications, with attention to problems in biomedical applications and psychology. The project will provide training for the next generation of data scientists.

This project has two main threads. For the first, the project will develop diagnostics that allow the analyst to assess the adequacy of portions of a posited model. Such assessments point the way toward elaborations that will bring the model closer to reality, improving the full collection of inferences. These assessments will also highlight limitations of the model, enabling the analyst to know when to make a decision and when to refrain from making one. The second thread will explore the use of sample-size adaptive loss functions for modelling and for inference. Adaptive loss functions have been used by classical statisticians to improve inference by exploiting the bias-variance tradeoff. This thread will blend adaptivity with Bayesian methods. This will robustify inference by providing smoother likelihoods for small and moderate sample sizes and by relying on smoother inference functions when the sample size is limited.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2413404","Collaborative Research: Statistical Optimal Transport: Foundation, Computation and Applications","DMS","STATISTICS","07/01/2024","06/18/2024","Xiaohui Chen","CA","University of Southern California","Standard Grant","Yong Zeng","06/30/2027","$180,000.00","","xiaohuic@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","900890701","2137407762","MPS","126900","079Z","$0.00","Comparing probability models is a fundamental task in almost every data-enabled problem, and Optimal Transport (OT) offers a powerful and versatile framework to do so. Recent years have witnessed a rapid development of computational OT, which has expanded applications of OT to statistics, including clustering, generative modeling, domain adaptation, distribution-to-distribution regression, dimension reduction, and sampling. Still, understanding the fundamental strengths and limitations of OT as a statistical tool is much to be desired. This research project aims to fill this important gap by advancing statistical analysis (estimation and inference) and practical approximation of two fundamental notions (average and quantiles) in statistics and machine learning, demonstrated through modern applications for measure-valued data. The project also provides research training opportunities for graduate students.

The award contains three main research projects. The first project will develop a new regularized formulation of the Wasserstein barycenter based on the multi-marginal OT and conduct an in-depth statistical analysis, encompassing sample complexity, limiting distributions, and bootstrap consistency. The second project will establish asymptotic distribution and bootstrap consistency results for linear functionals of OT maps and will study sharp asymptotics for entropically regularized OT maps when regularization parameters tend to zero. Building on the first two projects, the third project explores applications of the OT methodology to two important statistical tasks: dimension reduction and vector quantile regression. The research agenda will develop a novel and computationally efficient principal component method for measure-valued data and a statistically valid duality-based estimator for quantile regression with multivariate responses. The three projects will produce novel technical tools integrated from OT theory, empirical process theory, and partial differential equations, which are essential for OT-based inferential methods and will inspire new applications of OT to measure-valued and multivariate data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2413553","Collaborative Research: Statistical Network Integration","DMS","STATISTICS","07/01/2024","06/17/2024","Jesús Arroyo","TX","Texas A&M University","Continuing Grant","Yulia Gel","06/30/2027","$37,118.00","","jarroyo@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126900","1269","$0.00","This project pursues the contemporary problem of statistical network integration facing scientists, practitioners, and theoreticians. The study of networks and graph-structured data has received growing attention in recent years, motivated by investigations of complex systems throughout the biological and social sciences. Models and methods have been developed to analyze network data objects, often focused on single networks or homogeneous data settings, yet modern available data are increasingly heterogeneous, multi-sample, and multi-modal. Consequently, there is a growing need to leverage data arising from different sources that result in multiple network observations with attributes. This project will develop statistically principled data integration methodologies for neuroimaging studies, which routinely collect multiple subject data across different groups (strains, conditions, edge groups), modalities (functional and diffusion MRI), and brain covariate information (phenotypes, healthy status, gene expression data from brain tissue). The investigators will offer interdisciplinary mentoring opportunities to students participating in the research project and co-teach a workshop based on the proposed research.

The goals of this project are to establish flexible, parsimonious latent space models for network integration and to develop efficient, theoretically justified inference procedures for such models. More specifically, this project will develop latent space models to disentangle common and individual local and global latent features in samples of networks, propose efficient spectral matrix-based methods for data integration, provide high-dimensional structured penalties for dimensionality reduction and regularization in network data, and develop cross-validation methods for multiple network data integration. New theoretical developments spanning concentration inequalities, eigenvector perturbation analysis, and distributional asymptotic results will elucidate the advantages and limitations of these methods in terms of signal aggregation, heterogeneity, and flexibility. Applications of these methodologies to the analysis of multi-subject brain network data will be studied. Emphasis will be on interpretability, computation, and theoretical justification.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413484","New Approaches to Sensitivity Analysis in Observational Studies","DMS","STATISTICS","09/01/2024","06/17/2024","Colin Fogarty","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Yong Zeng","08/31/2027","$58,516.00","","fogartyc@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126900","075Z, 079Z","$0.00","While randomized experiments remain the gold standard for elucidating cause and effect relations, countless societally important ""what-if?"" questions cannot be addressed through clinical trials for a litany of reasons, ranging from ethical concerns to logistical infeasibility. For this reason, observational studies, wherein the assignment of group status to individuals is outside the control of the researcher, often represent the only path forward for inferring causal effects. While observational data are often inexpensive to collect and plentiful, regrettably, they suffer from inescapable biases due to self-selection. In short, associations between group status and outcomes of interest need not reflect causal effects, as the groups being compared might have considerable differences on the basis of factors unavailable for adjustment. This project will develop new methods for sensitivity analysis in observational studies, which answer the question, ""How much-unmeasured confounding would need to exist to overturn a study's finding of a causal effect?"" Quantifying the robustness of observational findings to hidden bias will help frame the debate around the reliability of such studies, allowing researchers to highlight findings that are particularly resilient to lurking variables. This project provides both theoretical guidance on how to extract the most out of a sensitivity analysis and computationally tractable methods for making this guidance actionable. Moreover, when randomized experimentation is possible, the developed methods will help researchers use existing observational studies for hypothesis generation, enabling them to find sets of promising outcome variables whose causal effects may be verified through follow-up experimentation. This award includes support for work with graduate students.

This project develops a new set of statistical methods for conducting sensitivity analyses after matching. These methods aim to overcome shortcomings of the existing approach, conferring computational, theoretical, and practical benefits. The project will provide a new approach to sensitivity analysis after matching called weighting-after-matching. The project will establish computational benefits, theoretical improvements in design sensitivity, and practical improvements in the power of a sensitivity analysis by using weighting-after-matching in lieu of the traditional unweighted approach. The project will also establish novel methods for sensitivity analysis with multiple outcome variables. These innovations will include a scalable multiple testing procedure for observational studies, facilitating exploratory analysis while providing control of the proportion of false discoveries, and methods for sensitivity analysis using weighting-after-matching for testing both sharp null hypotheses of no effect at all and hypotheses on average treatment effects. Finally, the project will establish previously unexplored benefits from using matching and weighting in combination, two modes of adjustment in observational studies commonly viewed as competitors. This will help bridge the divide between matching estimators and weighting estimators in the context of a sensitivity, in so doing providing a natural avenue for theoretical comparisons of these approaches.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412052","Tackling High Dimensionality for Modern Machine Learning: Theory and Visualization","DMS","STATISTICS","07/01/2024","06/17/2024","Yiqiao Zhong","WI","University of Wisconsin-Madison","Continuing Grant","Tapabrata Maiti","06/30/2027","$67,291.00","","yiqiao.zhong@wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","126900","","$0.00","This research project aims to address the recent challenges of modern machine learning from a statistical perspective. Deep Learning and particularly Large Language Models have the potential to transform our society, yet their scientific underpinning is much less developed. In particular, large-scale black-box models are deployed in applications with little understanding about when they may or may not work as expected. The research is expected to advance the understanding of modern machine learning. It will also provide accessible tools to improve the interpretations and safety of models. This award will involve and support graduate students.

The project is motivated by recent statistical phenomena such as double descent and benign overfitting that involve training a model with many parameters. Motivated by the empirical discoveries in Deep Learning, the project will develop insights into overfitting in imbalanced classification in high dimensions and the effects of reparametrization in contrastive learning. Understanding the generalization errors under overparametrization in practical scenarios, such as imbalanced classification, will likely lead to better practice of reducing overfitting. This project will also explore interpretations for black-box models and complicated methods: (1) in Transformers, high-dimensional embedding vectors are decomposed into interpretable components; (2) in t-SNE, embedding points are assessed by metrics related to map discontinuity. By using classical ideas from factor analysis and leave-one-out, this project will result in new visualization tools for interpretations and diagnosis.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2412629","Collaborative Research: Partial Priors, Regularization, and Valid & Efficient Probabilistic Structure Learning","DMS","STATISTICS","07/01/2024","06/17/2024","Chuanhai Liu","IN","Purdue University","Standard Grant","Yulia Gel","06/30/2027","$160,000.00","","chuanhai@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126900","","$0.00","Modern applications of statistics aim to solve complex scientific problems involving high-dimensional unknowns. One feature that these applications often share is that the high-dimensional unknown is believed to satisfy a complexity-limiting, low-dimensional structure. Specifics of the posited low-dimensional structure are mostly unknown, so a statistically interesting and scientifically relevant problem is structure learning, i.e., using data to learn the latent low-dimensional structure. Because structure learning problems are ubiquitous and reliable uncertainty quantification is imperative, results from this project will have an impact across the biomedical, physical, and social sciences. In addition, the project will offer multiple opportunities for career development of new generations of statisticians and data scientists.

Frequentist methods focus on data-driven estimation or selection of a candidate structure, but currently there are no general strategies for reliable uncertainty quantification concerning the unknown structure. Bayesian methods produce a data-dependent probability distribution over the space of structures that can be used for uncertainty quantification, but it comes with no reliability guarantees. A barrier to progress in reliable uncertainty quantification is the oppositely extreme perspectives: frequentists' anathema of modeling structural/parametric uncertainty versus Bayesians' insistence that such uncertainty always be modeled precisely and probabilistically. Overcoming this barrier requires a new perspective falling between these two extremes, and this project will develop a new framework that features a more general and flexible perspective on probability, namely, imprecise probability. Most importantly, this framework will resolve the aforementioned issues by offering new and powerful methods boasting provably reliable uncertainty quantification in structure learning applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413891","Nonparametric estimation in causal inference: optimality in traditional models and newer ones","DMS","STATISTICS","08/01/2024","06/14/2024","Matteo Bonvini","NJ","Rutgers University New Brunswick","Continuing Grant","Yong Zeng","07/31/2027","$59,393.00","","mb1662@stat.rutgers.edu","3 RUTGERS PLZ","NEW BRUNSWICK","NJ","089018559","8489320150","MPS","126900","075Z","$0.00","This project provides new methods for estimating causal effects from non-randomized studies. Quantifying the causal effect of a variable on another one is of fundamental importance in science because it allows for the understanding of what happens if a certain action is taken, e.g., if a drug is prescribed to a patient. When randomized experiments are not feasible, e.g., because of costs or ethical concerns, quantifying the effect of a treatment on an outcome can be very challenging. Roughly, this is because the analysis must ensure that the treated and untreated units are ?comparable,? a condition implied by proper randomization. In these settings, the analyst typically proceeds in two steps: 1) they introduce the key assumptions needed to identify the causal effect, and 2) they specify a model for the distribution of the data, often nonparametric, to accommodate modern, complex datasets, as well as the appropriate estimation strategy. One key difficulty in non-randomized studies is that estimating causal effects typically requires estimating nuisance components of the data distribution that are not of direct interest and that can be potentially quite hard to estimate. Focused on the second part of the analysis, this project aims to design optimal methods for estimating causal effects in different settings. Informally, an optimal estimator converges to the true causal effect ?as quickly as possible? as a function of the sample size and thus leads to the most precise inferences. Establishing optimality has thus two fundamental benefits: 1) it leads to procedures that make the most efficient use of the available data, and 2) it serves as a benchmark against which future methods can be evaluated. In this respect, the theoretical and methodological contributions of this project are expected to lead to substantial improvements in the analysis of data from many domains, such as medicine and the social sciences. The project also aims to offer opportunities for training and mentoring graduate and undergraduate students.

For certain estimands and data structures, the principles of semiparametric efficiency theory can be used to derive optimal estimators. However, they are not directly applicable to causal parameters that are ?non-smooth? or for which the nuisance parts of the data distribution can only be estimated at such slow rates that root-n convergence of the causal effect estimator is not attainable. As part of this project, the Principal Investigator aims to study the optimal estimation of prominent examples of non-smooth parameters, such as causal effects defined by continuous treatments. Furthermore, this project will consider optimal estimation of ?smooth? parameters, such as certain average causal effects, in newer nonparametric models for which relatively fast rates of convergence are possible, even if certain components of the data distribution can only be estimated at very slow rates. In doing so, the project aims to propose new techniques for reducing the detrimental effect of the nuisance estimators? bias on the quality of the causal effect estimator. It also aims to design and implement inferential procedures for the challenging settings considered, thereby enhancing the adoption of the methods proposed in practice.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413557","Collaborative Research: Systemic Shock Inference for High-Frequency Data","DMS","STATISTICS","07/01/2024","06/14/2024","Jose Figueroa-Lopez","MO","Washington University","Standard Grant","Jun Zhu","06/30/2027","$99,957.00","","figueroa@math.wustl.edu","ONE BROOKINGS DR","SAINT LOUIS","MO","63110","3147474134","MPS","126900","","$0.00","Unexpected ?shocks,? or abrupt deviations from periods of stability naturally occur in time-dependent data-generating mechanisms across a variety of disciplines. Examples include crashes in stock markets, flurries of activity on social media following news events, and changes in animal migratory patterns during global weather events, among countless others. Reliable detection and statistical analysis of shock events is crucial in applications, as shock inference can provide scientists deeper understanding of large systems of time-dependent variables, helping to mitigate risk and manage uncertainty. When large systems of time-dependent variables are observed at high sampling frequencies, information at fine timescales can reveal hidden connections and provide insights into the collective uncertainty shared by an entire system. High-frequency observations of such systems appear in econometrics, climatology, statistical physics, and many other areas of empirical science that can benefit from reliable inference of shock events. This project will develop new statistical techniques for the both the detection and analysis of shocks in large systems of time-dependent variables observed at high temporal sampling frequencies. The project will also involve mentoring students, organizing workshops, and promoting diversity in STEM.

The investigators will study shock inference problems in a variety of settings in high dimensions. Special focus will be paid to semi-parametric high-frequency models that display a factor structure. Detection based on time-localized principal component analysis and related techniques will be explored, with a goal towards accounting for shock events that impact a large number of component series in a possibly asynchronous manner. Time-localized bootstrapping methods will also be considered for feasible testing frameworks for quantifying the system-level impact of shocks. Complimentary lines of inquiry will concern estimation of jump behavior in high-frequency models in multivariate contexts and time-localized clustering methods.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2412629","Collaborative Research: Partial Priors, Regularization, and Valid & Efficient Probabilistic Structure Learning","DMS","STATISTICS","07/01/2024","06/17/2024","Chuanhai Liu","IN","Purdue University","Standard Grant","Yulia Gel","06/30/2027","$160,000.00","","chuanhai@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126900","","$0.00","Modern applications of statistics aim to solve complex scientific problems involving high-dimensional unknowns. One feature that these applications often share is that the high-dimensional unknown is believed to satisfy a complexity-limiting, low-dimensional structure. Specifics of the posited low-dimensional structure are mostly unknown, so a statistically interesting and scientifically relevant problem is structure learning, i.e., using data to learn the latent low-dimensional structure. Because structure learning problems are ubiquitous and reliable uncertainty quantification is imperative, results from this project will have an impact across the biomedical, physical, and social sciences. In addition, the project will offer multiple opportunities for career development of new generations of statisticians and data scientists.

Frequentist methods focus on data-driven estimation or selection of a candidate structure, but currently there are no general strategies for reliable uncertainty quantification concerning the unknown structure. Bayesian methods produce a data-dependent probability distribution over the space of structures that can be used for uncertainty quantification, but it comes with no reliability guarantees. A barrier to progress in reliable uncertainty quantification is the oppositely extreme perspectives: frequentists' anathema of modeling structural/parametric uncertainty versus Bayesians' insistence that such uncertainty always be modeled precisely and probabilistically. Overcoming this barrier requires a new perspective falling between these two extremes, and this project will develop a new framework that features a more general and flexible perspective on probability, namely, imprecise probability. Most importantly, this framework will resolve the aforementioned issues by offering new and powerful methods boasting provably reliable uncertainty quantification in structure learning applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413425","Collaborative Research: Synergies between Steins Identities and Reproducing Kernels: Modern Tools for Nonparametric Statistics","DMS","STATISTICS","07/01/2024","06/17/2024","Bharath Sriperumbudur","PA","Pennsylvania State Univ University Park","Standard Grant","Yong Zeng","06/30/2027","$179,999.00","","bks18@psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","126900","079Z","$0.00","The project aims to conduct comprehensive statistical and computational analyses, with the overarching objective of advancing innovative nonparametric data analysis techniques. The methodologies and theories developed are anticipated to push the boundaries of modern nonparametric statistical inference and find applicability in other statistical domains such as nonparametric latent variable models, time series analysis, and sequential nonparametric multiple testing. This project will enhance the interconnections among statistics, machine learning, and computation and provide training opportunities for postdoctoral fellows, graduate students, and undergraduates.

More specifically, the project covers key problems in nonparametric hypothesis testing, intending to establish a robust framework for goodness-of-fit testing for distributions on non-Euclidean domains with unknown normalization constants. The research also delves into nonparametric variational inference, aiming to create a particle-based algorithmic framework with discrete-time guarantees. Furthermore, the project focuses on nonparametric functional regression, with an emphasis on designing minimax optimal estimators using infinite-dimensional Stein's identities. The study also examines the trade-offs between statistics and computation in all the aforementioned methods. The common thread weaving through these endeavors is the synergy between various versions of Stein's identities and reproducing kernels, contributing substantially to the advancement of models, methods, and theories in contemporary nonparametric statistics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412833","Collaborative Research: Statistical Modeling and Inference for Object-valued Time Series","DMS","STATISTICS","07/01/2024","06/17/2024","Xiaofeng Shao","IL","University of Illinois at Urbana-Champaign","Standard Grant","Jun Zhu","06/30/2027","$174,997.00","","xshao@illinois.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","126900","","$0.00","Random objects in general metric spaces have become increasingly common in many fields. For example, the intraday return path of a financial asset, the age-at-death distributions, the annual composition of energy sources, social networks, phylogenetic trees, and EEG scans or MRI fiber tracts of patients can all be viewed as random objects in certain metric spaces. For many endeavors in this area, the data being analyzed is collected with a natural ordering, i.e., the data can be viewed as an object-valued time series. Despite its prevalence in many applied problems, statistical analysis for such time series is still in its early development. A fundamental difficulty of developing statistical techniques is that the spaces where these objects live are nonlinear and commonly used algebraic operations are not applicable. This research project aims to develop new models, methodology and theory for the analysis of object-valued time series. Research results from the project will be disseminated to the relevant scientific communities via publications, conference and seminar presentations. The investigators will jointly mentor a Ph.D. student and involve undergraduate students in the research, as well as offering advanced topic courses to introduce the state-of-the-art techniques in object-valued time series analysis.

The project will develop a systematic body of methods and theory on modeling and inference for object-valued time series. Specifically, the investigators propose to (1) develop a new autoregressive model for distributional time series in Wasserstein geometry and a suite of tools for model estimation, selection and diagnostic checking; (2) develop new specification testing procedures for distributional time series in the one-dimensional Euclidean space; and (3) develop new change-point detection methods to detect distribution shifts in a sequence of object-valued time series. The above three projects tackle several important modeling and inference issues in the analysis of object-valued time series, the investigation of which will lead to innovative methodological and theoretical developments, and lay groundwork for this emerging field.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413558","Collaborative Research: Systemic Shock Inference for High-Frequency Data","DMS","STATISTICS","07/01/2024","06/14/2024","Benjamin Boniece","PA","Drexel University","Continuing Grant","Jun Zhu","06/30/2027","$26,626.00","","cooper.boniece@drexel.edu","3141 CHESTNUT ST","PHILADELPHIA","PA","191042875","2158956342","MPS","126900","","$0.00","Unexpected ?shocks,? or abrupt deviations from periods of stability naturally occur in time-dependent data-generating mechanisms across a variety of disciplines. Examples include crashes in stock markets, flurries of activity on social media following news events, and changes in animal migratory patterns during global weather events, among countless others. Reliable detection and statistical analysis of shock events is crucial in applications, as shock inference can provide scientists deeper understanding of large systems of time-dependent variables, helping to mitigate risk and manage uncertainty. When large systems of time-dependent variables are observed at high sampling frequencies, information at fine timescales can reveal hidden connections and provide insights into the collective uncertainty shared by an entire system. High-frequency observations of such systems appear in econometrics, climatology, statistical physics, and many other areas of empirical science that can benefit from reliable inference of shock events. This project will develop new statistical techniques for the both the detection and analysis of shocks in large systems of time-dependent variables observed at high temporal sampling frequencies. The project will also involve mentoring students, organizing workshops, and promoting diversity in STEM.

The investigators will study shock inference problems in a variety of settings in high dimensions. Special focus will be paid to semi-parametric high-frequency models that display a factor structure. Detection based on time-localized principal component analysis and related techniques will be explored, with a goal towards accounting for shock events that impact a large number of component series in a possibly asynchronous manner. Time-localized bootstrapping methods will also be considered for feasible testing frameworks for quantifying the system-level impact of shocks. Complimentary lines of inquiry will concern estimation of jump behavior in high-frequency models in multivariate contexts and time-localized clustering methods.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -58,7 +66,6 @@ "2424045","Conference: 43rd Conference of Texas Statisticians","DMS","STATISTICS","06/15/2024","06/05/2024","Sunil Mathur","TX","The Methodist Hospital Research Institute","Standard Grant","Tapabrata Maiti","05/31/2025","$21,000.00","","smathur2@houstonmethodist.org","6670 BERTNER AVE","HOUSTON","TX","770302602","7134417885","MPS","126900","7556","$0.00","The 43rd Annual Conference of Texas Statisticians (COTS): AI, Machine Learning, and Other Related Statistical Techniques with Applications in Healthcare, scheduled for May 9-10, 2024, will be hosted at the Houston Methodist Research Institute (HMRI), situated at 6670 Bertner Ave, Houston, TX 77030, USA. Artificial intelligence (AI) and machine learning (ML) represent a transformative force across various industries, promising advancements in fields such as medical diagnosis, national security, and crime prevention. These technologies harness the power of data to generate models capable of learning, making decisions, and predicting outcomes. Over time, they refine and adapt, becoming more effective and versatile. However, the efficacy of AI and ML relies heavily on the principles and methodologies provided by statistical science. Statistical techniques underpin the construction of robust models in AI and ML, enabling the interpretation of their outputs. This synergy between AI, ML, and statistical science forms the backbone of cutting-edge advancements in data-driven decision-making. COTS, dedicated to AI, ML, and related statistical techniques serves as a crucial platform for statisticians to exchange insights and forge collaborative opportunities. Such gatherings drive innovation, pushing the boundaries of what is achievable with the integration of AI, ML, and statistical science.

COTS 2024 is dedicated to advancing the frontiers of AI and ML and related statistical techniques, particularly within healthcare. Experts will explore how AI can revolutionize treatment methodologies by harnessing patient-specific data, genetic profiles, and medical histories to tailor treatment plans with unprecedented precision, optimizing efficacy while minimizing adverse effects. COTS 2024 is committed to assembling a diverse array of leading experts, each bringing unique perspectives and expertise to the table. By fostering a robust scientific forum, the conference aims to facilitate rigorous discussions on the most recent research discoveries, spanning from fundamental research to practical applications aimed at enhancing human health and well-being. Moreover, COTS 2024 recognizes the importance of nurturing collaboration and mentorship within the scientific community. Through various networking opportunities and interactive sessions, the conference seeks to bridge the gap between junior and senior researchers, fostering an environment where knowledge exchange flourishes and innovative ideas take root and support underrepresented groups and minorities. In essence, COTS 2024 is not just a conference; it's a catalyst for transformative change, where cutting-edge research converges with real-world applications to shape the future of healthcare and beyond. Moreover, in collaboration with NSF, COTS 2024 is committed to uplifting underrepresented groups and minorities, ensuring that the benefits of progress are inclusive and accessible to all. NSF?s funding for COTS 2024 has facilitated the integration of diverse perspectives and expertise, driving forward the mission of COTS 2024 to enact meaningful change in healthcare and beyond, while prioritizing the empowerment of underrepresented groups and minorities.
Conference website: https://learn.houstonmethodist.org/AI-2024#group-tabs-node-course-default1

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413718","Computer-intensive methods for dependent and complex data","DMS","STATISTICS","06/15/2024","06/05/2024","Dimitris Politis","CA","University of California-San Diego","Standard Grant","Jun Zhu","05/31/2027","$300,000.00","","dpolitis@ucsd.edu","9500 GILMAN DR","LA JOLLA","CA","920930021","8585344896","MPS","126900","079Z","$0.00","Ever since the fundamental recognition of the potential role of the computer in modern statistics, the bootstrap and other computer-intensive statistical methods have been developed extensively for inference with independent data. Such methods are even more important in the context of dependent data where the distribution theory for estimators and test statistics may be difficult or impractical to obtain. Furthermore, the recent information explosion has resulted in datasets of unprecedented size that call for flexible, and by necessity computer-intensive, methods of data analysis. Time series analysis in particular is vital in many diverse scientific disciplines. As a consequence of the development of efficient and robust methods for the statistical analysis of dependent data, more accurate and reliable inferences may be drawn from datasets of practical importance resulting in appreciable benefits to the society. Examples include data from meteorology/atmospheric science (e.g. climate data), economics (e.g. stock market returns), biostatistics (e.g. fMRI data), and bioinformatics (e.g. genetics and microarray data). The project also involves developing curriculum, mentoring undergraduate students' research, supervising graduate students, and developing open-source software, organizing workshops.

The project focuses on the development of methods of inference for the analysis of dependent and otherwise complex data without relying on unrealistic and/or unverifiable model assumptions. In particular: (a) Subsampling and resampling for big data will be studied, including the notion of scalable subagging applied to deep learning to improve both speed as well as accuracy of estimation; (b) Central limit theorem for the median of a triangular array of dependent data will be proved with application to median-of-means and robust scalable subagging; (c) Model-free bootstrap will be studied and compared to conformal prediction in nonparametric regression; (d) A novel class of nonstationary dependent errors will be introduced with application to fitting large autoregressive (AR) models to nonstationary time series; (e) Markov resampling and linear process bootstrap will be developed for stationary random fields; (f) Skip-sampling of discrete Fourier transform ordinates will be introduced and compared to the traditional frequency domain bootstrap for stationary time series; (g) Smoothing estimators of time-varying covariance matrices will be constructed for locally stationary multivariate time series; (h) Bootstrap for time series with a seasonal component will be further developed; and (i) Multi-step ahead point and interval predictors will be constructed for nonlinear autoregressions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413074","False Discovery Control in Non-Standard Settings","DMS","STATISTICS","07/01/2024","06/05/2024","Armeen Taeb","WA","University of Washington","Continuing Grant","Yong Zeng","06/30/2027","$74,901.00","","ataeb@uw.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","126900","","$0.00","Controlling the false positive error in model selection is a prominent paradigm for gathering evidence in data-driven science. In model selection problems such as variable selection and graph estimation, models are characterized by an underlying Boolean structure, such as the presence or absence of a variable or an edge. Therefore, false positive error or false negative error can be conveniently specified as the number of variables/edges that are incorrectly included or excluded in an estimated model. However, the increasing complexity of modern datasets has been accompanied by the use of sophisticated modeling paradigms in which defining false positive error is a significant challenge. For example, models specified by structures such as partitions (for clustering), permutations (for ranking), directed acyclic graphs (for causal inference), or subspaces (for principal components analysis) are not characterized by a simple Boolean logical structure, which leads to difficulties with formalizing and controlling false positive error. A new perspective is needed to provide reliable inference in modern data analysis. The methods developed in this project have the potential to impact a wide range of fields as varied as image analysis, geosciences, computational genomics, and many others. The research will engage both graduate and undergraduate students and will be disseminated to a broader audience through the development of new courses.

In this project, the PI develops a generic framework to organize classes of models as partially ordered sets (posets), which leads to systematic approaches for defining natural generalizations of false positive error and methodology for controlling this error. The project aims to use the poset framework to address the following questions: what attributes of the poset structure determine the power and computational complexities of false positive error controlling procedures? How can we exploit specific structures in posets to design powerful model selection methods? How do we provide false discovery rate guarantees over posets? Can we utilize the framework for learning rooted phylogenetic trees and performing highly correlated variable selection?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2413715","Wasserstein guided nonparametric Bayes","DMS","STATISTICS","07/01/2024","05/30/2024","Debdeep Pati","TX","Texas A&M University","Standard Grant","Tapabrata Maiti","06/30/2027","$299,669.00","Anirban Bhattacharya","debdeep@stat.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126900","1269","$0.00","Stochastic generative models are a cornerstone of applied statistical modeling and inference. A generative model is an abstraction, and often a simplification, of a data generating mechanism using probabilistic tools, where specific features of interest regarding the generating mechanism are encapsulated into parameters of the generative model. Bayesian statistical inference is a popular statistical paradigm for combining such generative models for data with prior information about model parameters in a principled fashion to perform statistical inference on the unknown parameters. Some of the salient aspects behind the tremendous growth in popularity of Bayesian inference include principled incorporation of domain information, an in-built penalty for model complexity allowing automatic model selection, and facilitating borrowing of information across different domains via hierarchical modeling. However, being inherently model-based, Bayesian statistics is intrinsically susceptible to departures from the postulated generative model. Through this project, the investigators will explore and develop new statistical methodology for performing Bayesian inference allowing flexible departures from the generative model under consideration. A major focus will be the user-friendliness of the proposed approaches, circumventing the need for a user to explicitly build probabilistic models of increasing richness. The research will be disseminated through articles at prominent avenues and research presentations. Additionally, software packages for the methods developed will be made available publicly. The investigators are committed to enhancing the pedagogical component of the proposal through advising students and developing graduate and undergraduate topic courses.

Flexible nonparametric Bayesian methods have gained in popularity to address perceived issues of traditional Bayesian modeling regarding model-misspecification. The last thirty years have seen a proliferation of such methods, both in mainstream statistics as well as the machine learning community, as we continue to encounter increasing levels of complexities in modern datasets. However, nonparametric Bayesian methods can be challenging to implement as well as interpret. Furthermore, in many applications, the targets of interest are quite simple and it is essentially futile to model all aspects of the data. The fundamental aim of the proposed research is to develop a flexible Bayesian non-parametric approach that retains the generative modeling aspect of traditional parametric Bayesian modeling while avoiding a complete probabilistic specification of the data generating mechanism as typically performed in nonparametric Bayesian modeling. This will be performed by defining a modified likelihood function, leveraging ideas from the empirical likelihood literature as well as optimal transport theory, that centers around a user-specified parametric family of densities. An automated calibration procedure will be developed to control the extent of centering around the parametric model. The investigators will offer a firm theoretical underpinning of the proposed procedure and develop computationally efficient algorithms to carry out inferential tasks. The developed methods will be applied to scientific learning problems in neuroscience and nuclear physics to allow departures from existing scientific models in situations where their operating characteristics are less understood.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413858","Analysis of Non-Gaussian Tensor Time Series","DMS","STATISTICS","08/01/2024","05/29/2024","Rong Chen","NJ","Rutgers University New Brunswick","Standard Grant","Jun Zhu","07/31/2027","$300,001.00","Han Xiao","rongchen@stat.rutgers.edu","3 RUTGERS PLZ","NEW BRUNSWICK","NJ","089018559","8489320150","MPS","126900","","$0.00","The project is motivated by problems such as geo-political event prediction, crime data analysis, and modeling transportation and trading networks. Many data from these applications share three common and salient features: (i) they can be represented as tensors (multi-dimensional arrays), (ii) they are generated over time and exhibit dynamic relationship, and (iii) the values of the data are binary, counts, proportions etc. Such diverse data types, which are referred to as the non-Gaussian tensor time series, call urgently for the development of more adaptable analytical tools. The investigators introduce a general, flexible and efficient framework for the modeling, interpretation and prediction for such non-Gaussian tensor time series through dynamic factor models. The dynamic factor models contain an observation layer specified for the generation of the non-Gaussian observations, and a latent layer to account for the dynamic and concurrent dependence. They are capable of extracting dynamic information, enhancing comprehension of underlying mechanisms, and generating reliable forecasts, and are therefore poised to assist organizations and policymakers in making well-informed decisions. The project advances education through the research training of both undergraduate and graduate students, as well as its incorporation into special topic courses. The project is also committed to promoting diversity and inclusion in STEM fields, and actively seeks to recruit students from groups that are historically under-represented in science and engineering.

A novel dynamic matrix factor model for non-Gaussian data marks a significant advancement in modeling large and complex dependent data. These models effectively tackle challenges arising from the size, complexity, and discreteness of the data. More specifically, the dynamic is introduced in the hidden layer through the factor structure with tensor Tucker or CP decompositions, and a nonlinear or generalized linear model (Poisson, negative binomial, Gamma, zero-inflated, etc) is employed in the observation layer for the generation of the observations. An autocovariance-based approach is used for the estimation of the loading matrices and vectors, which takes advantage of the temporal dependence to reduce the bias. A tensor autoregressive model is imposed on the factors to enable the forecasting. For the estimation of the autoregressive model, again an autocovariance-based procedure is used to mitigate the impact of the estimation error of factors. This approach's computational efficiency is particularly well suited for handling big and complex data. The methodology and theoretical analysis lay the groundwork for applying the moment method in broader models and applications. Furthermore, the methodology underscores the significance of the ""blessing of dependence"" phenomenon, demonstrating how the temporal dependence can be utilized to enhance/reduce the signal/noise to achieve more accurate estimation, compared to the corresponding works under the IID setting. It is noteworthy that the framework accommodates extensions to more general distributions, and the developed methodology has broad applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413327","Scalable and Generalizable Inference for Network Data","DMS","STATISTICS","07/01/2024","05/22/2024","Srijan Sengupta","NC","North Carolina State University","Standard Grant","Yulia Gel","06/30/2027","$175,000.00","","ssengup2@ncsu.edu","2601 WOLF VILLAGE WAY","RALEIGH","NC","276950001","9195152444","MPS","126900","1269","$0.00","In an era where digital networks underpin crucial aspects of society and technology, from healthcare systems and social media to environmental monitoring and national security, understanding these complex networks is more important than ever. This project will advance the statistical analysis of complex and massive digital networks by addressing the challenges of accurately reflecting the diverse realities of networks and efficiently managing their vast scales. These advancements are expected to enable more reliable anomaly detection and robust analysis of large-scale networks through the introduction of novel statistical methods and computational tools. Furthermore, the project's educational and interdisciplinary initiatives are designed to equip the next generation of scientists, ensuring sustained impact across disciplines and contributing to the public good through engagement and nonprofit collaborations.

Addressing the limitations of traditional homogeneous models and computational inefficiencies, this project will contribute new methods to enhance statistical generalizability and scalability in network inference. The introduction of these flexible methodologies aims to improve the detection of anomalous motifs and the analysis of phenomena like the small-world property, core-periphery structures, and co-spectral graphs across diverse and complex network models. To overcome scalability challenges, the project introduces two novel algorithms, Predictive Subsampling (PredSub) and Aggregative Subsampling with Common Overlap (ASCO), designed to augment existing statistical methods for applicability to large datasets. These solutions will undergo thorough theoretical analysis and empirical validation, leveraging collaborations across fields such as epidemiology and digital health. With its potential to advance network data inference through methodological innovations and broad applications, the project promises significant intellectual merit and broader impacts, including educational programs, public engagement, and software development, fostering a multidisciplinary approach to solving contemporary scientific challenges.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406154","Conference: Workshop on Translational Research on Data Heterogeneity","DMS","STATISTICS","03/01/2024","01/18/2024","Xuming He","MO","Washington University","Standard Grant","Tapabrata Maiti","02/28/2025","$16,000.00","Lan Wang","hex@wustl.edu","ONE BROOKINGS DR","SAINT LOUIS","MO","63110","3147474134","MPS","126900","7556","$0.00","The Workshop on Translational Research on Data Heterogeneity is scheduled to take place at the University of Washington at St. Louis, April 6 -- 7, 2024. In this digital age, large-scale data offer many new opportunities, holding great promise for researchers and decision-makers to understand important variations among sub-populations (i.e., data heterogeneity), explore associations between features and rare outcomes (e.g., rare diseases or extreme events), and make optimal personalized recommendations in areas of immediate practical relevance such as precision medicine and social programs. The proposed workshop focuses on data heterogeneity to tap into the true potential of information-rich data.

There exist formidable computational and statistical challenges in the analysis of heterogenous data. Some of the key barriers include scalability to data size and dimensionality, deep exploration of heterogeneity and structures in the data, need for robustness and replicability, and the ability to make sense of incomplete observations (e.g., due to censoring). The proposed workshop will serve as a platform for bringing some of the leading scholars in statistics and data science together to exchange new research ideas and to train the next-generation data scientists in the analysis of heterogeneous data. The workshop will convene interdisciplinary researchers to discuss the forefront of heterogeneous data analysis and identify emerging areas for future research, emphasizing both methodology and applications.

Please visit https://sds.wustl.edu/events/workshop-translational-research-data-heterogeneity for updates.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -68,23 +75,17 @@ "2335570","Collaborative Research: Planning: FIRE-PLAN:High-Spatiotemporal-Resolution Sensing and Digital Twin to Advance Wildland Fire Science","DMS","S&CC: Smart & Connected Commun, STATISTICS, HDBE-Humans, Disasters, and th, Cross-BIO Activities, EPCN-Energy-Power-Ctrl-Netwrks","01/01/2024","08/09/2023","Ming Xin","MO","University of Missouri-Columbia","Standard Grant","Yulia Gel","12/31/2025","$51,998.00","","xin@missouri.edu","121 UNIVERSITY HALL","COLUMBIA","MO","652113020","5738827560","MPS","033Y00, 126900, 163800, 727500, 760700","019E, 042E, 042Z, 132Z, 5294, 7275","$0.00","The number of catastrophic wildfires in the United States has been steadily increasing in recent decades, which generate casualties, large loss of properties, and dramatic environmental changes. However, it is difficult to make accurate predictions of wildland fire spread in real time for firefighters and emergency response teams. Although many fire spread models have been developed, one of the biggest challenges in their operational use is the lack of ground truth fire data at high spatiotemporal resolutions, which are indispensable for model evaluation and improvements. The objective of this planning project is to bring together wildland fire science researchers, fire sensing and data science experts, and diverse stakeholders to develop standards and requirements for high-spatiotemporal-resolution wildland fire sensing and digital twin construction. An organizing committee will be formed from wildland fire science, engineering, and stake holder communities including fire ecology and behavior modeling, pollution monitoring, robotics, cyber physical systems (CPS), wildfire fighting, indigenous cultural burns, and prescribed fires. A series of physical and remote workshops will be held focusing on themes such as open fire data for wildland fire modeling validation, digital twins for prescribed fires, and safe and efficient wildland fire data collection.

Research tasks of this planning project include: 1) identification of key high-spatiotemporal-resolution fire metrics and data representations to support fire model validation and fire operations, 2) proposition of sensing strategies and algorithms for fire sensing and suppression robots and cyber physical systems that can support safe and efficient collection of desired high-resolution fire data, 3) development and evaluation of data assimilation and digital twin construction using high-resolution data to advance fire behavior modeling, coupled fire-atmosphere modeling, and smoke modeling, and 4) prototype and initial fire data ecosystem demonstration including collection of cultural burn data and establishment of GeoFireData, a benchmark fire data sharing and digital twin website, which can support different fire operation types such as fire spread model validation and controlled burn planning. The special attention will be devoted to interdisciplinary training of the next generation of scientists working with wildfire risks at the interface of computational sciences, engineering, ecology, and data sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2426029","Conference: Building a robust community: Joint International Conference on Robust Statistics and Conference on Data Science, Statistics, and Data Science","DMS","STATISTICS","07/01/2024","04/30/2024","David Kepplinger","VA","George Mason University","Standard Grant","Tapabrata Maiti","06/30/2025","$20,993.00","Anand Vidyashankar","dkepplin@gmu.edu","4400 UNIVERSITY DR","FAIRFAX","VA","220304422","7039932295","MPS","126900","7556","$0.00","The award will provide travel support for early-career researchers and students in statistics, data science and related fields to attend the International Conference on Robust Statistics (ICORS) and the Conference on Data Science, Statistics and Visualization (DSSV) hosted at George Mason University in Fairfax, VA, from July 29 ? August 1, 2024. The organizers will work to recruit under-represented minorities in the above groups to actively participate in the conference by actively reaching out through the Caucus of Women in Statistics, the Washington Statistical Society and other chapters and sections of the American Statistical Association. The joint conference will bring together researchers, students and practitioners interested in the interplay of robust statistics, data analysis, computer science, and visualization and to build bridges between these fields for interdisciplinary research. Creating a forum to discuss recent progress and emerging ideas in these disciplines, the joint conference will facilitate fruitful dissemination and cross-pollination amongst various research groups. Early-career researchers and students will have the opportunity to share their research and ideas through presentations and a poster competition, and build connections with senior experts and practitioners. Building upon the successful history of ICORS and DSSV, the conferences also play an essential role in maintaining a cohesive group of international experts interested in robust statistics and related topics, whose interactions transcend the meetings and endure year-round.

Artificial Intelligence (AI) is becoming an inherent part of our lives, and several federal and state government agencies, research institutes, and industries are adopting these AI tools for various activities that could potentially improve real-life experiences. While there are several issues to be addressed in AI-based methods, the robustness of the Machine learning (ML) algorithms is a fundamental issue wherein one is concerned with adversarial contamination that can cause ML algorithms to fail. Associated with AI methods are privacy challenges, as modern methods tend to focus on personalized responses to AI responses. This joint conference will create a forum to discuss recent progress and emerging ideas on the interplay of robustness, interpretability and visualization for AI- and ML-methods and encourage informal contacts and discussions among all the participants. The conference plans to achieve this goal through several sessions and keynote addresses in these areas, integrating multiple disciplines, including privacy, Omics, spatial analytics, urban analytics, biostatistics, robustness, and visualization. The conference website can be found at https://icors-dssv2024.statistics.gmu.edu.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413618","Conference: Inaugural Berkeley-Stanford Workshop on Veridical Data Science","DMS","STATISTICS","05/01/2024","04/25/2024","Bin Yu","CA","University of California-Berkeley","Standard Grant","Tapabrata Maiti","04/30/2025","$11,000.00","","binyu@stat.berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126900","7556","$0.00","The Inaugural Berkeley-Stanford Workshop on Veridical Data Science will be held on Friday
May 31, 2024, at BIDS on UC Berkeley campus. The organizing committee consists of
Bin Yu (UC Berkeley, co-chair), Russ Poldrack (Stanford, co-chair), Maya Mathur
(Stanford), and Tiffany Tang (University of Michigan). This conference is jointly hosted
by the Berkeley Institute of Data Science (BIDS) and the Department of Statistics, parts of
UC Berkeley's College of Computing, Data Science, and Society (CDSS) and Stanford
Data Science Center for Open and Reproducible Science (SDS-CORES).


Data science is playing a ubiquitous role in science, society, and beyond, underscoring
the urgent need to ensure the trustworthiness and safety of data science including
machine learning. The data science life cycle (DSLC) is often a complex and multi-step
process, including domain problem formulation, data collection and cleaning, data
visualization, model/algorithm development, post-hoc visualization, interpretation,
vetting and communication. In every step of a DSLC, human judgment calls are made
and often unaccounted for in the traditional uncertainty quantification. Veridical data
science (VDS) is the practice of rigorously conducting data analysis while making
human judgment calls and using domain knowledge to extract and communicate useful,
trustworthy information from data to solve a real-world domain problem. The
Predictability-Computability-Stability (PCS) framework and documentation have been
developed towards veridical data science. This conference is focused on veridical
(truthful) data science (VDS) for responsible data analysis and decision-making. There
will be 4 keynote speakers and 9 invited speakers. We expect around 100?150
attendees from both academia and industry. 8-10 lightning talk speakers will be
selected based on submitted abstracts. This workshop intends to build a community of
veridical data science researchers. https://na.eventscloud.com/website/69057

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2412746","New nonparametric theory and methods for censored data","DMS","STATISTICS","10/01/2024","04/23/2024","Bin Nan","CA","University of California-Irvine","Standard Grant","Jun Zhu","09/30/2027","$300,000.00","","nanb@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126900","079Z","$0.00","Estimating the survival time distribution given a set of predictors is of great importance in biomedical research and epidemiological studies, where the survival time is often censored, thus unobserved, due to dropouts or limited follow-up time. To obtain robust results, making weak model assumptions is desirable. This project focuses on two sets of tools without making assumptions about the functional form of any effect of a predictor on the survival time: one is a classical approach based on spline basis expansion, and the other is a modern approach based on deep neural networks. For the spline method, the project aims to develop a generally applicable distributional theory for the estimates of unknown functions in several widely used survival models, which is needed for making proper statistical inference but still lacking in the current literature. Furthermore, the deep neural network approach makes the weakest possible assumption and is the most flexible estimating method for an unknown multivariate function. The project considers deep neural networks with a full likelihood-based loss function for censored survival data and more general types of predictors that can randomly vary with time. The project aims to investigate both the numerical implementation and the theory for the estimation precision. This work will foster interdisciplinary research with epidemiologists, nephrologists, neurologists, and other scientists working on real scientific studies, and contribute to the well-being of human beings and the scientific community in a significant way through its versatile real-life applications, thus create an impact in and beyond statistical periphery.

Spline basis expansion is a commonly used approach for approximating an unknown smooth function, hence widely applied in estimating functional parameters. It is too often, however, that the approximation is treated as ?exact? in practice so to treat a nonparametric estimation problem as a parametric one because the asymptotic distributional theory for the spline estimation is lacking for models beyond the nonparametric linear model. The project takes advantages of recent developments in the random matrix theory to tackle the distributional theoretical problem of spline estimates in a broad range of commonly used statistical models in censored data analysis. The most general nonparametric problem is to estimate the conditional distribution other than, for example, the conditional mean or median. With the conditional distribution at hand, prediction becomes a choice of a particular characteristic of the conditional distribution and a prediction interval can be easily obtained. The project focuses on full likelihood-based loss functions characterized by the conditional hazard function and applies either deep neural networks or deep operator networks for the estimation of the conditional distribution function given functional covariates. In survival analysis, the functional covariates can be time-varying covariates that affect the hazard function in an arbitrarily way, for which no estimating method exists in the literature. Convergence rates of considered neural network methods with functional inputs will be established.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2423098","Conference: Forty Years at the Interplay of Information Theory, Probability and Statistical Learning","DMS","STATISTICS","05/01/2024","04/22/2024","Daniel Spielman","CT","Yale University","Standard Grant","Tapabrata Maiti","04/30/2025","$12,500.00","","spielman@cs.yale.edu","150 MUNSON ST","NEW HAVEN","CT","065113572","2037854689","MPS","126900","7556","$0.00","The award will support participants attending the conference ?Forty Years at the Interplay of Information Theory, Probability and Statistical Learning?, which will take place at Yale University during April 26?28, 2024. The conference is a three-day meeting comprising a diverse array of activities, including a poster session tailored for students, a reception aimed at fostering networking and connections among participants, and twenty-five research talks. The scientific theme of this conference is to explore the dynamic relationship and synergy between information theory, probability, and statistical learning. Beyond academic exploration, the conference aspires to nurture and inspire the next generation of scholars. Through engaging with leading experts, students and early career researchers will have the opportunity to gain insights into recent advancements and emerging challenges in these fields. We will actively encourage participants from underrepresented groups in several ways. We will collaborate with minority student organizations, professional associations, and community groups both within and outside Yale University to promote the workshop and leverage their networks for outreach, and we will offer financial assistance to minority participants to help cover the cost of attendance, travel, or accommodations to remove barriers to participation.

Statistics and information theory are deeply intertwined, both rooted in probability theory. Over the past four decades, this relationship has been meticulously explored and leveraged. In today's era marked by an unprecedented abundance of data across diverse domains and the growing influence of artificial intelligence, the indispensable tools wielded in these three disciplines continue to pave the way for discovering new limits of learning with complex data across various modalities. This conference serves as a gathering of leading researchers in these three disciplines and the next generation of data science leaders. Together, they will discuss new ideas to explore and enhance the connections between these fields, driving forward process and innovation. The website for the conference is: https://yalefds.swoogo.com/infotheory/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2413671","Travel: Junior travel support for the 2024 World Meeting of the International Society for Bayesian Analysis","DMS","STATISTICS","05/01/2024","04/19/2024","Sinead Williamson","TX","University of Texas at Austin","Standard Grant","Tapabrata Maiti","10/31/2024","$20,000.00","","sinead.williamson@mccombs.utexas.edu","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","126900","","$0.00","This grant will fund 25 travel awards for US-based junior researchers attending the 2024 ISBA (International Society for Bayesian Analysis) World Meeting, to be held in Venice, Italy from 1-7 July 2024. The meeting's website is https://www.unive.it/web/en/2208/home. The ISBA World Meetings are the largest conferences in Bayesian statistics, attracting attendees from all around the world. The travel awards, averaging $800 per person, will partially offset the cost of travelling to Venice from the US, helping PhD students and other junior researchers to participate in the meeting. The selection committee will prioritize funding female researchers and members of minority groups underrepresented in the field.

The 2024 ISBA World Meeting will feature keynote talks, invited and contributed talks, poster sessions, and short courses, selected to showcase cutting-edge research in Bayesian statistics. Attendance at the meeting will offer attendees a chance to learn about emerging research topics in Bayesian statistics. In addition, the scientific committee has selected as part of the program multiple talks and posters by junior researchers. This offers junior researchers an opportunity to share their research with an international audience of Bayesian statisticians.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2410953","Conference: ICSA 2024 Applied Statistical Symposium","DMS","STATISTICS","06/15/2024","02/27/2024","Qingxia Chen","TN","Vanderbilt University Medical Center","Standard Grant","Tapabrata Maiti","05/31/2025","$20,000.00","Dandan Liu","cindy.chen@vumc.org","1161 21ST AVE S STE D3300 MCN","NASHVILLE","TN","372320001","6153222450","MPS","126900","7556","$0.00","This award will play a pivotal role in promoting inclusivity and advancing the field of statistics by supporting the participation of graduate students, early-career researchers, and underrepresented groups in the International Chinese Statistical Association (ICSA) 2024 Applied Statistics Symposium, which will be held in Nashville, Tennessee from June 16-June 19, 2024. With the overarching theme of ""Data-Driven Decision Making: Unleashing the Power of Statistics?, the symposium will focus on collaboration and diversity. The event will not only promote education, research, and practical applications but also address broader societal goals by encouraging participation from women, minorities, and individuals with disabilities. The symposium's impact will extend beyond technical discussions, emphasizing professional development and bridging gaps in STEM fields through mentoring, career development, and opportunities for the next generation of statisticians.
The conference is a comprehensive platform designed to advance statistical theory, computational methods, and practical applications. With plenary talks, invited sessions, student paper competitions, contributed posters, and short courses, the conference covers a broad spectrum of topics crucial to the evolving landscape of statistics, data science, and artificial intelligence. A key technical component includes the integration of foundational statistical theory with advanced computational methods, addressing practical challenges in various scientific domains. Special sessions, such as the panels on mentoring and career development, provide a focused forum to discuss strategies for promoting diversity and inclusion, particularly for women and individuals underrepresented in STEM. The symposium's website, accessible at https://symposium2024.icsa.org/, serves as a hub for seamless communication and resource sharing among participants.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409890","Conference: SDSU Data Science Symposium","DMS","STATISTICS","02/01/2024","01/19/2024","Semhar Michael","SD","South Dakota State University","Standard Grant","Tapabrata Maiti","07/31/2024","$7,500.00","Gemechis Djira, Thomas Brandenburger","Semhar.Michael@sdstate.edu","940 ADMINISTRATION LN","BROOKINGS","SD","570070001","6056886696","MPS","126900","7556, 9150","$0.00","South Dakota State University will host the 6th Annual SDSU Data Science Symposium at the SDSU campus from February 5 to 6, 2024. The symposium brings together students, faculty, researchers, and industry professionals who engage in foundational research and applications of data science. This event, held annually since 2018 (excluding 2021 due to the COVID-19 pandemic) includes pre-conference workshops, keynote speakers, parallel oral presentations, undergraduate and graduate student poster presentations and competitions, as well as a career fair. Historically, more than 200 participants have attended, including students from up to 16 universities and representatives from up to 23 companies. With the 2024 event, this award will help expand both student participation and the number of junior speakers from rural, under-represented, and under-served areas of the Midwest and beyond.

The field of data science is expanding and interdisciplinary involving statisticians, computer scientists, mathematicians, etc. The SDSU-DSS stands out as a unique event in the region, bringing together participants from academia and industry to the Midwest. Parallel session tracks feature speakers from diverse fields such as statistics, mathematics, computer science, healthcare, finance, forensics, precision agriculture, and other data science-related topics. The symposium facilitates networking, collaborations, and exposes students to various career paths within mathematics, statistics, computer science, and other STEM areas. The symposium aims to 1) bring unique opportunities to the Midwest region, where students, faculty, business leaders of the region, and practitioners all gather to discuss the applications and foundation of data science; 2) provide hands-on, four-hour-long events on emerging topics/tools used in data science; 3) host presentations covering foundational and use-case aspects of data science and garnering interactive discussions and future collaborations 4) expand networks during the career fair and exhibit sessions, connecting faculty, students, and hiring managers of companies in the area. The presentations and other content will be disseminated through Open PRAIRIE, an open-access institutional repository, ensuring widespread knowledge dissemination. The conference website is www.sdstate.edu/datascience.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2339439","CAREER: Towards a general recipe for fast high-dimensional scientific computing","DMS","APPLIED MATHEMATICS, STATISTICS","02/15/2024","02/12/2024","Yuehaw Khoo","IL","University of Chicago","Continuing Grant","Dmitry Golovaty","01/31/2029","$84,529.00","","ykhoo@uchicago.edu","5801 S ELLIS AVE","CHICAGO","IL","606375418","7737028669","MPS","126600, 126900","1045","$0.00","This project addresses the curse of dimensionality in solving the many-body Fokker-Planck and Schrödinger partial differential equations (PDEs), which are fundamental to understanding and predicting molecular structures, material properties, chemical reactions, extreme weather events, and pattern formations at various physical scales. The investigator aims to develop a general method to overcome high dimensionality of these PDEs via developing an iterative solver that combines the advantages of tensor-network, Monte Carlo, and convex optimization methods. The main idea is to solve for only a small number of descriptors of the solution (e.g., the statistical moments of the solution) and then recover a compressed representation of the solution through these descriptors. An improved solution procedure will contribute to the Material Genome Initiative by developing new computational tools for physical and chemical simulations. The proposed education plan aims to train graduate students for quantitative research at the intersection of mathematical and physical sciences, fostering a new generation of researchers well-equipped to tackle problems of national interest in scientific computing, machine learning, and quantum computing. Through research advising, a summer mentoring program, and the development of a summer school for quantum mechanics, the proposal aims to encourage the participation of underrepresented students in scientific research and higher education.

Currently, Monte Carlo methods have been widely successful in many practical physical and chemical simulation tools due to their flexibility, despite potential drawbacks such as slow mixing time and high variance. An alternative approach to characterizing chemical/physical systems is to deterministically solve for the solution of a PDE over the entire space, which can work only for small (and consequently low-dimensional) problems. The proposed research attempts to address the limitations of sampling-based and PDE approaches through the development of an iterative solver. It involves fast iterations achieved by alternating between short-time Monte Carlo simulations and estimating a tensor-network ansatz. It relies on the initialization strategy underpinned by convex optimization in order to reduce the number of iterations. Monte Carlo variance of traditional sampling methods is significantly reduced since only a small number of tensor-network parameters need to be estimated. On the other hand, it significantly extends the flexibility of tensor-network methods by allowing stochastic operations. To this end, a novel tensor-network-based generative model is proposed where density can be learned from empirical samples without the use of any optimization. It would impact statistics by providing new density estimators and analysis without the curse of dimensionality. Further, a new moment method based on convex optimization is proposed for solving high-dimensional PDEs. This would develop mathematical programming, a tool traditionally used in operations research, into an effective tool for physics simulations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2409876","Conference: The 9th Workshop on Biostatistics and Bioinformatics","DMS","STATISTICS","05/01/2024","04/10/2024","Yichuan Zhao","GA","Georgia State University Research Foundation, Inc.","Standard Grant","Tapabrata Maiti","04/30/2025","$10,000.00","","yichuan@gsu.edu","58 EDGEWOOD AVE NE","ATLANTA","GA","303032921","4044133570","MPS","126900","7556","$0.00","The 9th Workshop on Biostatistics and Bioinformatics will be held at Georgia State University, May 03-05, 2024. It will provide a platform for senior researchers, junior researchers, and graduate students to discuss the latest advances and challenges in the field. The main objective of the workshop is to address emerging challenges in applications of AI, causal inference, and statistical genomics data analysis. The workshop will feature a keynote speaker, leading experts and young researchers, and it provides an invaluable opportunity for graduate students and young researchers to gain experience giving poster presentations. To present posters will help them to receive feedback from experts in the field, and engage in discussions with fellow attendees. The workshop will provide a distinctive opportunity for collaboration, discussion, and dissemination of ideas. In addition, the workshop places special emphasis on supporting young people, underrepresented individuals, and women through financial supports, aiming to cultivate an inclusive environment. Through the integration of interactive sessions, networking opportunities, and a commitment to the diversity, the workshop can enhance its overall impact.


The workshop aims to push the boundaries of biostatistics and bioinformatics through collaborative efforts among various universities. The workshop maintains a very strong program, which includes one keynote speech by a renowned statistician, invited talks by established and emerging experts, poster presentations from junior researchers and graduate students. The workshop will also offer a short course ""Tutorial on Deep Learning and Generative AI"" and five Best Student Poster Awards will be announced during the award ceremony. Special effort is dedicated to forging connections with historically black universities in the Metro Atlanta area, by inviting underrepresented individuals to participate in the workshop. We expect that the workshop will attract a significant number of participants from underrepresented groups. Travel support is available for junior researchers, graduate students, and underrepresented people by promoting the inclusivity and diversity within the workshop. More information about the workshop can be found at the website: https://math.gsu.edu/yichuan/2024Workshop/index.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404998","Conference: The 2024 Joint Research Conference on Statistics in Quality, Industry, and Technology (JRC 2024) - Data Science and Statistics for Industrial Innovation","DMS","STATISTICS","03/15/2024","03/11/2024","Yili Hong","VA","Virginia Polytechnic Institute and State University","Standard Grant","Tapabrata Maiti","02/28/2025","$12,000.00","","yilihong@vt.edu","300 TURNER ST NW","BLACKSBURG","VA","240603359","5402315281","MPS","126900","7556","$0.00","This project funds U.S. based student participation in the 2024 Joint Research Conference on Statistics in Quality, Industry and Technology (JRC 2024), which will be held in Waterloo, Ontario, Canada, from June 17-20, 2024, at the University of Waterloo. The organization of this
conference is also in partnership with Virginia Tech. JRC 2024 is a joint meeting of the 29th Spring Research Conference on Statistics
in Industry and Technology (SRC) and the 40th Quality and Productivity Research Conference (QPRC), which happens once every four years.
The theme of JRC 2024 is ""Data Science and Statistics for Industrial Innovation."" JRC 2024 aims to bring together researchers and
practitioners worldwide who use statistics in quality, technology, and industrial contexts. The conference promotes communication
among researchers and practitioners to enable and ensure the development and widespread use of novel insights and methodology.
JRC 2024 has the potential to benefit society by offering participants the opportunities to gain knowledge and reshape their
perspectives on topics associated with data science, statistics, and machine learning. JRC 2024 will advocate for the ethical
application and understanding of data science, statistics, and machine learning for industrial innovation, which is beneficial for
the long-term competitiveness of the U.S. industry. The conference provides a platform to disseminate knowledge to the broader
community by sharing short course lecture notes, presentation slides, and posters on the conference website. JRC 2024 aims to broaden
the participation of underrepresented groups (i.e., women, racial/ethnic minorities, etc.) in STEM disciplines.

JRC 2024 focuses on recent advancements in methodology, best practices, and innovative applications. Participation in JRC 2024 has the
potential to advance knowledge and understanding of topics related to data science, statistics, and machine learning and how they can
be relevant to industrial innovation. This conference traditionally attracts prominent statisticians, data scientists, quantitative
analysts, and others with an established record of highly influential, methodological, and interdisciplinary research. These individuals
will have the opportunity to discuss the current progress made in statistics and machine learning, such as big data technology,
text modeling, the use of generative artificial intelligence in industrial innovation, and exchange novel ideas and experiences in
working with modern data science to discover knowledge and apply it to numerous fields. JRC 2024 has the potential to disseminate
new methods and data-driven approaches, the evaluation of previous findings, and the validation of theoretical approaches,
stimulate further investigations regarding the benefits of working with statistics and machine learning methods for industry and
increase the awareness of the need to use data science approach in industry. The conference will include three plenary presentations,
18 invited paper sessions, four to six contributed sessions, a poster session, a technical tour, and a one-day short course.
More details on the conference can be found on its web page:
https://uwaterloo.ca/joint-research-conference-statistics-quality-industry-technology/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2347284","Conference: Design and Analysis of Experiments 2024","DMS","STATISTICS","02/01/2024","12/06/2023","John Morgan","VA","Virginia Polytechnic Institute and State University","Standard Grant","Tapabrata Maiti","01/31/2025","$18,000.00","Xinwei Deng, Anne Driscoll","jpmorgan@vt.edu","300 TURNER ST NW","BLACKSBURG","VA","240603359","5402315281","MPS","126900","7556","$0.00","The Design and Analysis of Experiments Conference 2024 (DAE 2024) will meet May 15-17, 2024 on the campus of Virginia Tech in Blacksburg, VA. It will bring together researchers from across the United States and beyond, and from both academia and industry, to focus on advancing the statistical techniques for experimentation that empower knowledge discovery. It will provide a forum for interaction, discussion, and exchange of ideas on novel research for designing effective experiments, and for analyzing the data that they produce. The aim of the conference is to increase the efficacy of data collection in areas as wide-ranging as autonomous driving, drug development, environmental monitoring, infectious disease dynamics, cybersecurity, and manufacturing, among many others, and so accelerate the pace of innovation in all of these domains. DAE 2024 will emphasize inclusion and mentoring of young researchers and minorities, and in so doing will be a cog in the development of the next generation of statistical experts in the techniques of experimental design.

Designed experimentation and the corresponding techniques for analysis are integral to the process of scientific discovery, be it in engineering, medicine, commerce, manufacturing, or indeed in any of the vast range of human activities where continuing knowledge acquisition is a requirement for advancement and success. Driven by these needs, developments are rapidly taking place in experimental design and analysis research, in both traditional and emerging areas of applications. As new areas of application arise, correspondingly new computational tools are enabling the development of better designs for data collection in complex problems. Technical sessions of DAE 2024 will include leading experts addressing Covering Arrays and Combinatorial Testing; Online Experimentation; Sequential Design, Active Learning, and Bayesian Optimization; Design Issues in Uncertainty Quantification; Orthogonal Arrays and Related Designs; Causal Inference and Experimental Design; Design Challenges in Transportation; and more. Additional features will include roundtable discussions, mentoring sessions for junior researchers, and poster sessions highlighting advancements in addition to those covered in the technical sessions. Further details about the conference may be found at https://sites.google.com/view/dae2024/dae-2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2342821","Conference: Emerging Statistical and Quantitative Issues in Genomic Research in Health Sciences","DMS","STATISTICS","02/01/2024","01/24/2024","Xihong Lin","MA","Harvard University","Standard Grant","Tapabrata Maiti","01/31/2027","$61,920.00","","xlin@hsph.harvard.edu","1033 MASSACHUSETTS AVE STE 3","CAMBRIDGE","MA","021385366","6174955501","MPS","126900","7556","$0.00","The 2023 Conference of the Program in Quantitative Genomics (PQG), entitled ?Diversity in Genetics and Genomics? will take place at the Joseph B. Martin Conference Center at the Harvard Medical School on October 17-18, 2023. This long-standing Harvard T. H. Chan School Public Health Program in Quantitative Genomics Conference series focuses on timely interdisciplinary discussions on emerging statistical and computational challenges in genetic and genomic science. The focus of each conference evolves in parallel to scientific frontiers. A key feature of the series is its interdisciplinary nature, where quantitative and subject-matter scientists jointly discuss statistical and quantitative issues that arise in cutting-edge genetic and genomic research in human diseases. Conference participants critique existing quantitative methods, discuss emerging statistical and quantitative issues, identify priorities for future research, and disseminate results. Diversity in genetic and genomics has been increasingly embraced not only for enabling more powerful studies but also because of the need to avoid further exacerbation of structured inequalities in healthcare systems and to chart a path forward for their amelioration. Significant effort has been made in recent years to improve study participant and workforce diversity in genetics and genomics, including the inclusion of diverse groups in discovery and functional studies and translational efforts to empower or pave the road for equitable clinical impact. The 2023 conference will provide a platform to engage inter-disciplinary researchers to have in-depth discussions on the quantitative challenges and opportunities in increasing diversity in genetic and genomic research. We will make serious efforts to recruit junior researchers, including graduate students, postdoctoral fellows, in particular underrepresented minorities and women, as speakers and participants.

The impetus for the 2023 conference theme comes from the pressing need to address the statistical and quantitative issues in diversity in genetic and genomic research. The three topics of the conference include (1) Diversity for gene mapping and studying variant functions; (2) Diversity for translational genetics: polygenic risk and clinical implementation; (3) How do we move forward while acknowledging the past? Examples of the first topic include multi-ancestry genetic association tests, fine-mapping, and eQTL analysis. Examples of the second topic include trans-ethnic polygenic risk prediction and transferred learning. Examples of the third topic include enhancing transparency in the use of population descriptors in genomics research and building global collaborative genetic research frameworks. The education and research activities discussed at the conference will make important contributions to advance efforts on increasing diversity of genetic and genomic research, and will help create the scientific basis and workforce required to ensure and sustain US competitiveness both economically and technologically, prolonging and saving lives, and promoting national security. For more information, see www.hsph.harvard.edu/pqg-conference/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2403813","Conference: Theory and Foundations of Statistics in the Era of Big Data","DMS","STATISTICS","02/01/2024","02/01/2024","Xin Zhang","FL","Florida State University","Standard Grant","Tapabrata Maiti","01/31/2025","$14,800.00","Srijan Sengupta","henry@stat.fsu.edu","874 TRADITIONS WAY","TALLAHASSEE","FL","323060001","8506445260","MPS","126900","7556","$0.00","The Department of Statistics at Florida State University (FSU) will host a three-day conference titled ""Theory and Foundations of Statistics in the Era of Big Data"" in Tallahassee, Florida, from April 19 to 21, 2024. The main objective of the conference is to bring together a global community of statisticians and data scientists to chart the state-of-the-art, challenges, and the future trajectory of contemporary statistical foundations, theory, and practice. The format of the conference includes three plenary sessions, six invited sessions showcasing current senior leaders in the field who have made foundational contributions to statistics, two special invited sessions for early-career researchers, a poster session for graduate students, and a banquet talk by a leading expert. The special invited sessions and poster session will provide a unique opportunity for early-career researchers and graduate students not only to showcase their research work but also to benefit from in-depth intellectual interactions with leaders in the field in a small conference setting.

The main objective of the conference is to bring together present-day statistics and science innovators and senior leaders with emerging young researchers to identify, discuss, and decipher solutions to these foundational issues and challenges faced by modern-day statistics and data science. Providing support for junior researchers and graduate students who do not have access to other sources of funding to attend this important and timely gathering of researchers working on the foundational aspects of statistical sciences is also key to maintaining the current leadership of U.S. institutions in this field. It is extremely timely to have such an event to stimulate and comprehend the major contemporary challenges in the foundation, theory, and implementation of the field that is currently playing such an important role in every sphere of social media, economic security, public health, and beyond. This conference will be in partnership with the International Indian Statistical Association (IISA) and co-sponsored by the American Statistical Association (ASA), the National Institute of Statistical Science (NISS), and the Institute of Mathematical Statistics (IMS). The conference website is https://sites.google.com/view/theory-and-foundations-of-stat/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349991","Conference: Statistics in the Age of AI","DMS","STATISTICS","03/01/2024","12/18/2023","Xiaoke Zhang","DC","George Washington University","Standard Grant","Tapabrata Maiti","02/28/2025","$18,400.00","","xkzhang@gwu.edu","1918 F ST NW","WASHINGTON","DC","200520042","2029940728","MPS","126900","7556","$0.00","The conference ?Statistics in the Age of AI? will be held at George Washington University, Washington, DC on May 9-11, 2024. With the boom of artificial intelligence (AI), partly accelerated by the launching of large language models (e.g., ChatGPT), AI tools have reached every corner of our society. In this era where many business and scientific problems are being tackled via AI systems, statistics has become more critical than ever since it can offer uncertainty quantification, causal analysis, and interpretability among others, which most AI systems are lacking. This conference will bring together researchers and practitioners in academics and industries to explore the impact of AI on statistical research, education, and practice and also to brainstorm how statistics can contribute to AI. The conference organizers encourage participation and attendance by students, post-doctoral scholars, early-career researchers, and individuals from underrepresented groups.

The conference features short courses, poster and oral presentations, and panel discussions. The two short courses will focus on causal inference and conformal inference respectively. The presentations and panel discussions will address efficient handling of data for AI models and architectures, uncertainty quantification, and responsible decision-making among other topics. Further information will become available on the conference website: https://statistics.columbian.gwu.edu/statistics-age-ai.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2340241","CAREER: New Frameworks for Ethical Statistical Learning: Algorithmic Fairness and Privacy","DMS","STATISTICS","07/01/2024","01/23/2024","Linjun Zhang","NJ","Rutgers University New Brunswick","Continuing Grant","Yong Zeng","06/30/2029","$90,127.00","","linjun.zhang@rutgers.edu","3 RUTGERS PLZ","NEW BRUNSWICK","NJ","089018559","8489320150","MPS","126900","1045","$0.00","With the unprecedented impact of data science and machine learning in many aspects of our daily lives, such as healthcare, finance, education, and law, there is an urgent need to design ethical statistical learning algorithms that account for fairness and privacy. This project tackles the challenge of integrating ethical principles into the fabric of statistical learning. The approach prioritizes fairness by enhancing statistical algorithms to perform equitably, particularly in scenarios with limited sample sizes and where sensitive attributes are restricted by legal or societal norms. In parallel, this project addresses privacy by developing a general framework for studying the privacy-accuracy trade-off under new privacy constraints emerging with the advances in generative AI. The practical upshot of this work is the application of these methods to biomedical fields, accompanied by the release of open-source software, broadening the impact and encouraging ethical practices in statistical learning across various domains. This project promotes equitable and private data handling and provides research training opportunities to students.

The research objective of this project is to develop rigorous statistical frameworks for ethical machine learning, with a focus on algorithmic fairness and data privacy. More specifically, the project will: (1) develop innovative statistical methods that ensure fairness in a finite-sample and distribution-free manner; (2) design algorithms that ensure fairness while complying with societal and legal constraints on sensitive data; (3) establish new frameworks to elucidate the trade-off between statistical accuracy and new privacy concepts in generative AI, including machine unlearning and copyright protection. Taken together, the outcome of this research will build a firm foundation of ethical statistical learning and shed light on the development of new theoretical understanding and practical methodology with algorithmic fairness and privacy guarantees.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2338760","CAREER: Statistical Inference in Observational Studies -- Theory, Methods, and Beyond","DMS","STATISTICS","07/01/2024","01/10/2024","Rajarshi Mukherjee","MA","Harvard University","Continuing Grant","Jun Zhu","06/30/2029","$81,885.00","","rmukherj@hsph.harvard.edu","1033 MASSACHUSETTS AVE STE 3","CAMBRIDGE","MA","021385366","6174955501","MPS","126900","1045","$0.00","Causal inference refers to a systematic way of deciphering causal relationships between entities from empirical observations ? an epistemic framework that underlies past, present, and future scientific and social development. For designing statistical methods for causal inference, the gold standard pertains to randomized clinical trials where the researcher assigns treatment/exposure to subjects under study based on pure chance mechanisms. The random assignment negates systematic bias between the observed relationship between the treatment/exposure and outcome due to unknown common factors referred to as confounders. However, randomized clinical trials are often infeasible, expensive, and ethically challenging. In contrast, modern technological advancement has paved the way for the collection of massive amounts of data across a spectrum of possibilities such as health outcomes, environmental pollution, medical claims, educational policy interventions, and genetic mutations among many others. Since accounting for confounders in such data is the fundamental aspect of conducting valid causal inference, one of the major foci of modern causal inference research have been to design procedures to account for complex confounding structures without pre-specifying unrealistic statistical models. Despite the existence of a large canvas of methods in this discourse, the complete picture of the best statistical methods for inferring the causal effect of an exposure on an outcome while adjusting for arbitrary confounders remains largely open. Moreover, there are several popularly used methods that require rigorous theoretical justification and subsequent modification for reproducible statistical research in the domain of causal inference. This project is motivated by addressing these gaps and will be divided into two broad interconnected themes. In the first part, this project provides the first rigorous theoretical lens to the most popular method of confounder adjustment in large-scale genetic studies to find causal variants of diseases. This will in turn bring forth deeper questions about optimal statistical causal inference procedures that will be explored in the second part of the project. Since the project is designed to connect ideas from across statistical methods, probability theory, computer science, and machine learning, it will provide unique learning opportunities to design new courses and discourses. The project will therefore integrate research with education through course development, research mentoring for undergraduate and graduate students, especially those from underrepresented groups, and summer programs.

This project will focus on two broad and interrelated themes tied together by the motivation of conducting statistical and causal inference with modern observational data. The first part of the project involves providing the first detailed theoretical picture of the most popular principal component-based method of population stratification adjustment in genome-wide association studies. This part of the project also aims to provide new methodologies to correct for existing and previously unknown possible biases in the existing methodology as well as guidelines for practitioners for choosing between methods and design of studies. By recognizing the fundamental tenet of large-scale genetic data analysis as the identification of causal genetic determinants of disease phenotypes, the second part of the project develops the first complete picture of optimal statistical inference of causal effects in both high-dimensional under sparsity and nonparametric models under smoothness conditions. Moreover, this part of the project responds to the fundamental question of tuning learning algorithms for estimating nuisance functions, such as outcome regression and propensity score for causal effect estimation, to optimize the downstream mean-squared error of causal effect estimates instead of prediction errors associated with these regression functions. The overall research will connect ideas from high-dimensional statistical inference, random matrix theory, higher-order semiparametric methods, and information theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2338018","CAREER: Single-Fidelity vs. Multi-Fidelity Computer Experiments: Unveiling the Effectiveness of Multi-Fidelity Emulation","DMS","STATISTICS","06/01/2024","12/05/2023","Chih-Li Sung","MI","Michigan State University","Continuing Grant","Jun Zhu","05/31/2029","$79,437.00","","sungchih@msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","126900","1045","$0.00","Computer models have become indispensable tools across diverse fields, enabling the simulation of complex phenomena and facilitating decision-making without costly real-world experiments. Traditionally, computer models are simulated using single, high-accuracy simulations, employing a high level of detail and resolution throughout. Recent advancements, however, have shifted attention towards multi-fidelity simulations, balancing computational cost and accuracy by leveraging various levels of detail and resolution in the simulation. A key question arises: is it more effective to use single-fidelity or multi-fidelity simulations? This is a question practitioners often confront when conducting computer simulations. The research aims to address this fundamental question directly, providing valuable insights for practical decision-making. By leveraging insights gained from computational cost comparisons, the research will enhance the ability to predict complex scientific phenomena accurately and has the potential to revolutionize fields such as engineering, medical science, and biology. The project contributes to outreach and diversity efforts, inspiring youth and increasing female representation in STEM research. Moreover, collaborations with diverse research groups, as well as involvement in the REU exchange program, provide opportunities to engage undergraduate students, nurturing their interest in research and encouraging them to pursue careers in STEM. Research findings will be disseminated through publications and conferences. The code developed will be shared to foster collaboration and encourage others to build upon these innovative methodologies.

This research addresses the fundamental question of whether to conduct single-fidelity or multi-fidelity computer experiments by investigating the effectiveness of multi-fidelity simulations. It begins by examining the computational cost comparison between the two approaches, finding that multi-fidelity simulations, under certain conditions, can theoretically require more computational resources while achieving the same predictive ability. To mitigate the negative effects of low-fidelity simulations, a novel and flexible statistical emulator, called the Recursive Nonadditive (RNA) emulator, is proposed to leverage multi-fidelity simulations, and a sequential design scheme based on this emulator is developed, which maximizes the effectiveness by selecting inputs and fidelity levels based on a criterion that balances uncertainty reduction and computational cost. Furthermore, two novel multi-fidelity emulators, called ""secure emulators,"" are developed, which theoretically guarantee superior predictive performance compared to single-fidelity emulators, regardless of design choices.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2339241","CAREER: Learning stochastic spatiotemporal dynamics in single-molecule genetics","DMS","Cellular Dynamics and Function, STATISTICS, MATHEMATICAL BIOLOGY","07/01/2024","01/29/2024","Christopher Miles","CA","University of California-Irvine","Continuing Grant","Amina Eladdadi","06/30/2029","$239,517.00","","cemiles@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","111400, 126900, 733400","068Z, 079Z, 1045, 7465, 8038","$0.00","The ability to measure which genes are expressed in cells has revolutionized our understanding of biological systems. Discoveries range from pinpointing what makes different cell types unique (e.g., a skin vs. brain cell) to how diseases emerge from genetic mutations. This gene expression data is now a ubiquitously used tool in every cell biologist?s toolbox. However, the mathematical theories for reliably extracting insight from this data have lagged behind the amazing progress of the techniques for harvesting it. This CAREER project will develop key theoretical foundations for analyzing imaging data of gene expression. The advances span theory to practice, including developing mathematical models and machine-learning approaches that will be used with data from experimental collaborators. Altogether, the project aims to create a new gold standard of techniques in studying spatial imaging data of gene expression and enable revelation of new biological and biomedical insights. In addition, this proposed research will incorporate interdisciplinary graduate students and local community college undergraduates to train the next generation of scientists in the ever-evolving intersection of data science, biology, and mathematics. Alongside research activities, the project will create mentorship networks for supporting first-generation student scientists in pursuit of diversifying the STEM workforce.

The supported research is a comprehensive program for studying single-molecule gene expression spatial patterns through the lens of stochastic reaction-diffusion models. The key aim is to generalize mathematical connections between these models and their observation as spatial point processes. The new theory will incorporate factors necessary to describe spatial gene expression at subcellular and multicellular scales including various reactions, spatial movements, and geometric effects. This project will also establish the statistical theory of inference on the resulting inverse problem of inferring stochastic rates from only snapshots of individual particle positions. Investigations into parameter identifiability, optimal experimental design, and model selection will ensure robust and reliable inference. In complement to the developed theory, this project will implement and benchmark cutting-edge approaches for efficiently performing large-scale statistical inference, including variational Bayesian Monte Carlo and physics-informed neural networks. The culmination of this work will be packaged into open-source software that infers interpretable biophysical parameters from multi-gene tissue-scale datasets.

This CAREER Award is co-funded by the Mathematical Biology and Statistics Programs at the Division of Mathematical Sciences and the Cellular Dynamics & Function Cluster in the Division of Molecular & Cellular Biosciences, BIO Directorate.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2340241","CAREER: New Frameworks for Ethical Statistical Learning: Algorithmic Fairness and Privacy","DMS","STATISTICS","07/01/2024","01/23/2024","Linjun Zhang","NJ","Rutgers University New Brunswick","Continuing Grant","Yong Zeng","06/30/2029","$90,127.00","","linjun.zhang@rutgers.edu","3 RUTGERS PLZ","NEW BRUNSWICK","NJ","089018559","8489320150","MPS","126900","1045","$0.00","With the unprecedented impact of data science and machine learning in many aspects of our daily lives, such as healthcare, finance, education, and law, there is an urgent need to design ethical statistical learning algorithms that account for fairness and privacy. This project tackles the challenge of integrating ethical principles into the fabric of statistical learning. The approach prioritizes fairness by enhancing statistical algorithms to perform equitably, particularly in scenarios with limited sample sizes and where sensitive attributes are restricted by legal or societal norms. In parallel, this project addresses privacy by developing a general framework for studying the privacy-accuracy trade-off under new privacy constraints emerging with the advances in generative AI. The practical upshot of this work is the application of these methods to biomedical fields, accompanied by the release of open-source software, broadening the impact and encouraging ethical practices in statistical learning across various domains. This project promotes equitable and private data handling and provides research training opportunities to students.

The research objective of this project is to develop rigorous statistical frameworks for ethical machine learning, with a focus on algorithmic fairness and data privacy. More specifically, the project will: (1) develop innovative statistical methods that ensure fairness in a finite-sample and distribution-free manner; (2) design algorithms that ensure fairness while complying with societal and legal constraints on sensitive data; (3) establish new frameworks to elucidate the trade-off between statistical accuracy and new privacy concepts in generative AI, including machine unlearning and copyright protection. Taken together, the outcome of this research will build a firm foundation of ethical statistical learning and shed light on the development of new theoretical understanding and practical methodology with algorithmic fairness and privacy guarantees.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2339829","CAREER: Statistical foundations of particle tracking and trajectory inference","DMS","STATISTICS","04/01/2024","01/19/2024","Jonathan Niles-Weed","NY","New York University","Continuing Grant","Yong Zeng","03/31/2029","$89,991.00","","jdw453@nyu.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","126900","1045","$0.00","Many problems in human microbiology, astronomy, high-energy physics, fluid dynamics, and aeronautics involve large collections of moving ""particles"" with complicated dynamics. Learning how these systems work requires developing statistical procedures for estimating these dynamics on the basis of noisy observations. The goal of this research is to develop scalable, practical, and reliable methods for this task, with a particular focus on developing statistical theory for applications in cosmology, cellular biology, and machine learning. This research will also include a large outreach component based on broadening access to research opportunities for undergraduates and graduate students.

The technical goals of this proposal are to develop computationally efficient estimators for multiple particle tracking in d dimensions when the particles evolve based on a known or unknown stochastic process, to develop Bayesian methods for posterior sampling based on observed trajectories, and to extend these methods to obtain minimax estimation procedures for smooth paths in the Wasserstein space of probability measures. The research also aims to develop estimators for more challenging models with the growth and interaction of particles.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2338464","CAREER: Distribution-Free and Adaptive Statistical Inference","DMS","STATISTICS","01/15/2024","01/11/2024","Lihua Lei","CA","Stanford University","Continuing Grant","Yulia Gel","12/31/2028","$75,564.00","","lihualei@stanford.edu","450 JANE STANFORD WAY","STANFORD","CA","943052004","6507232300","MPS","126900","1045","$0.00","Recent years have witnessed a growing trend across scientific disciplines to embrace complex modeling and black-box machine learning algorithms. Despite the remarkable success of handling complex data structures and fitting sophisticated regression functions, there remains a substantial gap regarding the integration of rigorous statistical principles into these pipelines. The main difficulty revolves around achieving reliable uncertainty quantification and robust statistical inference without artificially simplifying the complexity inherent in these advanced tools. Most existing frameworks that aim to bridge the gap rely on strong assumptions under which the machine learning algorithm can accurately estimate the data generating distribution. Nevertheless, these assumptions are often hard to justify, especially for modern machine learning algorithms that have yet to be fully understood. This research project aims to develop new frameworks for statistical inference that wrap around any machine learning algorithms or complex models without concerning about failure modes. The resulting methods are able to address the potential threats to inferential validity caused by black-box machine learning algorithms in a wide range of applied fields, including medicine, healthcare, economics, political science, epidemiology, and climate sciences. Open source software will also be developed to help applied researchers integrate rigorous statistical inference into their domain-specific modeling workflows without compromising the effectiveness of modern tools in non-inferential tasks. This may further alleviate hesitation in adopting modern machine learning methods and catalyze collaboration between scientific and engineering fields. Throughout the project, the PI will mentor undergraduate and graduate students, equipping them with solid understandings of statistical principles to become future leaders in face of rapidly evolving machine learning techniques.

This proposal will focus on distribution-free inference, which is immune to misspecification of parametric models, violation of nonparametric assumptions like smoothness or shape constraints, inaccuracy of asymptotic approximations due to limited sample size, high dimensionality, boundary cases, or irregularity. To avoid making uninformative decisions, an ideal distribution-free inference framework should also be adaptive to good modeling. This means that it should be as efficient as other frameworks that rely on distributional assumptions. Adaptivity alleviates the tradeoff between robustness and efficiency. The PI will develop distribution-free and adaptive inference frameworks for three specific problems. First, in causal inference, tighter identified set can be obtained for partially identified causal effects by incorporating pre-treatment covariates. However, existing frameworks for sharp inference require estimating conditional distributions of potential outcomes given covariates. The PI will develop a generic framework based on duality theory that is able to wrap around any estimates of conditional distributions and make distribution-free and adaptive inference. Second, many target parameters in medicine, political economy, and causal inference can be formulated through extremums of the conditional expectation of an outcome given covariates. In contrast to classical methods that impose distributional assumptions to enable consistent estimation of the conditional expectation, the PI will develop a distribution-free framework for testing statistical null hypotheses and constructing valid confidence intervals on the extremums directly. Finally, the use of complex models and prediction algorithms in time series nowcasting and forecasting presents challenges for reliable uncertainty quantification. To address this, the PI will develop a framework based on model predictive control and conformal prediction that is able to wrap around any forecasting algorithms and calibrate it to achieve long-term coverage, without any assumptions on the distribution of the time series. The ultimate goal of this research is to bring insights and present a suite of tools to empower statistical reasoning with machine learning and augment machine learning with statistical reasoning.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2335569","Collaborative Research: Planning: FIRE-PLAN:High-Spatiotemporal-Resolution Sensing and Digital Twin to Advance Wildland Fire Science","DMS","S&CC: Smart & Connected Commun, STATISTICS, HDBE-Humans, Disasters, and th, Cross-BIO Activities, EPCN-Energy-Power-Ctrl-Netwrks","01/01/2024","08/09/2023","Xiaolin Hu","GA","Georgia State University Research Foundation, Inc.","Standard Grant","Yulia Gel","12/31/2025","$52,000.00","","xhu@cs.gsu.edu","58 EDGEWOOD AVE NE","ATLANTA","GA","303032921","4044133570","MPS","033Y00, 126900, 163800, 727500, 760700","019E, 042E, 042Z, 132Z, 5294, 7275, 9150","$0.00","The number of catastrophic wildfires in the United States has been steadily increasing in recent decades, which generate casualties, large loss of properties, and dramatic environmental changes. However, it is difficult to make accurate predictions of wildland fire spread in real time for firefighters and emergency response teams. Although many fire spread models have been developed, one of the biggest challenges in their operational use is the lack of ground truth fire data at high spatiotemporal resolutions, which are indispensable for model evaluation and improvements. The objective of this planning project is to bring together wildland fire science researchers, fire sensing and data science experts, and diverse stakeholders to develop standards and requirements for high-spatiotemporal-resolution wildland fire sensing and digital twin construction. An organizing committee will be formed from wildland fire science, engineering, and stake holder communities including fire ecology and behavior modeling, pollution monitoring, robotics, cyber physical systems (CPS), wildfire fighting, indigenous cultural burns, and prescribed fires. A series of physical and remote workshops will be held focusing on themes such as open fire data for wildland fire modeling validation, digital twins for prescribed fires, and safe and efficient wildland fire data collection.

Research tasks of this planning project include: 1) identification of key high-spatiotemporal-resolution fire metrics and data representations to support fire model validation and fire operations, 2) proposition of sensing strategies and algorithms for fire sensing and suppression robots and cyber physical systems that can support safe and efficient collection of desired high-resolution fire data, 3) development and evaluation of data assimilation and digital twin construction using high-resolution data to advance fire behavior modeling, coupled fire-atmosphere modeling, and smoke modeling, and 4) prototype and initial fire data ecosystem demonstration including collection of cultural burn data and establishment of GeoFireData, a benchmark fire data sharing and digital twin website, which can support different fire operation types such as fire spread model validation and controlled burn planning. The special attention will be devoted to interdisciplinary training of the next generation of scientists working with wildfire risks at the interface of computational sciences, engineering, ecology, and data sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337943","CAREER: New data integration approaches for efficient and robust meta-estimation, model fusion and transfer learning","DMS","STATISTICS","06/01/2024","01/30/2024","Emily Hector","NC","North Carolina State University","Continuing Grant","Yulia Gel","05/31/2029","$85,143.00","","ehector@ncsu.edu","2601 WOLF VILLAGE WAY","RALEIGH","NC","276950001","9195152444","MPS","126900","1045","$0.00","Statistical science aims to learn about natural phenomena by drawing generalizable conclusions from an aggregate of similar experimental observations. With the recent ?Big Data? and ?Open Science? revolutions, scientists have shifted their focus from aggregating individual observations to aggregating massive publicly available datasets. This endeavor is premised on the hope of improving the robustness and generalizability of findings by combining information from multiple datasets. For example, combining data on rare disease outcomes across the United States can paint a more reliable picture than basing conclusions only on a small number of cases in one hospital. Similarly, combining data on disease risk factors across the United States can distinguish local from national health trends. To date, statistical approaches to these data aggregation objectives have been limited to simple settings with limited practical utility. In response to this gap, this project develops new methods for aggregating information from multiple datasets in three distinct data integration problems grounded in scientific practice. The developed approaches are intuitive, principled and robust to substantial differences between datasets, and are broadly applicable in medical, economic and social sciences, among others. Among other applications, the project will deliver new tools to extract health insights from large electronic health records databases. The project will support undergraduate and graduate student training, course development, and the recruitment and professional mentoring of under-represented minorities in statistics. Further, the project will impact STEM education through a data science teacher training program in underserved communities.

This project develops intuitive, principled, robust and efficient methods in three essential data integration problems: meta-analysis, model fusion and transfer learning. First, the project delivers a set of meta-analysis methods for privacy-preserving one-shot estimation and inference using a new notion of dataset similarity. The primary novelty in the approach is the joint estimation of both dataset-specific parameters and a combined parameter that bears some similarity to the classic meta-estimator. Second, the project establishes model fusion methods that learn the clustering of similar datasets. The methods? unique feature is a model fusion that dials data integration along a spectrum of more to less fusion and thereby does not force model parameters from clustered datasets to be exactly equal. Third, the project develops flexible and robust transfer learning approaches that leverage historical information for improved statistical efficiency in a target dataset of interest. An important element of these approaches is a flexible specification of the type of models fit to the source datasets. All three sets of methods place a premium on interpretability, statistical efficiency and robustness of the inferential output. The project unifies the three sets of proposed methods under a formal data integration framework formulated around two axioms of data integration. Data integration ideas pervade every field of scientific study in which data are collected, and so the research contributes to scientific endeavors in the medical, economic and social sciences, among others.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."