From 6d85fbd0c2d5fb4fc47af9c3c7eb86bf7942d57e Mon Sep 17 00:00:00 2001 From: Yimin Zhong Date: Sun, 9 Jun 2024 06:35:30 +0000 Subject: [PATCH] Update Awards --- .../Awards-Algebra-and-Number-Theory-2024.csv | 19 ++++++++++--------- .../Awards-Applied-Mathematics-2024.csv | 3 ++- .../Awards-Computational-Mathematics-2024.csv | 17 ++++++++--------- .../Awards-Geometric-Analysis-2024.csv | 3 ++- Probability/Awards-Probability-2024.csv | 7 ++++--- Topology/Awards-Topology-2024.csv | 13 ++++++------- 6 files changed, 32 insertions(+), 30 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 e08fa47..26a2aa2 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 @@ -1,6 +1,11 @@ "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" -"2401601","The Geometry of Hyperkähler Varieties and Rationality","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","06/15/2024","06/03/2024","Sarah Frei","NH","Dartmouth College","Standard Grant","James Matthew Douglass","05/31/2027","$260,000.00","","sarah.frei@dartmouth.edu","7 LEBANON ST","HANOVER","NH","037552170","6036463007","MPS","126400, 915000","9150","$0.00","Algebraic geometry is the study of geometric objects, called varieties, which are defined by the solution sets of systems of polynomial equations. It is a far-reaching branch of mathematics, making connections with many other research areas such as commutative algebra, number theory, differential and complex geometry, representation theory, and mathematical physics. In this project the PI will study certain families of varieties that play an important role in the classification of all varieties, namely hyperkaehler varieties and rational varieties. This project focuses on arithmetic questions about these two families. The project includes research training opportunities for undergraduate and graduate students, as well as outreach activities to strengthen the community of individuals in algebraic geometry from underrepresented backgrounds. This project is jointly funded by the Algebra and Number Theory Program and the Established Program to Stimulate Competitive Research.

This research program is centered around three projects. In the first, birational transformations of hyperkaehler varieties will be used to study Brauer classes on K3 surfaces in order to identify which Brauer classes can arise as exceptional loci in hyperkaehler contractions. This makes connections to questions about the rationality of families of cubic fourfolds. The second is to study the behavior of rationality of fourfolds in arithmetic families, giving an analogue to previous results in families over the complex numbers. The third project is centered around the intermediate Jacobian torsor obstruction to rationality for geometrically rational threefolds, with the goal of characterizing rationality for a certain family of conic bundle threefolds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2409946","Conference: URiCA 2024 and 2025","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/15/2024","Mark Walker","NE","University of Nebraska-Lincoln","Standard Grant","Tim Hodges","03/31/2026","$30,000.00","","mark.walker@unl.edu","2200 VINE ST # 830861","LINCOLN","NE","685032427","4024723171","MPS","126400","7556, 9150","$0.00","This award supports participation of graduate students and postdoctoral researchers in the conference ""Upcoming Researchers in Commutative Algebra"" (URiCA) to be held in Lincoln, Nebraska, May 11-12, 2024, and in May 2025. URiCA (formerly known as KUMUNU Jr), is an annual conference hosted by the Department of Mathematics at the University of Nebraska-Lincoln designed to promote visibility and interactions between graduate students and postdocs working in commutative algebra and related fields.

The conference will feature ten talks from graduate students and postdocs over the span of two days. These talks will be on original research done in commutative algebra and related fields of mathematics. While URiCA was initially focused on connecting mathematical communities in the Great Plains region, previous success has allowed us to extend our outreach and include more early career researchers from outside this region. The goal of the conference is to help foster a diverse and welcoming community of early researchers leading to increased collaborations and exposure to different areas of research being done in commutative algebra. This conference will continue to provide an opportunity for early researchers and underrepresented groups in math to share their work and gain visibility among their peers.

Conference Website: https://urica-unl.github.io/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2402177","Conference: Building Bridges: 6th EU/US Summer School on Automorphic Forms and Related Topics","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/15/2024","06/07/2024","James Brown","CA","Occidental College","Standard Grant","Adriana Salerno","05/31/2025","$14,965.00","","jimlb@oxy.edu","1600 CAMPUS RD","LOS ANGELES","CA","900413314","3232591414","MPS","126400","7556","$0.00","The Building Bridges: 6th EU/US Summer School on Automorphic forms and Related Topics (BB6) is held at Centre International de Rencontres Mathematiques (CIRM) in Marseille, France from September 2 - 7, 2024. CIRM provides an ideal location for such a school as it is one of the largest mathematics conference centers in the world. The BB6 summer school brings together students and early career researchers from around the world, with a particular emphasis on the US and EU. This school helps train the next generation of research mathematicians in the important field of automorphic forms, a notoriously difficult subject to begin research in as it requires a large amount of technical knowledge. This award supports some of the US-based participants at this workshop, including some instructors and organizers, and nine graduate students.

The BB6 summer school is composed of three classes each of which is team-taught by two instructors. Students attend lectures in the morning delivered by the course instructors. In the afternoon, students have the opportunity to work on problem sets with each other as well as ask questions of the instructors. These courses are designed by the instructors to move students quickly from the introduction of the topic to a particular research area of current interest. Students come away from the summer school with a foundational knowledge of automorphic forms as well as knowledge in three more specialized areas allowing them to move into further study or a research problem. The BB6 school website is hosted at: https://conferences.cirm-math.fr/3134.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." +"2423082","Conference: Women in Commutative Algebra III","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","05/21/2024","Alexandra Seceleanu","NE","University of Nebraska-Lincoln","Standard Grant","Tim Hodges","05/31/2025","$10,000.00","","aseceleanu@unl.edu","2200 VINE ST # 830861","LINCOLN","NE","685032427","4024723171","MPS","126400","7556, 9150","$0.00","This award provides travel and accommodation support for US-based participants in the workshop ""Women in Commutative Algebra III? (WICA III). The workshop is hosted by CMO (Casa Matematica Oaxaca), a research center located in Oaxaca, Mexico, which is affiliated with the Banff International Research Station for Mathematical Innovation and Discovery (BIRS). The conference takes place on June 2-7, 2024. Commutative algebra is a vibrant field of mathematical research. It has connections to many other fields of mathematics such as geometry, number theory, topology, and combinatorics, and has found many practical applications in recent years. The main objective of the workshop is to make advances in commutative algebra through state-of-the-art research.

The meeting will feature six research topics within commutative algebra: combinatorial commutative algebra, semigroup rings, toric ideals arising from degenerations of Grassmanians, arrangements of hyperplanes, reduction ideals of determinantal ideals, and invariant theory for group actions. Twelve group leaders will suggest problems for study and guide small teams in collaborative research during the meeting. WICA III will expand the research portfolio and collaborative network of the approximately forty participants in attendance. This workshop will create leadership opportunities and provide mentoring for early-career mathematicians, while also making an impact on those who are geographically isolated at their institutions. More information can be found at https://www.birs.ca/events/2024/5-day-workshops/24w5185 and https://mathstat.dal.ca/~faridi/WICAIII.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2422291","CAREER: New methods in curve counting","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/01/2024","02/23/2024","Felix Janda","IL","University of Illinois at Urbana-Champaign","Continuing Grant","James Matthew Douglass","06/30/2028","$144,329.00","","fjanda@illinois.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","126400","1045","$0.00","The past thirty years have seen a deep and surprising interplay between several branches in pure mathematics, and string theory in physics. In particular, physical predictions have led to the development of mathematical invariants which count algebraic curves in spaces, and conversely, the mathematical study of these invariants has led to advances in string theory. This project further develops two curve counting techniques, the ""logarithmic gauged linear sigma model"" (log GLSM) and ""quasimaps"", and their combination, with the goal of making progress on challenging conjectures from physics, which have appeared out of reach of mathematicians until recently. This project will offer ample training opportunities for graduate students and postdocs. In addition, the PI will organize a yearly intensive weekend learning workshop on a topic of interest, as well as organize events aiming to counter stereotypes in STEM.

More specifically, the project will result in a proof of the localization formula for log GLSM, which is of utmost importance for the application of this technique. In addition, effective invariants, which are a major ingredient of the localization formula, will be studied. In a different direction, the PI will explore applications of log GLSM to the tautological ring, to establish structural predictions observed in physics, such as the ""conifold gap condition"", for the quintic threefold and other one-parameter Calabi-Yau threefolds, and to establish the Landau-Ginzburg/Calabi-Yau correspondence for quintic threefolds in all genera. With regard to quasi-maps, the second main technique employed in this project, the PI will use quasi-maps for explicit computations of Gromov-Witten invariants of non-convex complete intersections. Quasi-maps appear necessary for approaching some of the more mysterious predictions from physics, and hence log GLSM will be extended to allow for quasi-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." +"2342256","RTG: Commutative Algebra at Nebraska","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","08/01/2024","04/26/2024","Mark Walker","NE","University of Nebraska-Lincoln","Continuing Grant","Andrew Pollington","07/31/2029","$600,000.00","Eloísa Grifo, Jack Jeffries, Alexandra Seceleanu, Brian Harbourne","mark.walker@unl.edu","2200 VINE ST # 830861","LINCOLN","NE","685032427","4024723171","MPS","126400, 915000","9150, 9229","$0.00","This project is jointly funded by the Algebra and Number Theory Program and the Established Program to Stimulate Competitive Research (EPSCoR). The Research Training Group (RTG) in Commutative Algebra at Nebraska will establish a number of activities for researchers at career stages ranging from undergraduate students to faculty. The training will provide opportunities for graduate students and postdoctoral scholars to jumpstart their research programs and develop broad skills as professionals, and for undergraduates to cement their interest and confidence in mathematics. This training will increase participation of first-generation and Hispanic students and enhance the competitiveness of junior researchers in algebra overall. Training activities supported by this grant include a first-year Research Experience for Undergraduates (REU) for first-generation college students, an international REU run in partnership with Centro de Investigación en Matemáticas in Guanajuato, Mexico, and a professional development workshop for early-career algebraists throughout the US. This grant will also create three postdoctoral positions and support numerous graduate students.

The University of Nebraska-Lincoln has a decades-long reputation as an international center for commutative algebra. Our research group has made significant advances in the study of Betti numbers and free resolutions, symbolic powers, numerics and asymptotics of fat point schemes, interpolation problems, p-derivations in commutative algebra, prime characteristic commutative algebra, differential operators and singularities, among other topics of current interest. This grant will propel further advances in these areas by increasing the participation of postdocs and graduate students in our research 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." "2422706","Conference: 21st International Fibonacci Conference","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/15/2024","06/05/2024","Steven Miller","MA","Williams College","Standard Grant","Andrew Pollington","05/31/2025","$10,000.00","","sjm1@williams.edu","880 MAIN ST","WILLIAMSTOWN","MA","012672600","4135974352","MPS","126400","7556","$0.00","This award is to provide partial support for attendees of The 21st International Fibonacci Conference which will run from July 8th to 12th, 2024 at Harvey Mudd College in California. Fibonacci numbers in particular and recurrence relations in general arise in many areas. Thus there are many colleagues at all levels, from R1 institutions to teaching colleges to general scientists, working on problems in the field. The goal is to provide an inviting avenue for people to present their work and meet other interested parties. By bringing together a diverse group of researchers and practitioners we expect, as has happened in previous years, to have a productive meeting where several vantage points are provided to researchers to help suggest approaches and related problems; based on successes from previous conferences we expect many new collaborations to form. We have expanded topics from previous years to include applications in mathematical biology, music, and secondary education to excite the next generation of students. Run by the Fibonacci Association, many of the talks will be recorded and made publicly available, and papers related to the talks will be published as a conference proceedings as a special issue of the Fibonacci Quarterly.

With two sessions each day which can be attended in person or by zoom, speakers will discuss their work in 20 minute talks. Topics range from applications to $L$-functions to graph theory to combinatorial games to mathematics education to music to expanded predator-prey models in mathematical biology. There will also be 1-2 problem sessions where researchers will discuss both problems related to their talks as well as accessible topics for young researchers; the goal is to build research groups with senior personnel mentoring the large number of young mathematicians in attendance. For more information see:
https://21stinternationalfibonacciconference.wordpress.com/ .

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401601","The Geometry of Hyperkähler Varieties and Rationality","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","06/15/2024","06/03/2024","Sarah Frei","NH","Dartmouth College","Standard Grant","James Matthew Douglass","05/31/2027","$260,000.00","","sarah.frei@dartmouth.edu","7 LEBANON ST","HANOVER","NH","037552170","6036463007","MPS","126400, 915000","9150","$0.00","Algebraic geometry is the study of geometric objects, called varieties, which are defined by the solution sets of systems of polynomial equations. It is a far-reaching branch of mathematics, making connections with many other research areas such as commutative algebra, number theory, differential and complex geometry, representation theory, and mathematical physics. In this project the PI will study certain families of varieties that play an important role in the classification of all varieties, namely hyperkaehler varieties and rational varieties. This project focuses on arithmetic questions about these two families. The project includes research training opportunities for undergraduate and graduate students, as well as outreach activities to strengthen the community of individuals in algebraic geometry from underrepresented backgrounds. This project is jointly funded by the Algebra and Number Theory Program and the Established Program to Stimulate Competitive Research.

This research program is centered around three projects. In the first, birational transformations of hyperkaehler varieties will be used to study Brauer classes on K3 surfaces in order to identify which Brauer classes can arise as exceptional loci in hyperkaehler contractions. This makes connections to questions about the rationality of families of cubic fourfolds. The second is to study the behavior of rationality of fourfolds in arithmetic families, giving an analogue to previous results in families over the complex numbers. The third project is centered around the intermediate Jacobian torsor obstruction to rationality for geometrically rational threefolds, with the goal of characterizing rationality for a certain family of conic bundle threefolds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "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." "2430098","Rational points on modular curves, and the geometry of arithmetic statistics","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/24/2024","David Zureick-Brown","MA","Amherst College","Continuing Grant","Andrew Pollington","05/31/2026","$37,130.00","","dzureickbrown@amherst.edu","155 S PLEASANT ST","AMHERST","MA","010022234","4135422804","MPS","126400","","$0.00","The project will explore various topics within number theory and algebraic geometry. These are ancient areas of inquiry rooted in very basic questions about solving polynomial equations and motivated by concrete applications. For example, the Greek astronomer Apollonius of Perga (240-190BC) developed his theory of conics and ellipses to facilitate the study of Astronomy. Questions about numbers and shapes still remain central to the frontier of mathematical research, and this project has a particular emphasis on using modern technical tools to study classical problems. The project includes problems accessible to undergraduates and graduate students, and includes efforts including substantial student focused conference organization (such as the Arizona Winter School).

Mazur's torsion and isogeny theorems are cornerstones of arithmetic geometry, and arithmetic statistics is an old field full of classical problems. In recent years both areas have enjoyed an influx of new ideas and progress, especially via ideas from the geometry of numbers, moduli spaces, algebraic topology, computational number theory, and more. In particular, this project will study Mazur's ``Program B'', higher degree torsion on elliptic curves, a generalization of the Batyrev--Manin and Malle conjectures to stacks (in a sense, an interpolation of these conjectures), and non-abelian (and infinite degree) Cohen--Lenstra heuristics (and, in the function field case, theorems). Each of these sub-projects will introduced new methods and toolkits/frameworks that are expected to be broadly useful, and suggests numerous open problems and new directions for research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -8,7 +13,6 @@ "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." -"2423082","Conference: Women in Commutative Algebra III","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","05/21/2024","Alexandra Seceleanu","NE","University of Nebraska-Lincoln","Standard Grant","Tim Hodges","05/31/2025","$10,000.00","","aseceleanu@unl.edu","2200 VINE ST","LINCOLN","NE","685032427","4024723171","MPS","126400","7556, 9150","$0.00","This award provides travel and accommodation support for US-based participants in the workshop ""Women in Commutative Algebra III? (WICA III). The workshop is hosted by CMO (Casa Matematica Oaxaca), a research center located in Oaxaca, Mexico, which is affiliated with the Banff International Research Station for Mathematical Innovation and Discovery (BIRS). The conference takes place on June 2-7, 2024. Commutative algebra is a vibrant field of mathematical research. It has connections to many other fields of mathematics such as geometry, number theory, topology, and combinatorics, and has found many practical applications in recent years. The main objective of the workshop is to make advances in commutative algebra through state-of-the-art research.

The meeting will feature six research topics within commutative algebra: combinatorial commutative algebra, semigroup rings, toric ideals arising from degenerations of Grassmanians, arrangements of hyperplanes, reduction ideals of determinantal ideals, and invariant theory for group actions. Twelve group leaders will suggest problems for study and guide small teams in collaborative research during the meeting. WICA III will expand the research portfolio and collaborative network of the approximately forty participants in attendance. This workshop will create leadership opportunities and provide mentoring for early-career mathematicians, while also making an impact on those who are geographically isolated at their institutions. More information can be found at https://www.birs.ca/events/2024/5-day-workshops/24w5185 and https://mathstat.dal.ca/~faridi/WICAIII.

This award reflects 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." "2409099","Conference: 2024-2026 Graduate Student Conference in Geometry, Topology, and Algebra","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","05/15/2024","05/15/2024","Matthew Stover","PA","Temple University","Standard Grant","Swatee Naik","04/30/2027","$90,000.00","David Futer, Jaclyn Lang","mstover@temple.edu","1805 N BROAD ST","PHILADELPHIA","PA","191226104","2157077547","MPS","126400, 126700","7556","$0.00","This award supports the next three events in the Annual Graduate Student Conference series in Algebra, Geometry, and Topology (GTA Philadelphia). The next conference will be held on May 31-June 2, 2024 at Temple University. The conference will bring together over 80 graduate students at all levels and from a variety of backgrounds and universities, along with four distinguished plenary speakers that work at the interface of algebra, geometry, and topology. Supplementing lectures by faculty and students, the conference features a professional development panel focused on career building and social responsibility. The conference provides a rare opportunity for a large number of early career mathematicians with similar research interests to come together and develop mathematical relationships. In addition, it strongly supports interactions between graduate students from different schools, different backgrounds, and different research areas.

The large majority of lectures will be given by graduate students, supplying them with opportunities to practice presenting their research ideas and interests to fellow students. The conference strives to include a wide range of topics and a broad diversity of speakers. In addition, talks by distinguished plenary speakers will provide insights into how different parts of algebra, geometry, and topology are connected, open research questions of interest, and recent techniques used in groundbreaking work in these fields. For further information, see https://math.temple.edu/events/conferences/gscagt/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -16,8 +20,6 @@ "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." -"2409946","Conference: URiCA 2024 and 2025","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/15/2024","Mark Walker","NE","University of Nebraska-Lincoln","Standard Grant","Tim Hodges","03/31/2026","$30,000.00","","mark.walker@unl.edu","2200 VINE ST","LINCOLN","NE","685032427","4024723171","MPS","126400","7556, 9150","$0.00","This award supports participation of graduate students and postdoctoral researchers in the conference ""Upcoming Researchers in Commutative Algebra"" (URiCA) to be held in Lincoln, Nebraska, May 11-12, 2024, and in May 2025. URiCA (formerly known as KUMUNU Jr), is an annual conference hosted by the Department of Mathematics at the University of Nebraska-Lincoln designed to promote visibility and interactions between graduate students and postdocs working in commutative algebra and related fields.

The conference will feature ten talks from graduate students and postdocs over the span of two days. These talks will be on original research done in commutative algebra and related fields of mathematics. While URiCA was initially focused on connecting mathematical communities in the Great Plains region, previous success has allowed us to extend our outreach and include more early career researchers from outside this region. The goal of the conference is to help foster a diverse and welcoming community of early researchers leading to increased collaborations and exposure to different areas of research being done in commutative algebra. This conference will continue to provide an opportunity for early researchers and underrepresented groups in math to share their work and gain visibility among their peers.

Conference Website: https://urica-unl.github.io/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2342256","RTG: Commutative Algebra at Nebraska","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","08/01/2024","04/26/2024","Mark Walker","NE","University of Nebraska-Lincoln","Continuing Grant","Andrew Pollington","07/31/2029","$600,000.00","Eloísa Grifo, Jack Jeffries, Alexandra Seceleanu, Brian Harbourne","mark.walker@unl.edu","2200 VINE ST","LINCOLN","NE","685032427","4024723171","MPS","126400, 915000","9150, 9229","$0.00","This project is jointly funded by the Algebra and Number Theory Program and the Established Program to Stimulate Competitive Research (EPSCoR). The Research Training Group (RTG) in Commutative Algebra at Nebraska will establish a number of activities for researchers at career stages ranging from undergraduate students to faculty. The training will provide opportunities for graduate students and postdoctoral scholars to jumpstart their research programs and develop broad skills as professionals, and for undergraduates to cement their interest and confidence in mathematics. This training will increase participation of first-generation and Hispanic students and enhance the competitiveness of junior researchers in algebra overall. Training activities supported by this grant include a first-year Research Experience for Undergraduates (REU) for first-generation college students, an international REU run in partnership with Centro de Investigación en Matemáticas in Guanajuato, Mexico, and a professional development workshop for early-career algebraists throughout the US. This grant will also create three postdoctoral positions and support numerous graduate students.

The University of Nebraska-Lincoln has a decades-long reputation as an international center for commutative algebra. Our research group has made significant advances in the study of Betti numbers and free resolutions, symbolic powers, numerics and asymptotics of fat point schemes, interpolation problems, p-derivations in commutative algebra, prime characteristic commutative algebra, differential operators and singularities, among other topics of current interest. This grant will propel further advances in these areas by increasing the participation of postdocs and graduate students in our research 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." "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." "2401484","On Enumerative and Tautological Invariants Defined by Perfect Obstruction Theories","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","07/01/2024","04/23/2024","Yunfeng Jiang","KS","University of Kansas Center for Research Inc","Standard Grant","Adriana Salerno","06/30/2027","$194,000.00","","y.jiang@ku.edu","2385 IRVING HILL RD","LAWRENCE","KS","660457563","7858643441","MPS","126400, 915000","9150","$0.00","This project focuses on two related topics in algebraic geometry, which are motivated by their connections with physical theories (string theory and gauge theory). The first topic is Donaldson-Thomas (DT) and Vafa-Witten (VW) theory, which studies the invariants of the space parametrizing sets of solutions of polynomials defining two dimensional objects with certain topological constraints in a space. The second topic is higher dimensional Gromov-Witten (GW) theory, which roughly speaking is about a systematic way of counting numbers of surfaces with particular constraints in a space defined by a set of polynomial equations. For a real dimension four space, a remarkable conjecture of electromagnetic duality (S-duality) from physics says that counting two dimensional objects in a topological space has nice modularity properties. Different branches of mathematics are linked together by these two theories and deep properties of geometric objects have been uncovered by calculating invariants. In this project the PI will investigate the S-duality conjecture between these two theories and relate them to other branches of mathematics and physics. This award will also support graduate student research.

In more detail, the projects are designed to define several new enumerative invariants of the moduli spaces of geometric objects in algebraic geometry. The first topic is Donaldson-Thomas and Vafa-Witten theory. The PI will study DT invariants for Calabi-Yau 4-folds, apply the DT invariants to prove the S-duality conjecture for real four and six dimensional manifolds. The second topic is higher dimensional Gromov-Witten theory. The PI will study GW counting surface invariants, construct the moduli space of surface case stable maps and the virtual fundamental class, and use the virtual fundamental class to define tautological invariants and study the original GW invariants of counting curves.

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." "2419068","Conference: Arithmetic, Geometric, and Computational Aspects of Drinfeld Modules and Anderson Motives","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/26/2024","Mihran Papikian","PA","Pennsylvania State Univ University Park","Standard Grant","Adriana Salerno","06/30/2025","$15,000.00","","papikian@math.psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","126400","7556","$0.00","A special session ""Arithmetic, Geometric, and Computational Aspects of Drinfeld Modules and Anderson Motives"", organized by the PI, Tuan Ngo Dac, Matthew Papanikolas, and Federico Pellarin, will take place July 23-26, 2024 in Palermo (Italy), at the joint meeting of the American Mathematical Society and Unione Matematica Italiana. The purpose of this session is to bring together international experts in a variety of areas of arithmetic geometry, automorphic forms, and function field arithmetic. The emphasis of the conference will be on recent spectacular developments in the theory of Drinfeld modules and their generalizations. The conference will increase international collaboration between mathematicians from different parts of the world. This award will cover the travel expenses of invited participants from the United States, with the priority given to junior researchers and members of underrepresented groups.

Since their emergence in 1970s, Drinfeld modules and their moduli spaces had a tremendous impact on arithmetic geometry, leading to a successful resolution of the global and local Langlands conjectures over function fields. Over the last few years, there has been an explosion of activity in function field arithmetic, with many spectacular results on special values of higher derivatives of L-functions of automorphic forms, special values of Carlitz-Goss L-functions, and Drinfeld modular forms. In all these works, Drinfeld modules and their generalizations play a prominent role. Moreover, new tantalizing connections have been discovered between different topics of function field arithmetic, such as special values of characteristic p zeta functions, deformations of Drinfeld modular forms, and function field analogue of Fontaine?s theory. These developments, along with possible future directions of research, will be addressed by the invited speakers of the special session with the hope to inspire new generations to take part in this important and very active area of Number Theory. Conference webpage: https://sites.google.com/uniroma1.it/drinfeld-modules/home-page

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -38,7 +40,6 @@ "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." -"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." "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." @@ -46,10 +47,11 @@ "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." +"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." "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." -"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." +"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." "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." @@ -63,23 +65,22 @@ "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." -"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." "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." "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." "2401548","Topics in automorphic Forms and Algebraic Cycles","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Wei Zhang","MA","Massachusetts Institute of Technology","Continuing Grant","Andrew Pollington","06/30/2029","$110,398.00","","wz2113@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126400","","$0.00","This awards concern research in Number Theory. Solving polynomial equations in rational numbers dates back to Diophantus in the 3rd century and has been a central subject in mathematics for generations. The modern study of Diophantine equations has incorporated the revolutionary idea of Riemann from his use of a class of special functions called ""zeta functions? or ""L-functions"". Such special functions are built up on counting the numbers of solutions of polynomial equations in the much simpler setting of modular arithmetic. In the 1960s, Birch and Swinnerton-Dyer came up with a remarkable conjecture revealing a relation between the zeros of L-functions and the solutions to a special class of polynomial equations in the rationals. Later Beilinson and Bloch conjectured that, for general polynomial equations in the rationals, there should always be a relation between the zeros of L-functions and algebraic cycles which are ?parameter solutions to polynomial equations?.

The project will study the zeros of L-functions through automorphic forms and special cycles on modular varieties. The theory of automorphic form provides a fruitful way to access the zeros of L-functions. The modular varieties are either Shimura varieties over number fields or moduli spaces of Shtukas over function fields. They play a central role in modern number theory and arithmetic geometry, and they often come with a great supply of algebraic cycles. The project aims to prove results relating zeros of L-functions and algebraic cycles on modular varieties, including new cases of the arithmetic Gan?Gross?Prasad conjecture for Shimura varieties associated to unitary groups, certain Higher Gross?Zagier formula over function fields, and the function field analog of Kudla?s program with an emphasis on the modularity of generating series of special cycles and the arithmetic Siegel?Weil formula. The project will also develop new relative trace formula, a powerful equation connecting spectral information and geometric structure, to study general automorphic period integral including the unitary Friedberg?Jacquet period. The broader impacts of this project include mentoring of graduate students and seminar organization.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2422291","CAREER: New methods in curve counting","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/01/2024","02/23/2024","Felix Janda","IL","University of Illinois at Urbana-Champaign","Continuing Grant","James Matthew Douglass","06/30/2028","$144,329.00","","fjanda@illinois.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","126400","1045","$0.00","The past thirty years have seen a deep and surprising interplay between several branches in pure mathematics, and string theory in physics. In particular, physical predictions have led to the development of mathematical invariants which count algebraic curves in spaces, and conversely, the mathematical study of these invariants has led to advances in string theory. This project further develops two curve counting techniques, the ""logarithmic gauged linear sigma model"" (log GLSM) and ""quasimaps"", and their combination, with the goal of making progress on challenging conjectures from physics, which have appeared out of reach of mathematicians until recently. This project will offer ample training opportunities for graduate students and postdocs. In addition, the PI will organize a yearly intensive weekend learning workshop on a topic of interest, as well as organize events aiming to counter stereotypes in STEM.

More specifically, the project will result in a proof of the localization formula for log GLSM, which is of utmost importance for the application of this technique. In addition, effective invariants, which are a major ingredient of the localization formula, will be studied. In a different direction, the PI will explore applications of log GLSM to the tautological ring, to establish structural predictions observed in physics, such as the ""conifold gap condition"", for the quintic threefold and other one-parameter Calabi-Yau threefolds, and to establish the Landau-Ginzburg/Calabi-Yau correspondence for quintic threefolds in all genera. With regard to quasi-maps, the second main technique employed in this project, the PI will use quasi-maps for explicit computations of Gromov-Witten invariants of non-convex complete intersections. Quasi-maps appear necessary for approaching some of the more mysterious predictions from physics, and hence log GLSM will be extended to allow for quasi-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." "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." diff --git a/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv b/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv index 45e2827..7a6fc3b 100644 --- a/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv +++ b/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv @@ -1,7 +1,8 @@ "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" +"2417985","Conference: The 42nd Southeastern-Atlantic Regional Conference on Differential Equations","DMS","APPLIED MATHEMATICS","07/01/2024","06/06/2024","Charis Tsikkou","WV","West Virginia University Research Corporation","Standard Grant","Hailiang Liu","06/30/2025","$30,000.00","Casian Pantea, Adrian Tudorascu, Adam Halasz","chtsikkou@mail.wvu.edu","886 CHESTNUT RIDGE ROAD","MORGANTOWN","WV","265052742","3042933998","MPS","126600","7556, 9150","$0.00","The 42nd Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE) will be held at West Virginia University, Morgantown, WV, on November 9-10, 2024. SEARCDE has devoted itself to bringing together the region?s leading experts and young researchers for over forty years. The meeting provides a valuable venue for researchers to exchange ideas and foster collaborations on questions arising from differential equations and applications. Moreover, it provides an excellent mentorship platform for students, postdoctoral researchers, and junior faculty. It has become a tradition for SEARCDE to include a significant proportion of talks by advanced undergraduates, graduate students, and postdocs, who are encouraged to present their research. Additionally, application-oriented talks that focus on numerical or experimental aspects will interest engineers, software developers, and other professionals in the region.

The 42nd SEARCDE is committed to inclusion and diversity. This year, the conference will be held ""in cooperation with the Association for Women in Mathematics (AWM)"" to boost visibility and awareness and further encourage the participation of women and underrepresented groups. The conference, which consists of four plenary speakers and parallel sessions with invited and contributed presentations, will focus on the following themes: (1) Analytical approaches to solving differential equations with physical, life, and material sciences applications, (2) Numerical and computational methods in solving differential equations, (3) Optimization and applications in control and data sciences. More information about the conference can be found at https://mathanddata.wvu.edu/searcde-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." "2404508","MPS/DMS-EPSRC: Stabilization Using Feedback Controls, Numerical Methods for Stochastic Systems, and Systems with Mean-Field Interactions","DMS","APPLIED MATHEMATICS","06/01/2024","05/30/2024","Gang George Yin","CT","University of Connecticut","Standard Grant","Pedro Embid","05/31/2027","$166,110.00","","gyin@uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","126600","075Z","$0.00","Many dynamical systems encountered in natural and engineered environments consist of networks made of numerous interacting agents. Examples can be found in power grids, the internet, social and financial networks, and host-pathogen networks in human-biological systems. Many of these systems have large size and complex network structure, and understanding and controlling those systems requires consideration of sudden effects at random times, and cope with the fact that only partial observations of the entire system are available. The research team, consisting of one US-based and one UK-based investigator, will carry out a theoretical and computational program for the design, analysis, and numerical implementation of controls for complex stochastic dynamical systems. The project will contribute to enhancing the collaboration of US and UK scientists and to provide students and postdocs with the opportunity to participate in this international collaborative research effort.

The US-UK team will work on the following tasks: (1) to design feedback controls for stabilization of random dynamic systems running in continuous time with additional random switching but with only discrete-time observations, where the focus will be on the design of control over suitable sampling interval to overcome the challenges posed by having to work with infinite dimensional dynamical systems with time delay, (2) To construct feedback strategies for stabilization using discrete-time-state-feedback control, where the focus is to investigate whether a discrete-time-state-feedback control can stabilize a regime-switching stochastic differential system in the sense of asymptotic stability in distribution. In addition, efficient numerical algorithms for approximating the desired stationary distributions will be developed. (3) To develop novel computational methods when the underlying systems can only be observed partially. Traditional approaches based on nonlinear filtering suffer the curse of dimensionality. Based on our recent work of computational nonlinear filtering using a deep neural network, a new computational approach will be developed. The asymptotic properties of the algorithms will be examined along with extensive numerical experiments. (4) To investigate mean-field control and game problems for complex dynamic systems with mean-field interactions and switching diffusions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2407694","NSF-UEFISCDI: Linear and Nonlinear Stability of Physical Flows","DMS","APPLIED MATHEMATICS, ANALYSIS PROGRAM","07/01/2024","05/30/2024","Alexandru Ionescu","NJ","Princeton University","Standard Grant","Pedro Embid","06/30/2027","$299,213.00","","aionescu@princeton.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","126600, 128100","","$0.00","The main goal of the project is to study the dynamics of solutions of several important partial differential equations. These equations describe some of the classical systems of Applied Mathematics and Physics, such as incompressible fluids, geophysical flows, plasma, and water waves, and stability or instability of their solutions is a fundamental question, with both theoretical and practical applications. We aim to analyze these solutions rigorously and to recover quantitative and qualitative information about their behavior as mathematical theorems. The project will establish links and collaborations between researchers at leading American and Romanian universities, as part of the new NSF-UEFISCDI initiative, support the training and development of early-career researchers and students, with a focus of enhancing diversity, and disseminate the research widely at conferences and summer schools.

The project will investigate the long-time dynamics of solutions of several evolution PDE, such as the Euler and the Navier-Stokes equations, geophysical flows, the Vlasov-Poisson system, and water waves models, mainly in dimensions 2 and 3. These equations have important explicit solutions, and the main questions to be considered have to do with the long-time stability of these solutions. Specific major problems will be investigated, concerning the global stability of shear flows and vortices for the 2D Euler and Navier-Stokes equations, the instability of mountain waves, the complex dynamics of oceanic flows, and the global stability of homogeneous solutions of the Vlasov-Poisson system. This is a very active field, with many recent methods and results. It is likely that other important problems will emerge and will become feasible during the course of the investigation.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406870","Mathematical Problems in Relativistic Fluid Dynamics","DMS","APPLIED MATHEMATICS","07/01/2024","05/30/2024","Marcelo Disconzi","TN","Vanderbilt University","Standard Grant","Dmitry Golovaty","06/30/2027","$305,000.00","","marcelo.disconzi@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126600","","$0.00","Relativistic fluid dynamics is concerned with the study of fluids (like water, gases, or the plasma that composes our Sun) when effects pertaining to Einstein?s theory of relativity cannot be neglected. It plays an essential role in many areas of physics, including high-energy nuclear physics, astrophysics, and cosmology. It is also a fertile source of mathematical problems. This project will advance the mathematical foundations and applications of relativistic fluid dynamics by studying problems of outstanding scientific merit in mathematics and physics. The project will contribute to the formation of the next generation of scientists via support of graduate students and dissemination of research findings through seminars and conferences. The project will also promote STEM education among children through events (such as reading sessions) related to the principal investigator?s book ?Who Me? I?m a Mathematician Now!? The book is part of the Who Me series, published by World Scientific, whose goal is to promote STEM fields among children. It targets children at about ten-years old and the goal of the book is to get children excited about mathematics.

The scientific goals of this project are (I) establish local well-posedness of the primary model of relativistic gaseous star dynamics, given by a free-boundary version of the Einstein-Euler system; (II) establish local and global well-posedness and causality for the two most widely used models of relativistic fluids with viscosity; and (III) devise mathematical tools to access the reliability of numerical simulations of relativistic fluids with viscosity pertinent to the study of heavy-ion collisions and mergers of neutron stars. A key element of the project is the development of tools to study quasilinear hyperbolic partial differential equations with multiple characteristic speeds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2407694","NSF-UEFISCDI: Linear and Nonlinear Stability of Physical Flows","DMS","APPLIED MATHEMATICS, ANALYSIS PROGRAM","07/01/2024","05/30/2024","Alexandru Ionescu","NJ","Princeton University","Standard Grant","Pedro Embid","06/30/2027","$299,213.00","","aionescu@princeton.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","126600, 128100","","$0.00","The main goal of the project is to study the dynamics of solutions of several important partial differential equations. These equations describe some of the classical systems of Applied Mathematics and Physics, such as incompressible fluids, geophysical flows, plasma, and water waves, and stability or instability of their solutions is a fundamental question, with both theoretical and practical applications. We aim to analyze these solutions rigorously and to recover quantitative and qualitative information about their behavior as mathematical theorems. The project will establish links and collaborations between researchers at leading American and Romanian universities, as part of the new NSF-UEFISCDI initiative, support the training and development of early-career researchers and students, with a focus of enhancing diversity, and disseminate the research widely at conferences and summer schools.

The project will investigate the long-time dynamics of solutions of several evolution PDE, such as the Euler and the Navier-Stokes equations, geophysical flows, the Vlasov-Poisson system, and water waves models, mainly in dimensions 2 and 3. These equations have important explicit solutions, and the main questions to be considered have to do with the long-time stability of these solutions. Specific major problems will be investigated, concerning the global stability of shear flows and vortices for the 2D Euler and Navier-Stokes equations, the instability of mountain waves, the complex dynamics of oceanic flows, and the global stability of homogeneous solutions of the Vlasov-Poisson system. This is a very active field, with many recent methods and results. It is likely that other important problems will emerge and will become feasible during the course of the investigation.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2420029","Hypoelliptic and Non-Markovian stochastic dynamical systems in machine learning and mathematical finance: from theory to application","DMS","APPLIED MATHEMATICS","02/01/2024","02/06/2024","Qi Feng","FL","Florida State University","Standard Grant","Pedro Embid","05/31/2026","$152,899.00","","qfeng2@fsu.edu","874 TRADITIONS WAY","TALLAHASSEE","FL","323060001","8506445260","MPS","126600","9251","$0.00","This project investigates stochastic analysis and numerical algorithms for stochastic dynamical systems, together with their applications in machine learning and finance. The first part focuses on the foundations of machine learning/data science, which guarantees the theoretical convergence of numerical algorithms (e.g., stochastic gradient descent, Markov Chain Monte Carlo) in non-convex optimization and multi-modal distribution sampling. This project will develop algorithms to solve such problems in big data and engineering, which include uncertainty quantification in AI safety problems, control robotics motions, and image processing. The second part focuses on the stochastic models in mathematical finance and algorithm designs in option/asset pricing. The applications in this part target efficient algorithms for path-dependent option pricing with rough volatilities, which are expected to significantly impact some computation-oriented financial instruments, such as model-based algorithm trading involving rough volatility and high-frequency data. This project will provide support and research opportunities for graduate and undergraduate students.

The stochastic systems in this project possess degenerate, mean-field, or non-Markovian properties. In the first part, the PI will study the ""hypocoercivity"" (i.e., convergence to equilibrium) for highly degenerate and mean-field stochastic dynamical systems and their applications to algorithms design in machine learning. One of the proposed topics will focus on the (non)-asymptotic analysis of the general degenerate/mean-field system and its exponential convergence rate to the equilibrium (e.g., Vlasov-Fokker-Planck equations; Langevin dynamics on higher order nilpotent Lie groups). As applications of the convergence of such dynamics, the PI will design algorithms focusing on non-convex optimizations and distribution samplings in machine learning. In the second part, the PI will study non-Markovian stochastic dynamical systems capturing path-dependent and mean-field features of the financial market. The topics include path-dependent PDEs, stochastic Volterra integral equations, conditional mean-field SDEs, and the Volterra signatures. The PI focuses on addressing the fundamental issues, including the density for the rough volatility model and conditional mean-field SDEs and the structure of Volterra signatures. Furthermore, the PI focuses on designing efficient numerical algorithms using the Volterra signature and deep neural networks. These algorithms target solving path-dependent PDEs, path-dependent option pricing, and optimal stopping/switching 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." "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." "2407549","Collaborative Research: Stochastic Modeling for Sustainable Management of Water Rights","DMS","APPLIED MATHEMATICS","07/01/2024","05/21/2024","Igor Cialenco","IL","Illinois Institute of Technology","Standard Grant","Pedro Embid","06/30/2027","$200,000.00","","cialenco@iit.edu","10 W 35TH ST","CHICAGO","IL","606163717","3125673035","MPS","126600","124Z, 5294","$0.00","Sustainable and equitable management of groundwater is one of the key aspects of adaptation to climate change in drought-affected regions nationwide. The rapid depletion of aquifers is spurring the creation of new groundwater management institutions to ensure conservation of groundwater supplies across generations. This project will provide new mathematical tools for designing efficient and fair water markets, that are free of predatory or exploitative behavior and flexibly respond to stakeholder needs, helping to build a water resilient future. The developed numerical algorithms would facilitate better market regulations and policies, supporting legislative mandates and their economic viability. The dissemination activities will enhance the exchange of ideas and knowledge between mathematicians, data scientists, resource economists and hydrologists. This award will also provide opportunities for student involvement in the research.

This project will address dynamic water allocation and equilibrium for tradeable water rights by establishing the foundations for an innovative mathematical framework for water management through the lens of stochastic games and market equilibria. The project will develop a tractable top-down stochastic model of groundwater levels to study the price formation of the groundwater rights as a Nash equilibrium of a non-cooperative game between the economic agents. In tandem, the project will characterize the Pareto optimal water rights allocation and water banking strategy from the perspective of a central planner. Modeling and pricing of groundwater rights and their fair distribution will articulate the benefits and dangers of potential management policies and quantify the efficiency of regulations. The project will also develop scalable computational schemes for multi-period equilibria with multiple stakeholders.

This award reflects 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/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv b/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv index 7ca7f5b..a335c81 100644 --- a/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv +++ b/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv @@ -1,30 +1,29 @@ "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" -"2411208","Collaborative Research: Numerical Methods and Differential Geometry","DMS","COMPUTATIONAL MATHEMATICS","06/15/2024","06/04/2024","Evan Gawlik","HI","University of Hawaii","Standard Grant","Yuliya Gorb","05/31/2027","$190,527.00","","egawlik@hawaii.edu","2425 CAMPUS RD SINCLAIR RM 1","HONOLULU","HI","968222247","8089567800","MPS","127100","9150, 9263","$0.00","Partial differential equations (PDEs) model a wide variety of phenomena, ranging from how an airplane wing deforms in response to turbulence, to how radio waves travel through and around objects, to how black holes generate gravitational waves when they merge. Numerical analysts develop algorithms for simulating these systems by solving PDEs on a computer; these simulations enable engineers and scientists to develop prototypes and to interpret data from sensors. For example, the NSF-funded Nobel-winning detection of gravitational waves would not have been possible without advances in numerical analysis. In recent decades, numerical analysts discovered that ideas from differential geometry, an area of pure mathematics, can be used to develop good algorithms for solving PDEs. In fact, these ideas help not only for geometric problems in fields of study like computer vision and general relativity, but also for fields like electromagnetism that have little to do with geometry. Although applying differential geometry to numerical analysis has been very successful, thus far this link has been explored only for a small number of differential geometry ideas. In this project, the investigators will continue exploring this link, taking more ideas from differential geometry and applying them to develop new numerical algorithms. These algorithms could then be used both in applied areas, by solving PDEs in science and engineering, and in pure areas, by solving PDEs in differential geometry itself. The project will also support the training of graduate student researchers.

This project focuses on problems at the cusp of numerical analysis and differential geometry. It deals specifically with the design of finite element methods for PDEs that involve vector fields and tensor fields on Riemannian manifolds. In the long term, these efforts have the potential to lead to robust numerical methods for solving geometric PDEs like the Einstein field equations, which are useful for studying gravitational wave signals, as well as PDEs like the elasticity equations, which model how objects deform under stress. This project has three main goals. The first is to develop a new family of finite elements for discretizing algebraic curvature tensors and other bi-forms---tensor products of differential forms---on simplicial triangulations. The second goal is to develop an intrinsic finite element discretization of the Bochner Laplacian, which is a basic differential operator in Riemannian geometry that differs from the familiar Hodge Laplacian from finite element exterior calculus. The third goal is to leverage what we learn to design numerical methods for a wide range of geometric problems, such as computing spectra of elliptic operators on manifolds, simulating intrinsic geometric flows, and solving prescribed curvature 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." +"2410678","Collaborative Research: Data-driven Realization of State-space Dynamical Systems via Low-complexity Algorithms","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","06/07/2024","Aaron Welters","FL","Florida Institute of Technology","Standard Grant","Jodi Mead","07/31/2027","$125,000.00","Xianqi Li","awelters@fit.edu","150 W UNIVERSITY BLVD","MELBOURNE","FL","329018995","3216748000","MPS","127100","079Z, 9263","$0.00","Data science is evolving rapidly and places a new perspective on realizing state-space dynamical systems. Predicting time-advanced states of dynamical systems is a challenging problem in STEM disciplines due to their nonlinear and complex nature. This project will utilize data-driven methods and analyze state-space dynamical systems to predict and understand future states, surpassing classical techniques. In addition, the PI team will (i) guide students to obtain cross-discipline PhD/Master's degrees, (ii) guide students to work in a peer-learning environment, and (iii) educate a diverse group of undergraduates.

In more detail, this project will utilize state-of-the-art machine learning (ML) algorithms to efficiently analyze and predict information within data matrices and tensor computations with low-complexity algorithms. Single-dimensional ML models are not efficient at extracting hidden semantic information in the time and space domains. As a result, it becomes challenging to simultaneously capture multi-dimensional spatiotemporal data in state-space dynamical systems. Using efficient ML algorithms to recover multi-dimensional spatiotemporal data simultaneously offers a breakthrough in understanding the chaotic behavior of dynamical systems. This project will (i) utilize ML to predict future states of dynamical systems based on high-dimensional data matrices captured at different time stamps, (ii) realize state-space controllable and observable systems via low-complexity algorithms to simultaneously analyze multiple states of the systems, (iii) analyze noise in state-space systems for uncertainty quantification, predict patterns in real-time states, generate counter-resonance states to suppress them, and optimize performance and stability, (iv) study system resilience via multiple state predictors and perturbations to assess performance and adaptation to disturbances and anomalies, and finally (v) optimize spacecraft trajectories, avoid impact, and use low-complexity algorithms to understand spacecraft launch dynamics on the space coast and support ERAU's mission in aeronautical research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2409918","Structure preservation in nonlinear, degenerate, evolution","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","06/03/2024","Abner Salgado","TN","University of Tennessee Knoxville","Standard Grant","Ludmil T. Zikatanov","07/31/2027","$204,533.00","","asalgad1@utk.edu","201 ANDY HOLT TOWER","KNOXVILLE","TN","379960001","8659743466","MPS","127100","9263","$0.00","A thorough treatment is feasible for the classical linear problems in the numerical approximation of partial differential equations. The continuous problem is well-posed. The numerical schemes are well-posed, parameter-robust, and convergent. It is even possible to prove convergence rates. However, the situation is more precarious for modern, complex systems of equations. Oftentimes, the uniqueness of solutions is not known. Even when there is uniqueness, the theory is far from complete, and so besides (weak) convergence of numerical solutions, little can be said about their behavior. In these scenarios, one must settle for simpler yet still relevant goals. An important goal in this front is that of structure preservation. The study of structure preservation in numerical methods is not new. Geometric numerical integration, many methods for electromagnetism, the finite element exterior calculus, and some novel approaches to hyperbolic systems of conservation laws, have this goal in mind: geometric, algebraic, or differential constraints must be preserved. This project does not focus on the problems mentioned above. Instead, it studies structure preservation in some evolution problems that have, possibly degenerate, diffusive behavior. This class of problems remains a largely unexplored topic when it comes to numerical discretizations. Bridging this gap will enhance modeling and prediction capabilities since diffusive models can be found in every aspect of scientific inquiry.

This project is focused on a class of diffusive problems in which stability of the solution cannot be obtained by standard energy arguments, in other words, by testing the equation with the solution to assert that certain space-time norms are under control. Norms are always convex. Structure preservation may then be a generalization of the approach given above. Instead of norms being under control, a (family of) convex functional(s) evaluated at the solution behave predictably during the evolution. The project aims to develop numerical schemes that mimic this in the discrete setting. While this is a largely unexplored topic, at the same time, many of the problems under consideration can be used to describe a wide range of phenomena. In particular, the project will develop new numerical schemes for an emerging theory of non-equilibrium thermodynamics, active scalar equations, and a class of problems in hyperbolic geometry. These models have a very rich intrinsic structure and a wide range of applications, and the developments of this project will serve as a stepping stone to bring these tools to the numerical treatment of more general problems. The students involved in the project will be trained in exciting, mathematically and computationally challenging, and practically relevant areas of research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2410676","Collaborative Research: Data-driven Realization of State-space Dynamical Systems via Low-complexity Algorithms","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","06/07/2024","Sirani Mututhanthrige-Perera","FL","Embry-Riddle Aeronautical University","Standard Grant","Jodi Mead","07/31/2027","$175,000.00","","pereras2@erau.edu","1 AEROSPACE BLVD","DAYTONA BEACH","FL","321143910","3862267695","MPS","127100","079Z, 9263","$0.00","Data science is evolving rapidly and places a new perspective on realizing state-space dynamical systems. Predicting time-advanced states of dynamical systems is a challenging problem in STEM disciplines due to their nonlinear and complex nature. This project will utilize data-driven methods and analyze state-space dynamical systems to predict and understand future states, surpassing classical techniques. In addition, the PI team will (i) guide students to obtain cross-discipline PhD/Master's degrees, (ii) guide students to work in a peer-learning environment, and (iii) educate a diverse group of undergraduates.

In more detail, this project will utilize state-of-the-art machine learning (ML) algorithms to efficiently analyze and predict information within data matrices and tensor computations with low-complexity algorithms. Single-dimensional ML models are not efficient at extracting hidden semantic information in the time and space domains. As a result, it becomes challenging to simultaneously capture multi-dimensional spatiotemporal data in state-space dynamical systems. Using efficient ML algorithms to recover multi-dimensional spatiotemporal data simultaneously offers a breakthrough in understanding the chaotic behavior of dynamical systems. This project will (i) utilize ML to predict future states of dynamical systems based on high-dimensional data matrices captured at different time stamps, (ii) realize state-space controllable and observable systems via low-complexity algorithms to simultaneously analyze multiple states of the systems, (iii) analyze noise in state-space systems for uncertainty quantification, predict patterns in real-time states, generate counter-resonance states to suppress them, and optimize performance and stability, (iv) study system resilience via multiple state predictors and perturbations to assess performance and adaptation to disturbances and anomalies, and finally (v) optimize spacecraft trajectories, avoid impact, and use low-complexity algorithms to understand spacecraft launch dynamics on the space coast and support ERAU's mission in aeronautical research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2410677","Collaborative Research: Data-driven Realization of State-space Dynamical Systems via Low-complexity Algorithms","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","06/07/2024","Kshitij Khare","FL","University of Florida","Standard Grant","Jodi Mead","07/31/2027","$89,853.00","","kdkhare@stat.ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","127100","079Z, 9263","$0.00","Data science is evolving rapidly and places a new perspective on realizing state-space dynamical systems. Predicting time-advanced states of dynamical systems is a challenging problem in STEM disciplines due to their nonlinear and complex nature. This project will utilize data-driven methods and analyze state-space dynamical systems to predict and understand future states, surpassing classical techniques. In addition, the PI team will (i) guide students to obtain cross-discipline PhD/Master's degrees, (ii) guide students to work in a peer-learning environment, and (iii) educate a diverse group of undergraduates.

In more detail, this project will utilize state-of-the-art machine learning (ML) algorithms to efficiently analyze and predict information within data matrices and tensor computations with low-complexity algorithms. Single-dimensional ML models are not efficient at extracting hidden semantic information in the time and space domains. As a result, it becomes challenging to simultaneously capture multi-dimensional spatiotemporal data in state-space dynamical systems. Using efficient ML algorithms to recover multi-dimensional spatiotemporal data simultaneously offers a breakthrough in understanding the chaotic behavior of dynamical systems. This project will (i) utilize ML to predict future states of dynamical systems based on high-dimensional data matrices captured at different time stamps, (ii) realize state-space controllable and observable systems via low-complexity algorithms to simultaneously analyze multiple states of the systems, (iii) analyze noise in state-space systems for uncertainty quantification, predict patterns in real-time states, generate counter-resonance states to suppress them, and optimize performance and stability, (iv) study system resilience via multiple state predictors and perturbations to assess performance and adaptation to disturbances and anomalies, and finally (v) optimize spacecraft trajectories, avoid impact, and use low-complexity algorithms to understand spacecraft launch dynamics on the space coast and support ERAU's mission in aeronautical research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2410943","Integral Equation Methods for the Efficient Simulation of Nonlinear Interface Phenomena","DMS","COMPUTATIONAL MATHEMATICS","10/01/2024","06/03/2024","Andreas Kloeckner","IL","University of Illinois at Urbana-Champaign","Continuing Grant","Yuliya Gorb","09/30/2027","$118,353.00","","andreask@illinois.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","127100","9263","$0.00","Simulation technology for nonlinear interface phenomena enabling high, managed accuracy with low cost is an urgent need in many fields of science and technology. This project seeks to develop new numerical methods that address these needs. The methods under consideration belong to the family of integral equation methods, which attain asymptotically optimal cost in the solution of certain (""linear homogeneous exterior elliptic boundary value"") problems. The project seeks to extend them to challenging nonlinear settings, while improving their efficiency when modeling boundary layers, and developing new methods for the case where volume contributions are needed. Examples of technical fields in which such methods are needed include the project's motivating applications, which will be used to demonstrate our methods' efficacy: (1) Wetting problems, relevant across chemical engineering and biology. (2) Nonlinear plasmonics, a promising avenue for the construction of optical networks. Accurate computer simulation can help confirm or refute scientific theories by comparison with experiment, can replace experiments, and can be used in engineering design processes. The PhD students trained under the project will add to the nation's scarce expert labor supply, and the methods and open-source software released under the project will enable science and industry users around the world to deploy the newly-developed methods for the advancement of science.

Since they are based on the superposition principle, integral equation methods (IEMs) are not often used to solve partial differential equation (PDE) problems with nonlinearities. This project removes important obstacles to the adoption of IEMs in such a setting, and it validates the case for them through two ambitious motivating nonlinear model applications involving interfaces. The efficient solution of elliptic (i.e. globally coupled) computational problems remains a major challenge, and IEMs have crucial strengths in this area. While one major strength of IEMs is the use of boundary (i.e. lower-dimensional) unknowns to represent volume solutions, the presence of nonlinearities invariably necessitates the use of volume unknowns. We demonstrate that this use can often be kept localized, particularly in problems modeling interfaces, while maintaining IEM's suitability for problems on unbounded domains. We propose a new method for the evaluation of the resulting volume potentials that retains high-order accuracy in the presence of complex geometry. The project builds on recent advances made by the PI on high-order accurate fast algorithms for the evaluation of layer potentials, the building blocks of IEMs, in the presence of complex geometry in two and three dimensions. We further propose research leading to major efficiency gains in the underlying singular quadrature method and, motivated by empirical observations, a theoretical investigation of the influence of geometry on the accuracy of that method. A final line of proposed research concerns the reduction of resolution demands posed by boundary layers, embodied in IEMs by rapidly-decaying Green's functions, which often result in increases of computational cost that threaten to make certain simulations infeasible.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2410717","Quantization and Compression for Neural Networks: Theory and Algorithms","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","06/03/2024","Rayan Saab","CA","University of California-San Diego","Standard Grant","Jodi Mead","07/31/2027","$299,889.00","","rsaab@ucsd.edu","9500 GILMAN DR","LA JOLLA","CA","920930021","8585344896","MPS","127100","079Z, 9263","$0.00","The research project focuses on making advanced AI technologies, like the neural networks used in language models and for image generation or analysis, more efficient and environmentally friendly. Today, these technologies require significant computational power, which makes them both costly and energy-intensive. This project aims at developing algorithms for replacing such networks with functionally equivalent ones that require fewer computational resources, without losing their effectiveness. The resulting reduction in computational complexity will also help enable the use of AI in real-time applications and on devices with limited resources, further expanding this critical technology's reach. Thus, the expected scientific outcome is the development of robust, efficient, practical algorithms that are also backed by rigorous theoretical guarantees. Moreover, we anticipate that the theoretical tools we develop in order to analyze these algorithms will find broader use in other application areas. The project also emphasizes the importance of education and academic community involvement. By integrating research findings into university courses and involving students from potentially diverse backgrounds, the project will help prepare the next generation of mathematicians and engineers. Additionally, it aims to share breakthroughs with broader communities through journal publications, workshops, and conferences, while also connecting students with real-world industry applications.

As previously stated, the project aims to address the challenge of compressing large neural networks, which are pivotal in modern AI applications but are resource-intensive. Thus, the research will focus on developing algorithms that reduce the computational demands of these networks by minimizing the memory and power needed without compromising their performance. Our approach involves three main strategies, quantization, pruning, and low-rank approximation. Among these, quantization transforms neural network parameters into formats that require fewer bits, thus reducing memory usage and computational intensity. Meanwhile, pruning selectively removes less important parameters from the network to streamline computations. Finally, low-rank approximation replaces large matrices representing the weights in the network with products of smaller matrices, in a way that retains essential information while requiring less memory and computation. We will develop algorithmic approaches for quantization, pruning, and low-rank approximation that are underpinned by rigorous mathematical theories to ensure the reliability and effectiveness of the compressed models. In our analysis, we will utilize stochastic process theory, geometric functional analysis, discrete geometry, discrepancy theory, optimization theory, compressed sensing, and dimensionality reduction, to name a few. These diverse areas will help us establish a solid theoretical foundation for our algorithms consisting of lower bounds on best-possible theoretical error guarantees as well as upper bounds on the errors resulting from our algorithms.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2411229","Taming nonlinearity in PDE systems using lifted Newton nonlinear preconditioning","DMS","COMPUTATIONAL MATHEMATICS","09/01/2024","06/04/2024","Georg Stadler","NY","New York University","Standard Grant","Yuliya Gorb","08/31/2027","$399,998.00","","stadler@courant.nyu.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","127100","9263","$0.00","Many important questions in the natural sciences and in engineering involve nonlinear phenomena, mathematically described by nonlinear equations. Solving these problems typically requires iterative algorithms like Newton's method, which linearizes the nonlinear problem in each iteration. Newton's method is known for its rapid local convergence. However, the convergence theory only applies when the initialization is (very) close to the unknown solution. Thus, relying on local convergence theory is often impractical. Farther from the solution, small Newton updates are typically necessary to prevent divergence, leading to slow overall convergence. This project aims to develop better nonlinear solvers. This will benefit outer-loop problems, such as parameter estimation, learning, control, or design problems, which typically require solving many nonlinear (inner) problems. The project will also support the training and research of at least one graduate student, the mentoring of undergraduate students through the Courant?s Summer Undergraduate Research Experience (SURE) program, and the outreach to K-12 students through the cSplash activity in New York City.

To address issues of slow nonlinear convergence, This project aims to develop methods that lift the nonlinear system to a higher-dimensional space, enabling the application of nonlinear transformations that can mitigate nonlinearity before Newton linearization. The project will develop and systematically study the resulting novel Newton methods for severely nonlinear systems of partial differential equations (PDEs). The proposed lifting and transformation method can be interpreted as nonlinear preconditioning, a research area much less developed than preconditioning for linear systems. The goal of this project is to study for which classes of nonlinear PDE problems this approach improves convergence, to theoretically analyze why, and to make these methods a more broadly accessible tool for solving severely nonlinear 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." +"2410893","Unsteady Reynolds averaged Navier-Stokes models and computational fluid dynamics","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","06/07/2024","William Layton","PA","University of Pittsburgh","Standard Grant","Ludmil T. Zikatanov","07/31/2027","$220,000.00","","wjl+@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","127100","9263","$0.00","The project will conduct research on the numerical solution of turbulent ?ows. Fluids transport and mix heat, chemical species, and contaminants. Accurate simulation of turbulent flow is essential for safety critical prediction and design in applications involving these and other e?ects. Turbulent ?ow prediction in science , engineering and industry requires the use of turbulence models. The research project has 3 objectives: increasing accuracy of these models, decreasing model complexity and exploring a promising algorithmic idea for computer solution of models. The proposed research also develops the expertise of graduate students in computational and applied mathematics while working on compelling problems addressing human needs. In their development into independent scientists, each student will develop their own research agenda and collaborate at points of contact among the problems studied.

Modeling turbulence presents challenges at every level in every discipline it touches. 2-equation Unsteady Reynolds Averaged Navier-Stokes models are common in applications and also the ones with the most incomplete mathematical foundation. They have many calibration parameters, work acceptably for ?ows similar to the calibration data set and require users to have an intuition about which model predictions to accept and which to ignore. The project?s model analysis will address model accuracy, complexity and reliability. Even after modeling, greater computational resources are often required for their computational solution. In 1991 Ramshaw and Mesina proposed a non-obvious synthesis of penalty and arti?cial compression methods, resulting in a dispersive regularization of ?uid motion. When the two effects were balanced, they reported a dramatic accuracy improvement over the most e?cient current methods. The project will develop, improve and test the method based on a new analysis of energy ?ow.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409900","Tensor-valued finite elements and applications","DMS","COMPUTATIONAL MATHEMATICS","09/01/2024","06/03/2024","Jay Gopalakrishnan","OR","Portland State University","Continuing Grant","Yuliya Gorb","08/31/2027","$56,009.00","","gjay@pdx.edu","1600 SW 4TH AVE","PORTLAND","OR","972015508","5037259900","MPS","127100","9263","$0.00","Tensor-valued functions are crucial mathematical abstractions in many areas of science. They are indispensable in modeling solids, fluids, electromagnetics, and even the spacetime we occupy, all areas touched upon in this project. The overarching goal of this project is to build new numerical facilities for approximating certain important tensor fields using new finite elements. The pursuit of this goal is guided not only by the utilitarian considerations of the applications, but also by the elegance of mathematical structures within which the new numerical tools potentially fit. These abstract structures have transdisciplinary connections, including applications of societal impact in material science, fluid dynamics, and optics.

Several specific tensor functions, rich in applications, are targeted in this study for finite element approximation. They include the Riemann curvature tensor on manifolds, the Cauchy stress tensor in solid mechanics, and viscous stresses in incompressible fluids. Certain second-order differential operators, like the incompatibility operator, arising in mechanics and linearized relativity, are targeted for approximation using distributional techniques suited for non-smooth finite elements. The project develops new simulation tools for temporal evolution of certain tensors using symplectic integrators and automatic locally variable timestepping using spacetime tents. Varied elements of this project are unified by a modern viewpoint, exemplified by fitting many existing scalar and vector finite elements into a subcomplex of the de Rham complex. The search for a similar unifying algebraic structure connecting tensor spaces, through certain natural second-order differential operators, is a common mathematical thread running through all aspects of this 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." "2409807","Approximating partial differential equations without boundary conditions","DMS","COMPUTATIONAL MATHEMATICS","10/01/2024","06/03/2024","Andrea Bonito","TX","Texas A&M University","Standard Grant","Yuliya Gorb","09/30/2027","$399,583.00","","bonito@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","127100","9263","$0.00","The predicting power of computational tools is of paramount importance in engineering and science. They offer insights into the behavior of complex systems, modeled by partial differential equations inside a region of interest. Boundary conditions expressing the influence of the surroundings must be provided to complete the mathematical models. However, there are many instances for which the boundary conditions are not available to practitioners: the understanding of the physical processes might be lacking, for instance when modeling the airflow around an airplane, or the boundary data is not accessible. This project aims to design numerical algorithms able to alleviate missing information on boundary conditions by incorporating physical measurements of the quantity of interest. The problems to be addressed fit under the strategic area of machine learning, and the potential scientific impact of this research is far-reaching. It includes improved meteorological forecasting, discovering biological pathways, and commercial design.

In traditional numerical treatments of elliptic partial differential equations, the solution to be approximated is completely characterized by the given data. However, there are many instances for which the boundary conditions are not available. While not sufficient to pinpoint the solution, measurements of the solution are provided to attenuate the incomplete information. The aim of this research program is to exploit the structure provided by the PDE to design and analyze practical numerical algorithms able to construct the best simultaneous approximation of all functions satisfying the PDE and the measurements. This project embeds the design, analysis, and implementation of numerical methods for PDEs within an optimal recovery framework. It uncovers uncharted problematics requiring new mathematical tools.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2410645","Computational Methods for Inverse and Optimal Design Problems in Topological Wave Insulators Based on Constructive Analysis","DMS","COMPUTATIONAL MATHEMATICS, EPSCoR Co-Funding","07/01/2024","06/04/2024","Junshan Lin","AL","Auburn University","Standard Grant","Troy D. Butler","06/30/2027","$300,263.00","","jzl0097@auburn.edu","321-A INGRAM HALL","AUBURN","AL","368490001","3348444438","MPS","127100, 915000","9150, 9263","$0.00","Topological wave insulators are a specialized material for transporting wave energy in various applications in modern science and engineering. This project will develop computational methods for several classes of inverse and optimal problems arising from the mathematical studies of partial differential equation (PDE) models for topological wave insulators. The goals of this project are to provide efficient computational algorithms that address several theoretical open questions in this area. Successful completion of this project should stimulate the mathematical research for topological insulators and beyond. The developed computational frameworks will also provide physical experimentalists and engineers with the computational tools to improve the performance and functionalities of topological materials. The project will also integrate students into the research team as part of their professional training.

The project will address several key scientific challenges arising from the inverse and optimal design of the spectrum of the PDE operators in topological wave insulators. First, based on the spectral analysis of the PDE operators in periodic media, a new optimization framework through the enforcement of parity for the eigenfunctions will be built to solve for wave insulators that attain Dirac points at desired Bloch wave vectors and eigenfrequencies. Numerical algorithms based on the construction of wave propagators in periodic media and the design of the spectral indicator function will be developed to efficiently identify the interface parameters that allow for the existence of edge modes in joint topological wave insulators. Finally, efficient convex semidefinite programming based numerical methods will be developed for solving the optimization problems that arise from maximizing the band gaps of the PDE operators for topological wave insulators in order to enlarge the spectral bandwidth of edge modes. This project is jointly funded by the Computational Mathematics 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." "2410272","Level Set Methods for Multiphase Motion by Mean Curvature","DMS","COMPUTATIONAL MATHEMATICS","06/15/2024","06/03/2024","Selim Esedoglu","MI","Regents of the University of Michigan - Ann Arbor","Standard Grant","Yuliya Gorb","05/31/2027","$349,518.00","","esedoglu@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","127100","9263","$0.00","This project will develop new algorithms for simulating on the computer a class of mathematical models that describe the evolution in time of a network of surfaces. These models play a prominent role in many applications. A very important example that will receive particular attention is the evolution of the internal structure (microstructure) of polycrystalline materials, such as most metals and ceramics, during manufacturing processes such as heat treatment (annealing). Polycrystalline materials are very common. They are composed of tiny crystallites, known as grains, stuck together. During annealing, the boundaries between the grains, described by a network of surfaces, start to move as some grains get larger, while others shrink and disappear. The shapes and sizes of the grains making up these materials are known to have profound implications for their physical properties, such as their strength and conductivity. Materials scientists have long had mathematical models that describe the motion of the network of grains; what has been lacking is accurate, efficient, reliable, and flexible numerical methods that would allow them to compare large scale simulations of their models against experimental measurements. In recent years, as experimental measurements of time evolution of the three dimensional internal structure of materials have become available, the need for algorithms to simulate the relevant models have become increasingly acute. The project will take steps to address this need. Resulting algorithms will be implemented in software, which will be made available to the broader scientific community. The project will also support the training and research of one graduate student working towards a Ph.D. in mathematics.

The project will take a new approach to designing level set methods for multiphase geometric motions such as motion by mean curvature of networks of surfaces. It will exploit a precise, mathematical connection between a particular discretization of the level set formulation of motion by mean curvature, known as the median filter scheme, and another class of algorithms known as threshold dynamics. This will allow extending advantages of one method to the other. The advantage of threshold dynamics is its generality and highly developed theory of stability and convergence. In particular, recent advances in our theoretical understanding of threshold dynamics enabled its extension to the more elaborate microstructure evolution models of interest to materials scientists. Via its precise connection to median filter schemes, elements of this theory will be carried over to level set methods. The new level set methods will allow arbitrary, normal dependent (anisotropic) surface tensions and mobilities to be assigned to any interface in the network of surfaces ? a level of generality that cannot even be attempted by most existing techniques. They will also allow subgrid accuracy in locating the interface even when implemented on uniform grids ? a distinct advantage of the level set method over threshold dynamics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2409918","Structure preservation in nonlinear, degenerate, evolution","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","06/03/2024","Abner Salgado","TN","University of Tennessee Knoxville","Standard Grant","Ludmil T. Zikatanov","07/31/2027","$204,533.00","","asalgad1@utk.edu","201 ANDY HOLT TOWER","KNOXVILLE","TN","379960001","8659743466","MPS","127100","9263","$0.00","A thorough treatment is feasible for the classical linear problems in the numerical approximation of partial differential equations. The continuous problem is well-posed. The numerical schemes are well-posed, parameter-robust, and convergent. It is even possible to prove convergence rates. However, the situation is more precarious for modern, complex systems of equations. Oftentimes, the uniqueness of solutions is not known. Even when there is uniqueness, the theory is far from complete, and so besides (weak) convergence of numerical solutions, little can be said about their behavior. In these scenarios, one must settle for simpler yet still relevant goals. An important goal in this front is that of structure preservation. The study of structure preservation in numerical methods is not new. Geometric numerical integration, many methods for electromagnetism, the finite element exterior calculus, and some novel approaches to hyperbolic systems of conservation laws, have this goal in mind: geometric, algebraic, or differential constraints must be preserved. This project does not focus on the problems mentioned above. Instead, it studies structure preservation in some evolution problems that have, possibly degenerate, diffusive behavior. This class of problems remains a largely unexplored topic when it comes to numerical discretizations. Bridging this gap will enhance modeling and prediction capabilities since diffusive models can be found in every aspect of scientific inquiry.

This project is focused on a class of diffusive problems in which stability of the solution cannot be obtained by standard energy arguments, in other words, by testing the equation with the solution to assert that certain space-time norms are under control. Norms are always convex. Structure preservation may then be a generalization of the approach given above. Instead of norms being under control, a (family of) convex functional(s) evaluated at the solution behave predictably during the evolution. The project aims to develop numerical schemes that mimic this in the discrete setting. While this is a largely unexplored topic, at the same time, many of the problems under consideration can be used to describe a wide range of phenomena. In particular, the project will develop new numerical schemes for an emerging theory of non-equilibrium thermodynamics, active scalar equations, and a class of problems in hyperbolic geometry. These models have a very rich intrinsic structure and a wide range of applications, and the developments of this project will serve as a stepping stone to bring these tools to the numerical treatment of more general problems. The students involved in the project will be trained in exciting, mathematically and computationally challenging, and practically relevant areas of research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2408978","Finite element methods for complex surface fluids","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","05/30/2024","Maxim Olshanskiy","TX","University of Houston","Standard Grant","Yuliya Gorb","06/30/2027","$319,951.00","","molshan@math.uh.edu","4300 MARTIN LUTHER KING BLVD","HOUSTON","TX","772043067","7137435773","MPS","127100","9263","$0.00","Material interfaces with lateral fluidity are widespread in biology and are vital for processes at various scales, from subcellular to tissue levels. Mathematical models describe these interfaces using systems of partial differential equations on deforming surfaces, sometimes linked to equations in the bulk. These equations govern the movement of interfaces and fluid flow along them and in the surrounding medium. While existing studies often focus on simple, homogeneous fluid flows on steady surfaces, real-life scenarios are more complex. This research project will develop and analyze new computational methods for studying these complex fluid systems. In addition, open-source software for simulating evolving surface PDEs will be developed and the project will provide research training opportunities for students.

This project will develop and analyze a finite element method for the tangential fluid system posed on a moving surface, a multi-component surface flow problem, and a fluid-elastic interface model, all arising in the continuum modeling of inextensible viscous deformable membranes. A numerical approach will be employed in the project that falls into the category of geometrically unfitted discretizations. It will allow for large surface deformations, avoid the need for surface parametrization and triangulation, and have optimal complexity. The developed technique will incorporate an Eulerian treatment of time derivatives in evolving domains and employ physics-based stable and linear splitting schemes. The particular problems that will be addressed include the analysis of finite element methods for the Boussinesq-Scriven fluid problem on a passively evolving surface; the development of a stable linear finite element scheme for a phase-field model of two-phase surface flows on both steady and evolving surfaces; and the construction of a splitting scheme for equations governing the motion of a material surface exhibiting lateral fluidity and out-of-plane elasticity.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2411209","Collaborative Research: Numerical Methods and Differential Geometry","DMS","COMPUTATIONAL MATHEMATICS","06/15/2024","06/04/2024","Yakov Berchenko-Kogan","FL","Florida Institute of Technology","Continuing Grant","Yuliya Gorb","05/31/2027","$48,279.00","","yberchenkokogan@fit.edu","150 W UNIVERSITY BLVD","MELBOURNE","FL","329018995","3216748000","MPS","127100","9263","$0.00","Partial differential equations (PDEs) model a wide variety of phenomena, ranging from how an airplane wing deforms in response to turbulence, to how radio waves travel through and around objects, to how black holes generate gravitational waves when they merge. Numerical analysts develop algorithms for simulating these systems by solving PDEs on a computer; these simulations enable engineers and scientists to develop prototypes and to interpret data from sensors. For example, the NSF-funded Nobel-winning detection of gravitational waves would not have been possible without advances in numerical analysis. In recent decades, numerical analysts discovered that ideas from differential geometry, an area of pure mathematics, can be used to develop good algorithms for solving PDEs. In fact, these ideas help not only for geometric problems in fields of study like computer vision and general relativity, but also for fields like electromagnetism that have little to do with geometry. Although applying differential geometry to numerical analysis has been very successful, thus far this link has been explored only for a small number of differential geometry ideas. In this project, the investigators will continue exploring this link, taking more ideas from differential geometry and applying them to develop new numerical algorithms. These algorithms could then be used both in applied areas, by solving PDEs in science and engineering, and in pure areas, by solving PDEs in differential geometry itself. The project will also support the training of graduate student researchers.

This project focuses on problems at the cusp of numerical analysis and differential geometry. It deals specifically with the design of finite element methods for PDEs that involve vector fields and tensor fields on Riemannian manifolds. In the long term, these efforts have the potential to lead to robust numerical methods for solving geometric PDEs like the Einstein field equations, which are useful for studying gravitational wave signals, as well as PDEs like the elasticity equations, which model how objects deform under stress. This project has three main goals. The first is to develop a new family of finite elements for discretizing algebraic curvature tensors and other bi-forms---tensor products of differential forms---on simplicial triangulations. The second goal is to develop an intrinsic finite element discretization of the Bochner Laplacian, which is a basic differential operator in Riemannian geometry that differs from the familiar Hodge Laplacian from finite element exterior calculus. The third goal is to leverage what we learn to design numerical methods for a wide range of geometric problems, such as computing spectra of elliptic operators on manifolds, simulating intrinsic geometric flows, and solving prescribed curvature 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." -"2411069","Hybrid Time Integration Algorithms for Co-Simulation of Multiscale Multiphysics Systems","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","06/04/2024","Adrian Sandu","VA","Virginia Polytechnic Institute and State University","Standard Grant","Yuliya Gorb","07/31/2027","$420,000.00","","sandu@cs.vt.edu","300 TURNER ST NW","BLACKSBURG","VA","240603359","5402315281","MPS","127100","9263","$0.00","Computer simulations of very complex systems are central to many fields in science and engineering, including mechanical and chemical engineering, aeronautics, astrophysics, plasma physics, meteorology and oceanography, finance, environmental sciences, and urban modeling. However, these simulations are hampered by the limitations of currently available numerical methodologies. Specifically, complex systems are driven by multiple simultaneous physical processes with different dynamic characteristics, e.g., atmospheric chemistry and atmospheric transport. Consequently, different components evolve at different rates, some very fast (e.g., concentrations of chemical tracers) and some very slow (e.g., ocean temperature). Traditional numerical methods are ill-suited to solve complex systems with multiple scales and multiple dynamics. This project develops new numerical algorithms that solve different complex system components with different discretizations and different time steps. This new approach will allow accurate and efficient simulations of complex systems and will positively impact many fields in science and engineering.

A novel hybrid time integration framework will be constructed to co-simulate complex systems governed by time-dependent partial differential equations. The particular innovation of the hybrid methodology is that it combines discrete and continuous internal stages during each integration step. The mathematical framework offers local truncation error estimates (unlike operator splitting), and provides solutions that do not depend on the convergence of an outer iteration process (unlike relaxation). It allows us to build methods with a higher order of accuracy than current co-simulation methodologies. The developed hybrid methods will have higher orders of accuracy than current co-simulation methodologies while offering tremendous implementation flexibility. High-quality implementations of the new methods will be made available to the community at large.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409841","Hydrodynamic models of electric charge transport: structure-preserving numerical methods","DMS","COMPUTATIONAL MATHEMATICS","09/01/2024","06/04/2024","Ignacio Tomas","TX","Texas Tech University","Standard Grant","Ludmil T. Zikatanov","08/31/2027","$219,782.00","","igtomas@ttu.edu","2500 BROADWAY","LUBBOCK","TX","79409","8067423884","MPS","127100","9263","$0.00","Electric charge transport physics is at the core of several technologies driving our economic and national security interests. For instance, the design of novel semiconductor devices requires a proper understanding of electron transport in the high-frequency regime. Similarly, the operation of directed energy systems hinges on the development of novel microwave sources and high-voltage high-current pulsed-power infrastructure. The project aims to provide innovative and robust numerical methods that will greatly enhance our predictive capabilities in the context of high-frequency electric charge transport simulation. This project will contribute to developing a new educational curriculum targeting the interdisciplinary training of graduate students at the intersection of mathematical modeling, numerical analysis, scientific computation, and physics.

The project will develop numerical methods to solve electrostatic and electrodynamic fluid models of electric charge transport. The Euler-Maxwell and Euler-Poisson systems are some of the simplest electrodynamic and electrostatic (respectively) fluid models of electric charge transport. These models describe electrically non-neutral plasmas, electron inertia effects, high-frequency electrostatic plasma oscillation, and collective cyclotron motions such as the Diocotron instability. This project comprises numerical analysis, scientific computing, and graduate-level education. The research program will advance space and time discretizations for hydrodynamic models of electric charge transport that are mathematically guaranteed to be robust and preserve key mathematical properties of interest. Among such properties, we have preservation of pointwise stability properties (e.g. positivity of density and minimum principle of the specific entropy), discrete energy-stability, and well-posedness of linear algebra systems. This project comprises three research tasks involving the development of: (I) Semi-implicit schemes for Euler-Maxwell and Euler-Poisson systems, (II) Maxwell's equations formulations and solvers, and (III) Graph-based solvers for nonlinear hyperbolic systems (mathematical theory and high-performance implementation). The resulting methods will be implemented using the library deal.II. It will extend the investigator and collaborators' high-performance software developments. This project will also lead to a new graduate-level class to train a new generation of students on the nature of these models and their technological 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." "2410045","Rational approximation for new structured methods in numerical linear algebra","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","06/03/2024","Heather Wilber","WA","University of Washington","Standard Grant","Ludmil T. Zikatanov","06/30/2027","$227,891.00","","hdw27@uw.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","127100","9263","$0.00","This grant supports the development of extremely fast methods for large-scale computing with structured matrices that appear pervasively in applications such as imaging, control theory, and signal processing. The Investigator will leverage new ideas in rational approximation that explain the structures in these matrices and imply the possibility of superfast algorithms. The matrices of primary interest are those with special displacement structures, including Toeplitz, Vandermonde, Hankel, Cauchy, and Loewner matrices, as well as block variants of these matrices. Such matrices and related matrix equations are ubiquitous across the sciences, and improved algorithms are greatly needed to overcome computational bottlenecks that currently impede progress and limit the scale of investigable problems. Collaborating with domain experts, the Investigator will develop open-source software that solves these problems under broader assumptions and at larger scales than what is currently possible. In areas such as MRI imaging, geophysical imaging, Fourier imaging in astrophysics and scattering, and in climate modeling, these improvements will ultimately benefit the public with positive impacts on medical technologies and other technologies deployed in the interest of citizens.

The goal and scope of the project is to advance scientific knowledge in two critical ways: (1) It will extend the applicability of rank-structured methods beyond what is currently possible and create new methods for working with rank-structured rectangular matrices. The solvers developed in this work are general and can be applied to any matrix with rectangular hierarchical structure. The work will develop general techniques for efficiently designing preconditioners, solving least squares and minimum norm problems, applying regularization, and solving constrained optimization problems that involve rectangular hierarchical matrices. It will inspire further research into both the design and application of direct methods in settings where previously they were too expensive or underdeveloped to consider. (2) This work tackles a collection of matrix families that lie at the heart of many applications. It supplies a new and general framework from which all of their compression properties can be theoretically understood. The foundation of that framework comes from rational approximation 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." "2409951","Low-rank gradient flow - a first order algorithm for non-convex optimization","DMS","COMPUTATIONAL MATHEMATICS","06/15/2024","06/03/2024","Andrei Draganescu","MD","University of Maryland Baltimore County","Standard Grant","Troy D. Butler","05/31/2027","$250,000.00","","adraganescu@gmail.com","1000 HILLTOP CIR","BALTIMORE","MD","212500001","4104553140","MPS","127100","075Z, 079Z, 9263","$0.00","Non-convex optimization problems are ubiquitous in science and engineering. They often present significant challenges for many existing classes of algorithms due to the presence of multiple suboptimal, undesirable solutions. The methods emerging from this project will circumvent some of these challenges due to their ability of bypassing more efficiently suboptimal solutions using a novel set of techniques. They will contribute to the numerical solution of non-convex optimization problems that can be found in a very wide range of applications, such as computer-aided design (shape and topology optimization), radiation therapy, optimization of manufacturing processes, inverse problems, optimal control of partial differential equations, statistics, and artificial intelligence. Open software will be shared with the community in order to facilitate the reproducibility of the results. One summer undergraduate student and one graduate student will benefit from training in areas that are relevant to topics of current interest to both academia and industry. Special attention will be given to the recruitment of students from underrepresented groups.

The project is centered around developing and analyzing a novel class of first order methods for solving optimization problems, called low-rank-gradient-flow (LRGF). The idea behind the method consists of developing, at each step, quadratic surrogates with low-rank Hessian, and computing analytically the gradient flow on that surrogate. The step will conclude with a line search along the curvilinear gradient flow, with the purpose of finding a point satisfying the Wolfe conditions. Convergence will be accelerated using a multilevel approach based on reduced order models. The convergence properties of the method will be studied, addressing both questions related to global convergence, efficient construction of low-rank models, as well as convergence rates. The method will be applied to maximum likelihood estimation, optimization of hyperbolic partial differential equations, and training of deep neural networks.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2408978","Finite element methods for complex surface fluids","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","05/30/2024","Maxim Olshanskiy","TX","University of Houston","Standard Grant","Yuliya Gorb","06/30/2027","$319,951.00","","molshan@math.uh.edu","4300 MARTIN LUTHER KING BLVD","HOUSTON","TX","772043067","7137435773","MPS","127100","9263","$0.00","Material interfaces with lateral fluidity are widespread in biology and are vital for processes at various scales, from subcellular to tissue levels. Mathematical models describe these interfaces using systems of partial differential equations on deforming surfaces, sometimes linked to equations in the bulk. These equations govern the movement of interfaces and fluid flow along them and in the surrounding medium. While existing studies often focus on simple, homogeneous fluid flows on steady surfaces, real-life scenarios are more complex. This research project will develop and analyze new computational methods for studying these complex fluid systems. In addition, open-source software for simulating evolving surface PDEs will be developed and the project will provide research training opportunities for students.

This project will develop and analyze a finite element method for the tangential fluid system posed on a moving surface, a multi-component surface flow problem, and a fluid-elastic interface model, all arising in the continuum modeling of inextensible viscous deformable membranes. A numerical approach will be employed in the project that falls into the category of geometrically unfitted discretizations. It will allow for large surface deformations, avoid the need for surface parametrization and triangulation, and have optimal complexity. The developed technique will incorporate an Eulerian treatment of time derivatives in evolving domains and employ physics-based stable and linear splitting schemes. The particular problems that will be addressed include the analysis of finite element methods for the Boussinesq-Scriven fluid problem on a passively evolving surface; the development of a stable linear finite element scheme for a phase-field model of two-phase surface flows on both steady and evolving surfaces; and the construction of a splitting scheme for equations governing the motion of a material surface exhibiting lateral fluidity and out-of-plane elasticity.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2410686","Modeling, discretizations, and solution strategies for multiphysics problems","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","05/29/2024","Ivan Yotov","PA","University of Pittsburgh","Standard Grant","Yuliya Gorb","06/30/2027","$420,000.00","","yotov@math.pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","127100","9263","$0.00","The goal of this project is to advance the state-of-the-art in modeling and computation of multiphysics systems that model the physical interactions between two or more media, such as couplings of fluid flows, rigid or deformable porous media, and elastic structures. Typical examples are coupling of free fluid and porous media flows, fluid-structure interaction, and fluid-poroelastic structure interaction (FPSI). The developed methods will be employed for several biomedical and geoscience applications. Biomedical applications include investigation of non-Newtonian and poroelastic effects in arterial flows on important clinical markers such as wall shear stress and relative residence time, modeling LDL transport and drug delivery in blood flows, as well as flows in the eye and the brain. Geoscience applications include tracing organic and inorganic contaminants in coupled surface-subsurface hydrological systems, predicting hydrocarbon extraction in hydraulic fracturing, geothermal energy production, and modeling the effect of proppant particles in injected polymers on the fracture width and flow patterns. While focused on FPSI, the developments in this project will be applicable to modeling and computation of a wide class of multiphysics problems with a broad range of applications.

The project consists of a comprehensive program for mathematical and computational modeling of multiphysics problems that includes 1) development and analysis of new mathematical models, 2) design and analysis of stable, accurate, and robust structure-preserving numerical methods, 3) development and analysis of efficient time-splitting and multiscale domain decomposition algorithms for the solution of the resulting algebraic problems, and 4) applications to the geosciences and biomedicine. Variational formulations of new fluid--poroelastic structure interaction (FPSI) models based on Navier-Stokes - Biot couplings will be developed, extending current model capabilities to flows with higher Reynolds numbers. Fully coupled nonlinear FPSI-transport models, including miscible displacement models with concentration-dependent fluid viscosity, stress-dependent diffusion, and non-isothermal models will also be studied. Novel discretization techniques will be investigated for the numerical approximation of the FPSI models. The focus will be on dual mixed and total pressure discretizations with local conservation of mass and momentum, accurate approximations with continuous normal components for velocities and stresses, and robustness with respect to physical parameters. These include multipoint stress-flux mixed finite element methods and local-stress mimetic finite difference methods that can be reduced to positive definite cell-centered schemes. Efficient multiscale domain decomposition and time-splitting algorithms will be developed for the solution of the resulting algebraic systems. The domain decomposition methodology will be based on space-time variational formulations and will allow for multiple subdomains within each region with non-matching grids along subdomain interfaces and local time-stepping. The convergence of the space-time coarse-scale mortar interface iteration will be studied by analyzing the spectrum of the interface operator. Iterative and non-iterative time-splitting methods will also be investigated.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408912","Equity Beyond the Algorithm: A Mathematical Quest for Fairer-ness in Machine Learning","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","05/29/2024","Deanna Needell","CA","University of California-Los Angeles","Standard Grant","Troy D. Butler","06/30/2027","$275,000.00","","deanna@math.ucla.edu","10889 WILSHIRE BLVD STE 700","LOS ANGELES","CA","900244200","3107940102","MPS","127100","075Z, 079Z, 9263","$0.00","While machine learning (ML) and artificial intelligence (AI) are seeing widespread and rapid use across the world, very little is understood about many of their underlying mechanisms, and especially those revolving around fairness and bias. More examples are being reported every day that range from racist outputs of ChatGPT to imaging AI that predicts former president Barack Obama's face to be white. The mathematical community has fallen behind the rush to use ML and AI, yet mathematics is at the heart of the algorithmic designs and mechanisms behind ML and AI. This project will study fairness in ML and AI from several angles. First, it will create a framework that identifies fairness metrics throughout the algorithmic pipelines. Second, it will develop technologies to mitigate biases and improve fairness. Third, it will develop mathematical foundations to help us understand the mechanisms at work inside of many of these so-called black-box methods. In addition, medical and social justice applications will be integrated throughout the project, helping many nonprofits with high data driven needs meet their goals. These include medical applications helping to understand manifestations of Lyme disease as well as tools to help Innocence projects that work to free innocent people from prison, make appeal decisions, and synthesize case files. This synergistic approach both serves the community while also allowing those applications to fuel motivation for new and better mathematics. In addition, students will be integrated within the research team as part of their training.

Although ML and AI methods have expanded by leaps and bounds, there are still critical issues around fairness and bias that remain unresolved. The focus of this project consists of two main goals. First, it will create a framework where ML and AI methods generate informative descriptions about fairness across population groups. Subsequently, a mechanism will be applied based on this assessment to promote fairness across the population. This direction will both establish a structured framework for researchers and practitioners to report fairness metrics and emphasize their significance, while also enabling algorithms to adjust for fairness. The majority of the first goal revolves around showcasing this framework in ML applications including dimension reduction, topic modeling, classification, clustering, data completion, and prediction modeling. Second, the project will provide foundational mathematical support for more complex, seemingly opaque techniques such as neural networks and large language models. This includes the investigation of mathematically tangible shallow networks to understand their behavior in benign and non-benign overfitting. The project will also analyze the geometry of embeddings derived from large language models using a linear algebraic topic modeling approach, which is tied to the first goal. Applications with nonprofit community partners will be included throughout the duration of the project, including those in medicine and criminal and social justice. In total, successful completion of the proposed work will provide a pivotal step towards creating a more equitable and mathematically grounded machine learning landscape.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2411198","Collaborative Research: Randomized algorithms for dynamic and hierarchical Bayesian inverse problems","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","05/30/2024","Arvind Saibaba","NC","North Carolina State University","Standard Grant","Troy D. Butler","07/31/2027","$170,000.00","","asaibab@ncsu.edu","2601 WOLF VILLAGE WAY","RALEIGH","NC","276950001","9195152444","MPS","127100","9263","$0.00","Inverse problems appear in a diverse array of applications - in medical imaging, for X-ray computerized tomography, ultrasound, and magnetic resonance imaging; in geophysics, for atmospheric tomography, electrical resistivity tomography, seismic tomography, and weather prediction; in material sciences, for X-ray ptychography; in homeland security applications, for luggage scanning; in astrophysics, to image black holes and cosmic background estimation. The main goal of solving inverse problems is to use measurements to estimate the parameters of physical models. Being able to solve inverse problems efficiently, accurately, and with quantifiable certainty remains an open challenge. Randomized algorithms have made several advances in numerical linear algebra due to their ability to dramatically reduce computational costs without significantly compromising the accuracy of the computations. However, there is a rich and relatively unexplored field of research that lies between randomized numerical linear algebra and inverse problems, in particular for dynamic and hierarchical problems, where randomization can and should be exploited in unique ways. This project will address fundamental issues in the development of computationally efficient solvers for inverse problems and uncertainty quantification. The project will also train graduate students on start-of-the-art randomized algorithms.

The project will develop new and efficient randomized algorithms for mitigating the computational burdens of two types of inverse problems: hierarchical Bayesian inverse problems and dynamical inverse problems. The two main thrusts of this project are (i) to develop efficient algorithms to quantify the uncertainty of the hyperparameters that govern Bayesian inverse problems, and (ii) to develop new iterative methods that leverage randomization to efficiently approximate solutions and enable uncertainty quantification for large-scale inverse problems. This project will advance knowledge in the field of randomized algorithms for computational inverse problems and uncertainty quantification. It will also create numerical methods that are expected to be broadly applicable to many areas of science and engineering.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2410140","Manifold learning in Wasserstein space using Laplacians: From graphs to submanifolds","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","05/29/2024","Caroline Moosmueller","NC","University of North Carolina at Chapel Hill","Standard Grant","Troy D. Butler","07/31/2027","$419,962.00","Shiying Li","cmoosm@unc.edu","104 AIRPORT DR STE 2200","CHAPEL HILL","NC","275995023","9199663411","MPS","127100","079Z, 9263","$0.00","Manifold learning algorithms are tools used to reveal the underlying structure of high-dimensional datasets. This can be achieved by finding a lower-dimensional representation of the dataset, thereby enhancing the efficiency of subsequent data analysis. They find applications across various fields such as single-cell analysis, natural language processing, and neuroscience. While most existing algorithms are designed for datasets represented in vector spaces, real-world data often comprises distributions or point-clouds, presenting both theoretical and computational challenges for manifold learning algorithms. This project will develop manifold learning algorithms tailored for distributional or point-cloud datasets, with a particular emphasis on theoretical analysis and computational efficiency. Leveraging the framework of optimal transport and established manifold learning theory in vector spaces, the project will address these challenges. This project will also train students in interdisciplinary aspects of the research.

This project will develop and analyze algorithms for uncovering low-dimensional intrinsic structures of data sets within Wasserstein space, a natural space for distributions or point-clouds. This is motivated by the recent success in representing data as elements in Wasserstein space, as opposed to Euclidean space, and the necessity to develop efficient algorithms for their analysis. To accomplish the goals of this project, the research team will leverage the eigenvectors of a Laplacian matrix built from a data-dependent graph. Specifically, consistency theory of operators such as the Laplacian between the discrete (graph) and the continuous (submanifold) setting will be developed, drawing inspiration from the well-established theory for finite-dimensional Riemannian manifolds. The project will develop theoretically provable methods that provide algorithmic insights, which in turn can be used for efficient algorithms. The aims are threefold: (1) define dimensionality reduction algorithms for point-cloud data that can uncover curved submanifolds through suitable embeddings, (2) provide theoretical guarantees for these embeddings, and (3) design efficient algorithms for applications in high-dimensional settings such as single-cell data 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." "2411141","Nonlinear Eigenvalue Problems: Building a New Paradigm Through the Lens of Systems Theory and Rational Interpolation","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","05/29/2024","Serkan Gugercin","VA","Virginia Polytechnic Institute and State University","Continuing Grant","Jodi Mead","07/31/2027","$89,958.00","Mark Embree","gugercin@math.vt.edu","300 TURNER ST NW","BLACKSBURG","VA","240603359","5402315281","MPS","127100","9263","$0.00","When building new devices or products, engineers naturally want to optimize performance with respect to some design variables; this process typically involves simulation with large-scale mathematical models. One desirable goal of this optimization is to maximize the stability of a system, to avoid designs for which small disturbances can get magnified until failure occurs. This project will study new approaches for assessing such stability, including a technique for simultaneously analyzing an entire ensemble of systems across a range of design variables, rather than analyzing individual systems one at a time. These techniques involve the symbiotic interplay of data and mathematical models. The project will involve graduate student training and professional development through summer research and capstone projects for Virginia Tech?s Computational Modeling and Data Analytics major.

Nonlinear eigenvalue problems (NLEVPs) arise naturally in many applications throughout science and engineering, from networks of vibrating structures to dynamical systems with time delays. In contrast to the linear eigenvalue problem, algorithms for solving NLEVPs remain in an unsettled state due to the fundamental challenges these problems pose. This project approaches NLEVPs through the lens of control theory, identifying contour-based eigenvalue algorithms as examples of system realization techniques. Given this perspective, this research program seeks to develop robust, reliable algorithms and software for NLEVPs, with an eye toward optimal parameter selection and efficiency for large-scale problems. This analysis and computational methods will be extended to handle parameter-dependent NLEVPs, where the problem varies based on one or more physical parameters. The project will also look in the opposite direction, using contour integral algorithms from eigenvalue computations to offer new approaches to data-driven modeling of 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." "2410699","Collaborative Research: Memory-aware Accelerated Solvers for Nonlinear Problems in High Dimensional Imaging Applications","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","05/30/2024","Mirjeta Pasha","VA","Virginia Polytechnic Institute and State University","Standard Grant","Troy D. Butler","06/30/2027","$162,490.00","","mpasha@vt.edu","300 TURNER ST NW","BLACKSBURG","VA","240603359","5402315281","MPS","127100","9263","$0.00","Achieving significant advances over the state-of-the-art methods for imaging applications such as reconstruction and high-dimensional image/video compression requires fundamentally new approaches to keep up with the volumes of (multi-dimensional and possibly streaming) data that have become pervasive in science and engineering applications. Consider, for instance, the need to continuously monitor, diagnose, and visualize anomalies within the body through modern magnetic resonance (MR) and computerized tomography (CT) scans, to inspect objects at crowded checkpoints, or check surveillance video for possible threats. These applications present a common challenge: the need to process an ever-increasing amount of data quickly and accurately to enable real-time decisions at a low computational cost while respecting limited memory capacities. This collaborative project will address these challenges through an innovative, multi-pronged, mathematical and algorithmic framework that capitalizes on properties inherent in the data as well as on features in the solutions (i.e. images, video frames) that persist over time and/or as the solutions are being resolved. The work produced will have broad scientific impact: for example, the newly offered speed of the image reconstruction methods may improve the ability to detect anomalies in tissue, underground or in luggage, while the compression algorithms hold promise for other disciplines where the ability to compress and explain multi-way (a.k.a tensor) data is paramount, such as satellite imaging, biology, and data science. Graduate students will be trained as part of this project.

Digital images and video are inherently multi-way objects. A single, grayscale, digital image is a two-dimensional array of numbers with the numbers coded to appear as shades of gray whereas a collection of such grayscale images, such as video frames, are three-way arrays, also called third order tensors. The benefit of tensor compression (or completion, if some image values are missing or obscured) techniques in terms of quality over more traditional matrix-based methods merit their use. Reconstructing images that preserve edges is also of paramount importance: consider that an image edge defines the boundary between a tumor and normal tissue, for instance. This project will focus on these two distinct imaging problems, edge-based reconstruction and compressed tensor data representation, whose solution requires memory-efficient iterative approaches, but for which the state-of-the-art iterative techniques are slow to converge and memory intensive. The acceleration will be achieved by a combination of judicious choice of limited memory recycled subspaces, classical acceleration approaches (e.g., NGMRES or Anderson Acceleration), and operator approximation. Furthermore, if the data arrives asynchronously or the regularized problem cannot all fit into memory at once, the method will extend to streamed-recycling. The streamed-recycling approach will break the problem up into memory-manageable chunks while keeping a small-dimensional subspace that encodes and retains the most important features to enable solution to the original, large-scale problem. The impact of the accelerated edge-preserving image reconstruction algorithms will be demonstrated on X-ray CT, but the algorithms will have much wider applicability in other imaging modalities.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2411197","Collaborative Research: Randomized algorithms for dynamic and hierarchical Bayesian inverse problems","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","05/30/2024","Julianne Chung","GA","Emory University","Standard Grant","Troy D. Butler","07/31/2027","$170,000.00","","jmchung@emory.edu","201 DOWMAN DR NE","ATLANTA","GA","303221061","4047272503","MPS","127100","9263","$0.00","Inverse problems appear in a diverse array of applications - in medical imaging, for X-ray computerized tomography, ultrasound, and magnetic resonance imaging; in geophysics, for atmospheric tomography, electrical resistivity tomography, seismic tomography, and weather prediction; in material sciences, for X-ray ptychography; in homeland security applications, for luggage scanning; in astrophysics, to image black holes and cosmic background estimation. The main goal of solving inverse problems is to use measurements to estimate the parameters of physical models. Being able to solve inverse problems efficiently, accurately, and with quantifiable certainty remains an open challenge. Randomized algorithms have made several advances in numerical linear algebra due to their ability to dramatically reduce computational costs without significantly compromising the accuracy of the computations. However, there is a rich and relatively unexplored field of research that lies between randomized numerical linear algebra and inverse problems, in particular for dynamic and hierarchical problems, where randomization can and should be exploited in unique ways. This project will address fundamental issues in the development of computationally efficient solvers for inverse problems and uncertainty quantification. The project will also train graduate students on start-of-the-art randomized algorithms.

The project will develop new and efficient randomized algorithms for mitigating the computational burdens of two types of inverse problems: hierarchical Bayesian inverse problems and dynamical inverse problems. The two main thrusts of this project are (i) to develop efficient algorithms to quantify the uncertainty of the hyperparameters that govern Bayesian inverse problems, and (ii) to develop new iterative methods that leverage randomization to efficiently approximate solutions and enable uncertainty quantification for large-scale inverse problems. This project will advance knowledge in the field of randomized algorithms for computational inverse problems and uncertainty quantification. It will also create numerical methods that are expected to be broadly applicable to many areas of science and engineering.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2410698","Collaborative Research: Memory-aware Accelerated Solvers for Nonlinear Problems in High Dimensional Imaging Applications","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","05/30/2024","Misha Kilmer","MA","Tufts University","Standard Grant","Troy D. Butler","06/30/2027","$162,510.00","","misha.kilmer@tufts.edu","169 HOLLAND ST","SOMERVILLE","MA","021442401","6176273696","MPS","127100","9263","$0.00","Achieving significant advances over the state-of-the-art methods for imaging applications such as reconstruction and high-dimensional image/video compression requires fundamentally new approaches to keep up with the volumes of (multi-dimensional and possibly streaming) data that have become pervasive in science and engineering applications. Consider, for instance, the need to continuously monitor, diagnose, and visualize anomalies within the body through modern magnetic resonance (MR) and computerized tomography (CT) scans, to inspect objects at crowded checkpoints, or check surveillance video for possible threats. These applications present a common challenge: the need to process an ever-increasing amount of data quickly and accurately to enable real-time decisions at a low computational cost while respecting limited memory capacities. This collaborative project will address these challenges through an innovative, multi-pronged, mathematical and algorithmic framework that capitalizes on properties inherent in the data as well as on features in the solutions (i.e. images, video frames) that persist over time and/or as the solutions are being resolved. The work produced will have broad scientific impact: for example, the newly offered speed of the image reconstruction methods may improve the ability to detect anomalies in tissue, underground or in luggage, while the compression algorithms hold promise for other disciplines where the ability to compress and explain multi-way (a.k.a tensor) data is paramount, such as satellite imaging, biology, and data science. Graduate students will be trained as part of this project.

Digital images and video are inherently multi-way objects. A single, grayscale, digital image is a two-dimensional array of numbers with the numbers coded to appear as shades of gray whereas a collection of such grayscale images, such as video frames, are three-way arrays, also called third order tensors. The benefit of tensor compression (or completion, if some image values are missing or obscured) techniques in terms of quality over more traditional matrix-based methods merit their use. Reconstructing images that preserve edges is also of paramount importance: consider that an image edge defines the boundary between a tumor and normal tissue, for instance. This project will focus on these two distinct imaging problems, edge-based reconstruction and compressed tensor data representation, whose solution requires memory-efficient iterative approaches, but for which the state-of-the-art iterative techniques are slow to converge and memory intensive. The acceleration will be achieved by a combination of judicious choice of limited memory recycled subspaces, classical acceleration approaches (e.g., NGMRES or Anderson Acceleration), and operator approximation. Furthermore, if the data arrives asynchronously or the regularized problem cannot all fit into memory at once, the method will extend to streamed-recycling. The streamed-recycling approach will break the problem up into memory-manageable chunks while keeping a small-dimensional subspace that encodes and retains the most important features to enable solution to the original, large-scale problem. The impact of the accelerated edge-preserving image reconstruction algorithms will be demonstrated on X-ray CT, but the algorithms will have much wider applicability in other imaging modalities.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2410140","Manifold learning in Wasserstein space using Laplacians: From graphs to submanifolds","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","05/29/2024","Caroline Moosmueller","NC","University of North Carolina at Chapel Hill","Standard Grant","Troy D. Butler","07/31/2027","$419,962.00","Shiying Li","cmoosm@unc.edu","104 AIRPORT DR STE 2200","CHAPEL HILL","NC","275995023","9199663411","MPS","127100","079Z, 9263","$0.00","Manifold learning algorithms are tools used to reveal the underlying structure of high-dimensional datasets. This can be achieved by finding a lower-dimensional representation of the dataset, thereby enhancing the efficiency of subsequent data analysis. They find applications across various fields such as single-cell analysis, natural language processing, and neuroscience. While most existing algorithms are designed for datasets represented in vector spaces, real-world data often comprises distributions or point-clouds, presenting both theoretical and computational challenges for manifold learning algorithms. This project will develop manifold learning algorithms tailored for distributional or point-cloud datasets, with a particular emphasis on theoretical analysis and computational efficiency. Leveraging the framework of optimal transport and established manifold learning theory in vector spaces, the project will address these challenges. This project will also train students in interdisciplinary aspects of the research.

This project will develop and analyze algorithms for uncovering low-dimensional intrinsic structures of data sets within Wasserstein space, a natural space for distributions or point-clouds. This is motivated by the recent success in representing data as elements in Wasserstein space, as opposed to Euclidean space, and the necessity to develop efficient algorithms for their analysis. To accomplish the goals of this project, the research team will leverage the eigenvectors of a Laplacian matrix built from a data-dependent graph. Specifically, consistency theory of operators such as the Laplacian between the discrete (graph) and the continuous (submanifold) setting will be developed, drawing inspiration from the well-established theory for finite-dimensional Riemannian manifolds. The project will develop theoretically provable methods that provide algorithmic insights, which in turn can be used for efficient algorithms. The aims are threefold: (1) define dimensionality reduction algorithms for point-cloud data that can uncover curved submanifolds through suitable embeddings, (2) provide theoretical guarantees for these embeddings, and (3) design efficient algorithms for applications in high-dimensional settings such as single-cell data 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." +"2409868","On Iteratively Regularized Alternating Minimization under Nonlinear Dynamics Constraints with Applications to Epidemiology","DMS","COMPUTATIONAL MATHEMATICS","09/01/2024","05/29/2024","Alexandra Smirnova","GA","Georgia State University Research Foundation, Inc.","Standard Grant","Troy D. Butler","08/31/2027","$200,000.00","Xiaojing Ye","asmirnova@gsu.edu","58 EDGEWOOD AVE NE","ATLANTA","GA","303032921","4044133570","MPS","127100","9263","$0.00","How widely has the virus spread? This important and often overlooked question was brought to light by the recent COVID-19 outbreak. Several techniques have been used to account for silent spreaders along with varying testing and healthcare seeking habits as the main reasons for under-reporting of incidence cases. It has been observed that silent spreaders play a more significant role in disease progression than previously understood, highlighting the need for policymakers to incorporate these hidden figures into their strategic responses. Unlike other disease parameters, i.e., incubation and recovery rates, the case reporting rate and the time-dependent effective reproduction number are directly influenced by a large number of factors making it impossible to directly quantify these parameters in any meaningful way. This project will advance iteratively regularized numerical algorithms, which have emerged as a powerful tool for reliable estimation (from noise-contaminated data) of infectious disease parameters that are crucial for future projections, prevention, and control. Apart from epidemiology, the project will benefit all real-world applications involving massive amounts of observation data for multiple stages of the inversion process with a shared model parameter. In the course of their theoretical and numerical studies, the PIs will continue to create research opportunities for undergraduate and graduate students, including women and students from groups traditionally underrepresented in STEM disciplines. A number of project topics are particularly suitable for student research and will be used to train some of the next generation of computational mathematicians.

In the framework of this project, the PIs will develop new regularized alternating minimization algorithms for solving ill-posed parameter-estimation problems constrained by nonlinear dynamics. While significant computational challenges are shared by both deterministic trust-region and Bayesian methods (such as numerical solutions requiring solutions to possibly complex ODE or PDE systems at every step of the iterative process), the team will address these challenges by constructing a family of fast and stable iteratively regularized optimization algorithms, which carefully alternate between updating model parameters and state variables.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409858","Dynamical Low Rank Methods for Multiscale Kinetic Plasma Simulations","DMS","COMPUTATIONAL MATHEMATICS","08/01/2024","05/29/2024","Jingwei Hu","WA","University of Washington","Standard Grant","Ludmil T. Zikatanov","07/31/2027","$220,000.00","","hujw@uw.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","127100","9263","$0.00","Plasmas consist of many charged particles, such as electrons and ions. The Boltzmann equation is often regarded as the first-principle model for plasmas; however, its numerical simulation is prohibitively expensive even on today?s most powerful supercomputers. The challenges manifest as: 1) High-dimensionality. The Boltzmann equation resides in six-dimensional phase space. Hence, full 6D deterministic simulation requires excessive computing effort and memory. 2) Collision operator. Collisions between particles are described by nonlinear, nonlocal integral operators that are extremely difficult to approximate. Yet, they play a critical role in driving the system towards local thermodynamic equilibrium and must be included in the simulation, especially in transition and fluid regimes. 3) Multiple scales. Plasmas inherently exhibit multiscale physics. Different scaling can lead to different asymptotic models. How to conduct efficient kinetic simulations such that multiscale behaviors are properly captured is a long-standing problem. The overall objective of this project is to develop a set of ultra-efficient deterministic numerical methods for multiscale kinetic plasma simulations. The algorithms to be developed in this project have the potential to provide high-fidelity kinetic plasma simulations across a range of regimes at a manageable computational cost.

The basic framework we will employ is the dynamical low-rank method (DLRM), a robust dimension reduction technique for solving high-dimensional partial differential equations. In essence, DLRM can be viewed as a time-dependent singular value decomposition; instead of solving the 6D equation, it tracks the dynamics of low-rank factors of the solution, which depend on either the three-dimensional position variable or the three-dimensional velocity variable, thus drastically reducing the computational cost and memory footprint. Our focus will be on the nonlinear collisional kinetic equations for plasmas, allowing us to address a broader range of regimes beyond the collisionless ones. We will design an efficient low-rank ansatz inspired by various asymptotic limits of plasma kinetic equations such that the method only requires a few ranks in the limiting regime and is as efficient as solving the reduced fluid models. We will also study the uniform stability and longtime behavior of DLRM rigorously, justifying the method's robustness for treating multiscale 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." "2411120","Improving quantum speedup for solving differential equations","DMS","COMPUTATIONAL MATHEMATICS","09/01/2024","05/30/2024","Xiantao Li","PA","Pennsylvania State Univ University Park","Continuing Grant","Troy D. Butler","08/31/2027","$59,632.00","","xli@math.psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","127100","9263","$0.00","The ultimate challenge in many areas of applied science can be attributed to the limited capability of solving large-scale differential equations. Classical computers encounter a fundamental bottleneck due to the nonlinearity, vast number of degrees of freedom, and inherent stochasticity of these equations. Motivated by the emergence of quantum computing, which promises significant speedups over classical methods for many scientific computing problems, particularly those involving quantum dynamics governed by the Schrodinger equation, this research aims to establish an innovative mathematical framework. This framework will transform a broad range of differential equations into the Schrodinger equation, enabling the application of quantum algorithms. Such quantum speedup has the potential to enhance the prediction of physical properties and optimize system performance based on differential equation models. To ensure broader scientific and societal impacts, the research team will disseminate results at quantum information processing conferences and also integrate graduate students within the research plan as part of their professional training.

The principal investigator will develop an encoding scheme to represent large-scale differential equations within unitary dynamics through a shadow Hamiltonian. Using backward error analysis, the research aims to systematically construct a shadow Hamiltonian with an arbitrarily higher order of accuracy. Moreover, a precise procedure will be developed for mapping nonlinear and stochastic differential equations into such unitary evolution, significantly broadening the applicability of the proposed encoding scheme. The quantum algorithms derived from this project will be applied to non-Hermitian dynamics from topological materials and chemical Langevin dynamics from biomolecular modeling, aiming to make a direct impact on critical physics and engineering fields.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2409868","On Iteratively Regularized Alternating Minimization under Nonlinear Dynamics Constraints with Applications to Epidemiology","DMS","COMPUTATIONAL MATHEMATICS","09/01/2024","05/29/2024","Alexandra Smirnova","GA","Georgia State University Research Foundation, Inc.","Standard Grant","Troy D. Butler","08/31/2027","$200,000.00","Xiaojing Ye","asmirnova@gsu.edu","58 EDGEWOOD AVE NE","ATLANTA","GA","303032921","4044133570","MPS","127100","9263","$0.00","How widely has the virus spread? This important and often overlooked question was brought to light by the recent COVID-19 outbreak. Several techniques have been used to account for silent spreaders along with varying testing and healthcare seeking habits as the main reasons for under-reporting of incidence cases. It has been observed that silent spreaders play a more significant role in disease progression than previously understood, highlighting the need for policymakers to incorporate these hidden figures into their strategic responses. Unlike other disease parameters, i.e., incubation and recovery rates, the case reporting rate and the time-dependent effective reproduction number are directly influenced by a large number of factors making it impossible to directly quantify these parameters in any meaningful way. This project will advance iteratively regularized numerical algorithms, which have emerged as a powerful tool for reliable estimation (from noise-contaminated data) of infectious disease parameters that are crucial for future projections, prevention, and control. Apart from epidemiology, the project will benefit all real-world applications involving massive amounts of observation data for multiple stages of the inversion process with a shared model parameter. In the course of their theoretical and numerical studies, the PIs will continue to create research opportunities for undergraduate and graduate students, including women and students from groups traditionally underrepresented in STEM disciplines. A number of project topics are particularly suitable for student research and will be used to train some of the next generation of computational mathematicians.

In the framework of this project, the PIs will develop new regularized alternating minimization algorithms for solving ill-posed parameter-estimation problems constrained by nonlinear dynamics. While significant computational challenges are shared by both deterministic trust-region and Bayesian methods (such as numerical solutions requiring solutions to possibly complex ODE or PDE systems at every step of the iterative process), the team will address these challenges by constructing a family of fast and stable iteratively regularized optimization algorithms, which carefully alternate between updating model parameters and state variables.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409855","Metric-Dependent Strategies for Inverse Problem Analysis and Computation","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","05/29/2024","Yunan Yang","NY","Cornell University","Standard Grant","Troy D. Butler","06/30/2027","$275,000.00","","yunan.yang@cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","127100","9263","$0.00","This project will develop novel approaches to solving inverse problems, which are pivotal in many scientific fields, including biology, geophysics, and medical imaging. Inverse problems often involve deducing unknown parameters from observed data, a task complicated by issues such as sensitivity to measurement noise and complex modeling procedures. The broader significance of this research lies in its potential to significantly enhance the accuracy and efficiency of computational methods used in critical applications such as electrical impedance tomography (EIT), inverse scattering, and cryo-electron microscopy (cryo-EM). For instance, improvements in cryo-EM computation will accelerate breakthroughs in molecular biology and aid in rapid drug development, directly benefiting medical research and public health. Additionally, this project will also (1) engage undergraduate and graduate students in research to foster a new generation of computational mathematicians, and (2) promote STEM careers among K-12 students through outreach activities.

The technical focus of this project will be on the development of metric-dependent strategies to improve the stability and computational efficiency of solving inverse problems. Lipschitz-type stability will be established by selecting metrics tailored to the data and unknown parameters to facilitate more robust algorithmic solutions. A key highlight of the project will be the investigation of the stochastic inverse problem's well-posedness. Sampling methods inspired by metric-dependent gradient flows will serve as the novel computational tool for the practical solution of stochastic inverse problems. These analytical and computational strategies will be designed to handle the randomness inherent in many practical scenarios, shifting the traditional deterministic approach for solving inverse problems to a probabilistic framework that better captures the intricacies of real-world data. This research has the promise to not only advance theoretical knowledge in studying inverse problems but also to develop practical, efficient tools for a wide range of applications in science and engineering.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2432134","Collaborative Research: Computational Methods for Optimal Transport via Fluid Flows","DMS","COMPUTATIONAL MATHEMATICS","05/15/2024","05/17/2024","Yangwen Zhang","LA","University of Louisiana at Lafayette","Continuing Grant","Yuliya Gorb","06/30/2025","$56,877.00","","yangwen.zhang@louisiana.edu","104 E UNIVERSITY AVE","LAFAYETTE","LA","705032014","3374825811","MPS","127100","9150, 9263","$0.00","Transport and mixing in fluids is a topic of fundamental interest in engineering and natural sciences, with broad applications ranging from industrial and chemical mixing on small and large scales, to preventing the spreading of pollutants in geophysical flows. This project focuses on computational methods for control of optimal transport and mixing of some quantity of interest in fluid flows. The question of what fluid flow maximizes mixing rate, slows it down, or even steers a quantity of interest toward a desired target distribution draws great attention from a broad range of scientists and engineers in the area of complex dynamical systems. The goal of this project is to place these problems within a flexible computational framework, and to develop a solution strategy based on optimal control tools, data compression strategies, and methods to reduce the complexity of the mathematical models. This project will also help the training and development of graduate students across different disciplines to conduct collaborative research in optimal transport and mixing, flow control, and computational methods for solving these problems.


The project is concerned with the development and analysis of numerical methods for optimal control for mixing in fluid flows. More precisely, the transport equation is used to describe the non-dissipative scalar field advected by the incompressible Stokes and Navier-Stokes flows. The research aims at achieving optimal mixing via an active control of the flow velocity and constructing efficient numerical schemes for solving this problem. Various control designs will be investigated to steer the fluid flows. Sparsity of the optimal boundary control will be promoted via a non-smooth penalty term in the objective functional. This essentially leads to a highly challenging nonlinear non-smooth control problem for a coupled parabolic and hyperbolic system, or a semi-dissipative system. The project will establish a novel and rigorous mathematical framework and also new accurate and efficient computational techniques for these difficult optimal control problems. Compatible discretization methods for coupled flow and transport will be employed to discretize the controlled system and implement the optimal control designs numerically. Numerical schemes for the highly complicated optimality system will be constructed and analyzed in a systematic fashion. New incremental data compression techniques will be utilized to avoid storing extremely large solution data sets in the iterative solvers, and new model order reduction techniques specifically designed for the optimal mixing problem will be developed to increase efficiency. The synthesis of optimal control and numerical approximation will enable the study of similar phenomena arising in many other complex and real-world flow dynamics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2414705","CAREER: Mathematical Modeling from Data to Insights and Beyond","DMS","COMPUTATIONAL MATHEMATICS","01/15/2024","01/22/2024","Yifei Lou","NC","University of North Carolina at Chapel Hill","Continuing Grant","Yuliya Gorb","05/31/2025","$141,540.00","","yflou@unc.edu","104 AIRPORT DR STE 2200","CHAPEL HILL","NC","275995023","9199663411","MPS","127100","1045, 9263","$0.00","This project will develop both analytical and computational tools for data-driven applications. In particular, analytical tools will hold great promise to provide theoretical guidance on how to acquire data more efficiently than current practices. To retrieve useful information from data, numerical methods will be investigated with emphasis on guaranteed convergence and algorithmic acceleration. Thanks to close interactions with collaborators in data science and information technology, the investigator will ensure the practicability of the proposed research, leading to a real impact. The investigator will also devote herself to various outreach activities in the field of data science. For example, she will initiate a local network of students, faculty members, and domain experts to develop close ties between mathematics and industry as well as to broaden career opportunities for mathematics students. This initiative will have a positive impact on the entire mathematical sciences community. In addition, she will advocate for the integration of mathematical modeling into K-16 education by collaborating with The University of Texas at Dallas Diversity Scholarship Program to reach out to mathematics/sciences teachers.

This project addresses important issues in extracting insights from data and training the next generation in the ""big data"" era. The research focuses on signal/image recovery from a limited number of measurements, in which ""limited"" refers to the fact that the amount of data that can be taken or transmitted is limited by technical or economic constraints. When data is insufficient, one often requires additional information from the application domain to build a mathematical model, followed by numerical methods. Questions to be explored in this project include: (1) how difficult is the process of extracting insights from data? (2) how should reasonable assumptions be taken into account to build a mathematical model? (3) how should an efficient algorithm be designed to find a model solution? More importantly, a feedback loop from insights to data will be introduced, i.e., (4) how to improve upon data acquisition so that information becomes easier to retrieve? As these questions mimic the standard procedure in mathematical modeling, the proposed research provides a plethora of illustrative examples to enrich the education of mathematical modeling. In fact, one of this CAREER award's educational objectives is to advocate the integration of mathematical modeling into K-16 education so that students will develop problem-solving skills in early ages. In addition, the proposed research requires close interactions with domain experts in business, industry, and government (BIG), where real-world problems come from. This requirement helps to fulfill another educational objective, that is, to promote BIG employment by providing adequate training for students in successful approaches to BIG problems together with BIG workforce skills.

This award reflects 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/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv b/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv index 403a2c6..366bead 100644 --- a/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv +++ b/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv @@ -1,6 +1,7 @@ "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" -"2411029","Curvature, Metric Geometry and Topology","DMS","GEOMETRIC ANALYSIS","07/01/2024","06/03/2024","Krishnan Shankar","VA","James Madison University","Standard Grant","Qun Li","06/30/2027","$142,565.00","","shankakx@jmu.edu","800 S MAIN ST","HARRISONBURG","VA","228013104","5405686872","MPS","126500","","$0.00","The PI?s focus is the study of objects in dimensions higher than three that admit positive or non-negative curvature. Intuitively one may think of positive curvature in the following manner: On the surface of Earth any two longitudes from the North pole appear to bend towards each other and indeed they meet at the South pole. This is true of all points on Earth if we imagine longitudes emanating from each point. Because of this, we say that the surface of Earth has positive curvature everywhere. By the same token, a saddle has negative curvature at the point where the rider sits while a flat table has zero curvature. In higher dimensions, matters are far less visually apparent. One deals almost exclusively with equations and sophisticated geometrical techniques that describe the curvature of manifolds, a term that refers to objects that, roughly speaking, have no sharp edges. Manifolds of bounded size are called compact manifolds. One of the great mysteries in the study of positive or non-negative curvature is the dearth of examples. The techniques at hand are few and the number of known examples remains relatively small. In this project the PI aims to study positively and non-negatively curved manifolds with proposed new methods of construction. The project also presents several broader impact activities including outreach, inclusivity, and undergraduate research.


The study of manifolds with positive or non-negative sectional curvature has a long history with roots as far back as Felix Klein in the late nineteenth century. The PI's work for many years has been to try and construct new examples while attempting to prove rigidity theorems in the presence of additional hypotheses. Complete manifolds of non-negative sectional curvature fall into two broad categories: compact and non-compact. In the non-compact case we have the beautiful Soul theorem of Cheeger and Gromoll: A complete, non-compact manifold with non-negative sectional curvature is diffeomorphic to a vector bundle over a closed, totally convex submanifold. In the compact case, Gromov's theorem restricts the topology sharply: The total Betti number is bounded by a constant depending only on the dimension. Beyond these theorems the question remains: which closed manifolds admit metrics of non-negative sectional curvature? In this project the PI continues their recently successful research program on constructing new manifolds with non-negative curvature as well as a new proposed method for constructing positive curvature.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2405266","RUI: Quotient Spaces and the Double Soul Conjecture","DMS","GEOMETRIC ANALYSIS","07/01/2024","06/07/2024","Jason DeVito","TN","University of Tennessee Martin","Standard Grant","Qun Li","06/30/2027","$136,007.00","","jdevito@utm.edu","304 ADMINISTRATION BLDG","MARTIN","TN","382380001","7318817015","MPS","126500","","$0.00","The Principal Investigator will investigate shapes called manifolds which are of particular importance due to the critical role they play in Einstein's general theory of relativity. His main focus will be on a special class of manifolds which are called double disk bundles. The PI intends to increase our understanding of the relationships which exist between double disk bundles and other important classes of manifolds. The PI will accomplish this via projects ranging in scope from undergraduate research experiences to international collaborations.

The PI's work, motivated by the Double Soul Conjecture and the recent introduction of codimension one biquotient foliations, seeks to improve our understanding of double disk bundles both topologically and geometrically. From the topological side, he intends to increase our understanding of when certain spaces of geometric interest, such as homogeneous spaces and biquotients, carry a double disk bundle structure. On the geometric side, he intends to use double disk bundle structures in the construction of new examples of manifolds with interesting Riemannian metrics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405440","Rigidity and Flexibility through Group Actions","DMS","GEOMETRIC ANALYSIS","07/01/2024","06/03/2024","Kurt Vinhage","UT","University of Utah","Standard Grant","Eriko Hironaka","06/30/2027","$207,485.00","","vinhage@math.utah.edu","201 PRESIDENTS CIR","SALT LAKE CITY","UT","841129049","8015816903","MPS","126500","","$0.00","A traditional dynamical system is a time lapse of a space that describes the motion of points. The time lapse can be in a single, discrete time step or a continuous time flow. One natural way in which dynamical systems can be considered the same, called conjugacy, is through change of coordinates. That is, two dynamical systems are conjugate if there is an equivalence between the spaces which connects the way in which time steps are made. One of the central classification questions in dynamics is to classify dynamical systems up to conjugacy. This question has variations based on what it means for two systems to be equivalent, usually taking the forms of measurable, continuous and smooth equivalences. The goal of the proposal is to study the classification question from various perspectives, including generalizing the notion of a dynamical system to a group action, understanding possible values for conjugacy invariants and relaxing the notion of conjugacy to allow for time reparameterization. The proposal also includes work with students at various levels to deepen the collective understanding.

The proposal aims to capitalize on momentum in 3 key areas: smooth rigidity for actions of abelian groups and higher-rank semisimple Lie groups, Kakutani equivalence for flows and group actions, and flexibility for conjugacy invariants. Each of these questions is related to a classification question, the first working toward the Katok-Spatzier conjecture and Zimmer program, the second being an extension of results about Kakutani equivalence of parabolic flows to the setting of abelian group actions, and the third being a natural extension of the seminal work of Erchonko-Katok describing the possible values for topological and metric entropy for geodesic flows on 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." +"2411029","Curvature, Metric Geometry and Topology","DMS","GEOMETRIC ANALYSIS","07/01/2024","06/03/2024","Krishnan Shankar","VA","James Madison University","Standard Grant","Qun Li","06/30/2027","$142,565.00","","shankakx@jmu.edu","800 S MAIN ST","HARRISONBURG","VA","228013104","5405686872","MPS","126500","","$0.00","The PI?s focus is the study of objects in dimensions higher than three that admit positive or non-negative curvature. Intuitively one may think of positive curvature in the following manner: On the surface of Earth any two longitudes from the North pole appear to bend towards each other and indeed they meet at the South pole. This is true of all points on Earth if we imagine longitudes emanating from each point. Because of this, we say that the surface of Earth has positive curvature everywhere. By the same token, a saddle has negative curvature at the point where the rider sits while a flat table has zero curvature. In higher dimensions, matters are far less visually apparent. One deals almost exclusively with equations and sophisticated geometrical techniques that describe the curvature of manifolds, a term that refers to objects that, roughly speaking, have no sharp edges. Manifolds of bounded size are called compact manifolds. One of the great mysteries in the study of positive or non-negative curvature is the dearth of examples. The techniques at hand are few and the number of known examples remains relatively small. In this project the PI aims to study positively and non-negatively curved manifolds with proposed new methods of construction. The project also presents several broader impact activities including outreach, inclusivity, and undergraduate research.


The study of manifolds with positive or non-negative sectional curvature has a long history with roots as far back as Felix Klein in the late nineteenth century. The PI's work for many years has been to try and construct new examples while attempting to prove rigidity theorems in the presence of additional hypotheses. Complete manifolds of non-negative sectional curvature fall into two broad categories: compact and non-compact. In the non-compact case we have the beautiful Soul theorem of Cheeger and Gromoll: A complete, non-compact manifold with non-negative sectional curvature is diffeomorphic to a vector bundle over a closed, totally convex submanifold. In the compact case, Gromov's theorem restricts the topology sharply: The total Betti number is bounded by a constant depending only on the dimension. Beyond these theorems the question remains: which closed manifolds admit metrics of non-negative sectional curvature? In this project the PI continues their recently successful research program on constructing new manifolds with non-negative curvature as well as a new proposed method for constructing positive curvature.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2428771","RUI: Configuration Spaces of Rigid Origami","DMS","GEOMETRIC ANALYSIS","04/15/2024","04/22/2024","Thomas Hull","PA","Franklin and Marshall College","Continuing Grant","Christopher Stark","08/31/2025","$59,029.00","","thull@wne.edu","415 HARRISBURG AVE","LANCASTER","PA","176032827","7173584517","MPS","126500","9229","$0.00","Origami, the art of paper folding, has been practiced for centuries. The mathematics behind origami, however, is not yet fully understood. In particular, some origami models can be folded and unfolded in such a way that we could make the crease lines be hinges and the paper between them stiff like sheet metal. Such models are called rigidly flexible origami and have applications that span the physical and biological sciences, ranging from unfolding solar sails to collapsible heart stents. This project will add mathematical tools that allow industrial applications to employ cutting-edge research, from large-scale architectural structures to nano-scale robotics driven by origami mechanics. The tools from this project will help design self-foldable structures. Currently self-folding designs in engineering, architecture, and the biological sciences involve building physical models in a trial-and-error approach, wasting time and resources. The self-folding research provided by this project will allow designers to avoid pitfalls and tighten the design-to-realization process significantly. In addition to the research component, the PI shall organize a diverse range of educational activities including in-service teacher training and education, undergraduate mentoring and preparation for graduate school; high-school and undergraduate classes on the mathematics of folding; for the public, general-audience articles, lectures, and exhibitions. This will increase interest in STEM fields through the fun, hands-on nature of origami while simultaneously disseminating project results.

The methods of this project involve a blend of practical experimentation with theory. Programmed self-foldability of structures will be achieved by trimming away undesired paths from the configuration space of all possible rigid foldings. One approach is to transform a given rigid folding of a crease pattern into a kinematically equivalent rigid folding with fewer degrees of freedom. The PI has proposed such a transform and will develop others. Key to all of this, however, is gaining a better understanding of rigid origami configuration spaces, which are algebraically complicated and not well understood. The project seeks to understand, and exploit, local-to-global behavior that is present in many known examples of rigid origami. In these examples approximating the configuration space near the origin (the unfolded state) leads to exact equations for the global configuration space. Formulating rigid origami configuration spaces in this way will add insight into the general field of flexible polyhedral surfaces, as well as provide the data needed to prove the feasibility of origami crease pattern transforms and design reliably self-foldable origami mechanisms.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404529","Semi-global Kuranishi Structures in Symplectic Field Theory","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/22/2024","Erkao Bao","MN","University of Minnesota-Twin Cities","Continuing Grant","Swatee Naik","06/30/2027","$110,904.00","","bao@umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","126500","9251","$0.00","Contact manifolds are a special type of space that naturally emerges in various contexts. For instance, they are used to describe the orbital paths of satellites. Taking the satellite scenario, for example, a natural question to ask is whether there are recurring orbits that a satellite can traverse. Contact homology offers a systematic way to explore the geometric features of these contact manifolds. In the satellite scenario, one can gain deep insights into all possible orbital paths of satellites by analyzing recurring satellite orbits. Contact homology has been highly successful in distinguishing different contact manifolds. This project aims to refine our understanding of contact manifolds using an enhanced approach based on contact homology. Furthermore, the PI intends to apply the techniques developed in this process to study other types of spaces beyond contact manifolds, such as spaces with symmetries. Symmetries play a crucial role in many aspects of daily life. For instance, ensuring that machine learning models treat people fairly, irrespective of their gender or race, reflects a key symmetry requirement. To address these issues, the PI will conduct an REU (Research Experience for Undergraduates) program focused on developing symmetrical neural networks to mitigate gender and racial biases.

Symplectic Field Theory, introduced two decades ago, aims to provide invariants for symplectic and contact manifolds. It encompasses essential concepts such as cylindrical contact homology, contact homology, chain homotopy types of contact differential graded algebras (dga), and linearized contact homology. The projects presented here revolve around the foundational aspects of Symplectic Field Theory. The primary challenge addressed by the Principal Investigator (PI) concerns achieving transversality while preserving symmetries to derive the desired algebraic formula. Various tools and techniques, including obstruction bundle gluing and evaluation maps for cylindrical contact homology, and semi-global Kuranishi structures for contact homology, have been introduced or employed by the PI. The project applies these tools to investigate two specific invariants: the chain homotopy type of contact dga and linearized contact homology. Furthermore, the PI has developed a new tool, the semi-global Kuranishi structure for clean intersections, which lies between obstruction bundle gluing and semi-global Kuranishi structures. This tool offers increased computational efficiency and bridges seemingly unrelated techniques. The project also aims to establish a Smith-type rank inequality related to the Floer homology of the fixed point set, contributing to the understanding of the L-space 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." "2350423","Conference: Moving to higher rank: from hyperbolic to Anosov","DMS","GEOMETRIC ANALYSIS","07/01/2024","01/30/2024","Ilesanmi Adeboye","CT","Wesleyan University","Standard Grant","Eriko Hironaka","06/30/2025","$40,000.00","Sara Maloni","iadeboye@wesleyan.edu","237 HIGH ST","MIDDLETOWN","CT","064593208","8606853683","MPS","126500","7556","$0.00","This award supports participation of US based mathematicians in the conference entitled ""Moving to higher rank: from hyperbolic to Anosov,"" which will take place in Centraro, Italy, from July 15- 19, 2024. The conference will bring together researchers and students from the classical field of hyperbolic geometry and the more recent area of higher Teichmuller theory to explore and further develop the rich connection between them. The conference will facilitate the exchange of ideas, and promote collaboration between experts in both fields, while reinforcing cooperation between the US and European mathematical communities. The organizing committee will encourage and support broad and diverse participation, and the training of the new generation of researchers.

In recent decades, the areas of hyperbolic geometry and Higher Teichmuller theory have undergone a dynamic convergence of concepts, attracting numerous scholars from hyperbolic geometry who have shifted their focus toward higher rank phenomena. Concurrently, a new generation of researchers has emerged, working at the juncture of these two domains. The conference will focus on how phenomena from hyperbolic geometry generalize to higher Teichmuller theory. Past success along these lines includes generalizations of Fenchel-Nielssen coordinates, Weil- Petersson geometry, Collar Lemmas, Length rigidity, and Patterson-Sullivan Theory. The conference will feature 18 research talks, and two lightening talk sessions for junior researchers. The URL for the conference website is https://tinyurl.com/hyp2anosov.

This award reflects 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 0a36cc8..f7cac31 100644 --- a/Probability/Awards-Probability-2024.csv +++ b/Probability/Awards-Probability-2024.csv @@ -1,11 +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" -"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." +"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","Jason Swanson, Wai Fan, Krzysztof Burdzy","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." +"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." +"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","","ariesfanhk@gmail.com","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." "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." "2348024","Permutations in Random Geometry","DMS","PROBABILITY","06/01/2024","05/22/2024","Jacopo Borga","CA","Stanford University","Continuing Grant","Elizabeth Wilmer","05/31/2027","$43,582.00","","jborga@stanford.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." "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." -"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." "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." "2413604","Conference: Cincinnati Symposium on Probability 2024","DMS","PROBABILITY","05/01/2024","04/16/2024","Yizao Wang","OH","University of Cincinnati Main Campus","Standard Grant","Elizabeth Wilmer","04/30/2025","$48,620.00","Magda Peligrad, Robert Buckingham, Ju-Yi Yen, Xiaoqin Guo","Yizao.wang@uc.edu","2600 CLIFTON AVE","CINCINNATI","OH","452202872","5135564358","MPS","126300","7556","$0.00","The 6th Cincinnati Symposium on Probability will take place on May 1-4, 2024 at the University of Cincinnati, Ohio (earlier Cincinnati Symposia took place in 2018, 2014, 2009, 1986, and 1985). This year's symposium will highlight 16 senior invited speakers, 7 junior invited speakers, and a poster session for other junior participants, hosting a total of around 70 participants. The first major goal is to bring leading experts on stochastic processes with weak dependence and stochastic models in mathematical physics to Cincinnati; they will present their latest results. Several invited speakers are from Europe and Asia, and their presence will be much appreciated by junior probabilists in the midwest. The second major goal is to provide graduate students and postdocs in probability a platform to present their own results and establish connections with well-established scholars. All non-speaking and junior participants are encouraged to present their research results in the poster session. Last but not least, the organizing committee is committed to diversity and will ensure that conference attendees reflect the populations of graduate students and new researchers who form the primary audience of the conference.

The two main themes of the symposium are stochastic processes with weak dependence and stochastic models in mathematical physics. Stochastic processes with weak dependence have a long history in the development of probability theory and its applications, particularly in statistics. Recently several key techniques have found new applications in other mathematical areas, including random fields, random matrices, and random walks on groups. Such extensions will also be showcased by the talks of invited speakers. Mathematical physics has been another source of main motivations for the development of probability theory, and invited speakers will present latest results on selected models from random motions in random media and integrable probability. The Symposium website is https://homepages.uc.edu/~wangyz/CSP2024/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." "2400990","Conference: Universality and Integrability in KPZ","DMS","PROBABILITY","05/01/2024","04/19/2024","Ivan Corwin","NY","Columbia University","Standard Grant","Elizabeth Wilmer","04/30/2025","$39,500.00","","ivan.corwin@gmail.com","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126300","7556","$0.00","The conference ""Universality & Integrability in KPZ"" occurs from March 11 - 15, 2024 at Columbia University in the City of New York. The conference brings together experts and early career researchers across mathematics and theoretical physics around a common area of interest -- how do randomly evolving interfaces behave statistically over large periods of time? Such growth is ubiquitous, for instance coming up in models of cancer or bacteria growth, liquid crystal growth, or liquid diffusion through textiles. Methods to study random growth models come from a host of different fields such as probability theory, combinatorics, integrable systems, statistical physics, random matrix theory, and stochastic partial differential equations. Thus, one of the goals of this conference is to share ideas across these different areas as well as educate early career researchers on the state-of-the-art methods. Indeed, this award's entire purpose is supporting early career researcher participation.

In the area of random interface growth, some models enjoy special ""integrable"" structure whereby their statistical behavior can be described through exact formulas or relations. Studying the asymptotics of these formulas and relations leads to universal predictions of the behavior of a much wider class of models, including many that are not integrable. This workshop addresses promising methods both to find and utilize integrable structures and to prove that the resulting predictions are universal. The overall class of random growth models considered here is known as the Kardar-Parisi-Zhang universality class. There has been tremendous progress in recent years both on the integrability and universality front, for instance with the construction of the KPZ fixed point, directed landscape, the study of multi-species models and description of invariant measures for models with boundaries. This conference highlights these advances and inspires a new generation of researchers. https://sites.google.com/view/universalityintegrabilityinkpz

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -13,4 +15,3 @@ "2413465","Conference: The 52nd John and Lida Barrett Memorial Lectures - Stochastic Analysis and its Application","DMS","PROBABILITY","05/01/2024","04/18/2024","Hung Nguyen","TN","University of Tennessee Knoxville","Standard Grant","Elizabeth Wilmer","04/30/2025","$31,300.00","xia chen, Jan Rosinski","hnguye53@utk.edu","201 ANDY HOLT TOWER","KNOXVILLE","TN","379960001","8659743466","MPS","126300","7556","$0.00","This award supports attendance of junior and other researchers the 52nd anniversary of the John Barrett Memorial Lectures which will be held on May 16-18, 2024, at the University of Tennessee, Knoxville. This three-day workshop will be focused on stochastic analysis and its applications. Stochastic analysis, a subfield of probability, is a powerful mathematical tool for modeling phenomena under the impact of random perturbations. Stochastic differential equations in particular have been widely employed in stochastic modeling, in fields including networking, finance, engineering, and other disciplines. The workshop will bring prominent researchers in these active areas to Knoxville, as a service to both the university and to the southeastern region of the country. The topic of the Barrett Lectures has the additional advantage of broad appeal to members of other departments and at the nearby Oak Ridge National Laboratory, thereby fostering interdisciplinary collaborations, particularly with researchers in applied sciences. The workshop welcomes the inclusion and participation of junior scientists and members of under-represented groups. This award will present them with the opportunity to learn from leading experts working on stochastic modeling by enabling their attendance.

Invited speakers and participants will bring expertise from a wide array of theoretical aspects of stochastic analysis, namely, the study of ordinary/partial differential equations in the presence of external stochastic forcing driven by Wiener processes and Levy jump processes, random walks in random media, and random polynomials. The scientific program of the Lecture also emphasizes on a selection of applied topics, including the theory of well-posedness, large deviations and ergodicity of dispersive equations, parabolic equations, Navier-Stokes equations as well as KPZ equations. Other applications in finance and engineering will include filtering and stochastic control.
The conference website is https://www.math.utk.edu/barrett/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2343868","Diffusions and jump processes on groups and manifolds","DMS","PROBABILITY","07/01/2024","03/19/2024","Laurent Saloff-Coste","NY","Cornell University","Continuing Grant","Elizabeth Wilmer","06/30/2027","$118,236.00","","lsc@math.cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","126300","","$0.00","Modeling scientific experiments or human activities often involves randomness. Card shuffling procedures provide a familiar, yet complex and mathematically interesting example that serves as a model for many mixing phenomena. Randomness is used to understand image restoration and recognition, communication and social networks, the behavior of financial markets, as well as in the analysis of large data sets in general. It is an important tool in the study of efficient computations and scientific simulations. In all these applications, strong structural constraints associated with the complex combinatorial or geometric structure underlying the problem determine the behavior. This project is concerned with the fundamental properties of basic stochastic processes and how the behavior of these processes relates to the global geometric structure of their different environments. Postdoctoral associates, graduate students, and undergraduate students will be mentored and trained as part of this project.

The funded research focusses on random processes that are defined by a related geometric or algebraic structure (e.g., Riemannian manifolds and groups). The global behaviors of these processes are determined by this underlying structure. In some cases, these behaviors can provide information on the underlying space and its structure. These explorations are at the interface between analysis, geometry, and probability, with the notion of group structure playing a key part. Partial differential equations and potential theory, i.e. the study of harmonic functions and solutions of the heat equation, are also central. Brownian motion on Riemannian Manifolds and random walks on Cayley graphs of finitely generated groups provide key examples. The notion of stable-like processes on nilpotent groups is also studied.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347177","STATISTICAL AND COMPUTATIONAL THRESHOLDS IN SPIN GLASSES AND GRAPH INFERENCE PROBLEMS","DMS","PROBABILITY","09/01/2024","03/19/2024","Nike Sun","MA","Massachusetts Institute of Technology","Standard Grant","Elizabeth Wilmer","08/31/2027","$395,910.00","","nsun@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126300","","$0.00","This research concerns large systems whose constituent components undergo simple interactions, such as nearest-neighbor constraints, leading to more complex aggregate behaviors, such as phase transitions. Systems that naturally exhibit long-range dependencies are of particular interest. A basic goal of the work is to develop new methods to analyze such dependencies, and thereby to characterize typical behaviors of large complex systems. A longer-term goal is to connect our understanding of static behaviors to algorithmic limits in high-dimensional computational and inference problems.

The project has two main components. The first considers questions on phase transitions in random graph inference problems, both statistical and computational. The second will investigate statistical and algorithmic limits in random optimization problems, specifically in the context of mean-field spin glass models and random constraint satisfaction problems (CSPs). Postdoctoral researchers, graduate and undergraduate students will all be involved in the research.

This award reflects 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","","waifan@iu.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." diff --git a/Topology/Awards-Topology-2024.csv b/Topology/Awards-Topology-2024.csv index 2dc2fae..15f689e 100644 --- a/Topology/Awards-Topology-2024.csv +++ b/Topology/Awards-Topology-2024.csv @@ -1,8 +1,11 @@ "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" +"2422651","Topology Students Workshop","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","02/15/2024","02/27/2024","Dan Margalit","TN","Vanderbilt University","Standard Grant","Swatee Naik","12/31/2024","$4,293.00","","dan.margalit@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126000, 126700","7556","$0.00","The Topology Students Workshop (TSW) will be held at Georgia Institute of Technology during June 6-10, 2022. This conference is a 5-day research and professional development workshop for graduate students in the fields of geometric group theory, geometry, and topology. Its primary goals are to a) expose graduate students to a wide range of current research in topology, b) build their communication, networking, and problem-sharing skills, and c) give guidance on necessary but typically untaught aspects of the profession. Approximately 50 graduate students will participate, guided by 10 mentors, who come from a wide range of career stages and represent a broad array of topics within geometry and topology including contact and symplectic topology, 3-manifolds, hyperbolic geometry, group actions, and complex dynamics. The conference provides the participants, especially those from underrepresented groups, with many tools that will help them to succeed as scientists at the highest levels, in graduate school and beyond.

For many of the students, the TSW is the first conference they attend and at which they present their own results. The workshop is designed to facilitate this experience (for instance, our first professional development session is an introduction to conferences and how best to benefit from them). The goal is to build confidence and research potential among students, as well as to build community. The skills addressed here are not typically taught in grad school and can be disproportionately beneficial to students from minority groups, as indicated from responses from participants in previous iterations of the program. The professional development and research sides of the workshop run in tandem, with mentors giving guidance in both areas. The workshop includes structured sessions on networking and etiquette, the job application process, communication skills, and a panel discussion on career paths (which also involves mathematicians from organizations such as NSA, Amazon, Google, and private high schools). Mentors also give research talks, both to model good communication and introduce their research areas (deliberately chosen broadly) and relevant problems to students who are embarking on a research career. Effective communication is a major theme: two evening sessions are devoted to workshopping presentations in small groups; the final presentations are videotaped and critiqued by those in attendance. The web site for the conference is http://tsw.gatech.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." +"2350343","Collaborative Research: Conference: Trisections Workshops: Connections with Knotted Surfaces and Diffeomorphisms","DMS","TOPOLOGY","05/01/2024","02/13/2024","Alexander Zupan","NE","University of Nebraska-Lincoln","Standard Grant","Eriko Hironaka","04/30/2026","$49,910.00","","zupan@unl.edu","2200 VINE ST # 830861","LINCOLN","NE","685032427","4024723171","MPS","126700","7556, 9150","$0.00","This proposal will fund the ?Trisections Workshop: Connections with Knotted Surfaces,? which will take place at the University of Nebraska-Lincoln from June 24-28, 2024, and the ?Trisections Workshop: Connections with Diffeomorphisms,? which will take place at the University of Texas at Austin during one week in the summer of 2025. Workshop attendees will include established experts, early-career researchers, and students, and the program will actively engage all participants. Each morning will feature plenary talks by experts and/or lightning talks highlighting the work of junior researchers. The afternoons will be devoted to working in groups on open problems. This series of regular workshops has been critical to the development of an enthusiastic community of researchers in low-dimensional topology, helping this new and growing area gain momentum and fostering numerous collaborations across career stages and demographics. The organizers take pride in the camaraderie and welcoming atmosphere they strive to create, and many in the community deeply value and appreciate these events.

A trisection splits a 4-dimensional space into three simple pieces. Since their introduction roughly a decade ago, trisections have proven to be a successful new tool with which to study smooth 4-manifolds, with numerous articles written in the interim to develop the foundations for trisection theory. An important strength of the theory of trisections is the way it interfaces with a variety of other topics in low-dimensional topology. This interface provides an opportunity to explore many classical areas of 4-manifold topology through a new lens. Such areas include, for example, the study of knotted surfaces in 4-space, diffeomorphisms of 4-manifolds, exotic smooth structures, group actions and (branched) covering spaces, and symplectic structures. The main goal of these workshops is to bring together researchers from multiple areas to propose and to work on open problems, with a particular focus on the inclusion of early career researchers. The workshops are preceded by a series of introductory virtual pre-workshop talks, which serve to bring new researchers up to speed, to facilitate the work to be done in groups, and to incorporate a broader, worldwide audience. The website for the 2024 workshop can be found here: https://sites.google.com/view/tw2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2405301","The Topology of 3- and 4-Manifolds","DMS","OFFICE OF MULTIDISCIPLINARY AC, TOPOLOGY","07/01/2024","05/15/2024","Alexander Zupan","NE","University of Nebraska-Lincoln","Standard Grant","Swatee Naik","06/30/2027","$317,407.00","","zupan@unl.edu","2200 VINE ST # 830861","LINCOLN","NE","685032427","4024723171","MPS","125300, 126700","9150","$0.00","The field of topology involves understanding properties of abstract shapes that are unchanged by twisting, stretching, and bending (but not breaking or tearing). A n-dimensional manifold is a space that locally resembles n-dimensional real space. For example, the surface of a donut is a two-dimensional manifold, because under very high magnification, this surface looks like a two-dimensional plane. Three-dimensional objects arise naturally in our physical world, and four-dimensional objects can be motivated by thinking about the evolution of three-dimensional objects over time. Notably, low-dimensional topology has a number of interesting applications to biology, chemistry, physics, and quantum computing. This project focuses on the search for deep connections between manifold theory in dimensions three and four. In addition, the project includes funding for graduate and undergraduate student research, and it will support the Great Plains Alliance, a program that pairs graduate students with speaking opportunities at other institutions for the purpose of broadening the impact of their work and promoting graduate school in mathematics to the undergraduate attendees. The project will also fund the Distinguished Women in Mathematics colloquium series at the University of Nebraska-Lincoln, the PI?s home institution. This series connects UNL faculty and graduate students with prominent women mathematicians and their research.

Topology in dimension three has seen an explosion of activity over the last several decades, and a number of important open problems have now been resolved. In contrast, the topology of four-dimensional manifolds has become an increasingly active area of research, motivated by fundamental conjectures that have stubbornly resisted progress. Two of the most famous examples include the smooth four-dimensional Poincaré conjecture (SPC4) and the slice-ribbon conjecture. Recently, the PI has shown that a substantial family of four-manifolds satisfies the SPC4 in joint work with Jeffrey Meier. The work connects four-dimensional handle calculus with results about Dehn surgery on knots and links in three-manifolds; it brings together a wide range of tools and techniques; and it subsumes several historically important results. The collection of manifolds can be characterized by families of links, including some of the most promising potential counterexamples to the slice-ribbon conjecture. This project describes a varied set of problems stemming from past work and interweaving ideas from knot theory, three-manifolds, and smooth four-manifold topology. Specific objectives include proving additional cases of the SPC4, finding new relationships between the topology of certain homotopy four-spheres and the Andrews-Curtis conjecture in combinatorial group theory, developing connections between three- and four-dimensional knot invariants, and utilizing bridge trisections in new constructions of surfaces in four-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." +"2414922","Stable Homotopy Theory in Algebra, Topology, and Geometry","DMS","TOPOLOGY","01/15/2024","01/23/2024","James Quigley","VA","University of Virginia Main Campus","Standard Grant","Christopher Stark","11/30/2025","$185,923.00","","jquigley1993@gmail.com","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126700","","$0.00","Stable homotopy theory was developed throughout the twentieth century to study high-dimensional topological spaces. Since spheres are the fundamental building blocks of topological spaces, the stable stems, which encode the possible relations between high-dimensional spheres up to continuous deformation, are a central object of study. Beyond topology, the stable stems have surprisingly broad applications throughout mathematics, ranging from geometric problems, such as classifying differentiable structures on spheres, to algebraic problems, such as classifying projective modules over rings. This project will explore further applications of stable homotopy theory in algebra, topology, and geometry. Broader impacts center on online community building. The PI will continue co-organizing the Electronic Computational Homotopy Theory Online Research Community, which aims to increase inclusion at the undergraduate, graduate, and senior levels by organizing undergraduate research opportunities, graduate courses, online seminars, mini-courses, and networking events. To address inequality at the K-12 level, the PI will develop and manage a program pairing undergraduates from his home institution with students from local after-school programs for online tutoring. This program would circumvent certain barriers to participation, such as lack of access to transportation and facilities, which are common in traditional outreach.

Specific research projects include the study of the stable stems and their applications in geometric topology, algebro-geometric analogues of the stable stems and their connections to number theory, and equivariant analogues of algebraic K-theory and their applications in algebra and geometry. More specifically, building on previous work, the PI will study the stable stems using topological modular forms and the Mahowald invariant, aiming to deduce the existence of exotic spheres in new dimensions. In a related direction, the PI will use the kq-resolution introduced in previous work to study the motivic stable stems, an algebro-geometric analogues of the stable stems. The main goal is to apply the kq-resolution to relate the motivic stable stems to arithmetic invariants like Hermitian K-theory. Real algebraic K-theory, which encodes classical invariants like algebraic K-theory, Hermitian K-theory, and L-theory, will also be studied using the trace methods developed in previous work. The overarching goal is extending results from algebraic K-theory to real algebraic K-theory, thereby obtaining results for Hermitian K-theory and L-theory that will have applications in algebra and 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." "2405324","RUI: Knot Theory and the Four-Sphere","DMS","TOPOLOGY","06/01/2024","05/30/2024","Jeffrey Meier","WA","Western Washington University","Standard Grant","Swatee Naik","05/31/2027","$199,256.00","","jeffrey.meier@wwu.edu","516 HIGH ST","BELLINGHAM","WA","982255996","3606502884","MPS","126700","","$0.00","Understanding four-dimensional spaces holds significant scientific importance. It offers insights into fundamental theories like relativity and quantum mechanics, enhancing our conception of the structure and dynamics of the universe. Additionally, it enables exploration of complex phenomena such as higher-dimensional geometry, offering solutions to theoretical puzzles and practical challenges. Embracing the concept of four-dimensional spaces expands our intellectual horizons and has the potential to lead to advancements in technology and change how we interact with our surroundings. The focus of this research program is the study of knotted objects in dimension four and the connections that arise between the topology and geometry of the ambient four dimensional manifold and the knotted objects found within. This grant will allow the PI to carry out a robust program of undergraduate research, training, and mentoring; organize conferences, seminars, and an undergraduate math club; and implement student-centered teaching pedagogies. All of these activities help to create a new generation of researchers who will grapple with the challenging problem of understanding four-dimensional topology.

The four-dimensional sphere is the simplest closed, four-dimensional manifold, yet it remains little understood in several important ways. First, it is unknown whether the four-sphere admits an exotic smooth structure, a question that has been settled in all other dimensions. Second, it is unknown whether a smoothly knotted two-sphere in the four-sphere with the same knot group as the unknotted two-sphere must itself be unknotted. Finally, it is unknown which four-manifolds arise as irregular three-fold covers of the four-sphere. This research program aims to make progress on these and important related problems through the study of knotted disks in homotopy four-balls; the diagrams of knotted surfaces in the four-sphere; and the topology, geometry, and symmetries of the four-manifolds obtained as branched covers over these 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." "2348092","Conference: Algebraic Structures in Topology 2024","DMS","TOPOLOGY","03/01/2024","01/04/2024","Manuel Rivera","IN","Purdue University","Standard Grant","Swatee Naik","02/28/2025","$46,650.00","Ralph Kaufmann, Mona Merling, Jeremy Miller","river227@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126700","7556","$0.00","This award provides support for US based participants in the conference ""Algebraic structures in topology 2024? that will take place from June 5th to June 14th, 2024 in San Juan, Puerto Rico. Algebraic topology is a field of theoretical mathematics whose main goal is to study different notions of ?shape? that belong to the realm of ?continuous? mathematics, using tools from algebra that belong to the ?discrete? realm. Algebraic topology has been applied successfully to other fields of mathematics, and, more recently, to science including quantum physics, solid state physics, string theory, data science, and computer science. This conference will focus on recent developments in algebraic topology and its applications. The conference will feature a series of events accessible to audiences at different levels. These include: 1) a three-day school with mini-courses accessible to graduate students and mathematicians from fields outside algebraic topology, 2) a public event with talks and discussions accessible to a general audience, 3) a week-long research conference featuring invited speakers and contributed talks in algebraic topology. Furthermore, the conference aims to engage with groups that are historically underrepresented in academic research in mathematics, particularly with mathematicians of Hispanic and Latin American origin, in a deep and direct manner. Geographically, culturally, as well as politically, the strategically selected location, Puerto Rico, sits between the mathematical communities based in United States, Canada, Europe, and Latin America. Along with a strong engagement with the local community, the event will feature works by a significant number of Hispanic mathematicians.

The overarching theme of the conference is the use of algebra to give structure to geometric contexts. The mini-courses will be on the topics of algebraic K-theory, configuration spaces, and string topology and aim to bring participants to the state-of-the-art in these subjects. The research talks will highlight recent breakthroughs in different sub-fields of algebraic topology including stable and chromatic homotopy theory, K-theory, higher category theory, higher algebra, derived geometry, operads, homological stability, configuration spaces, string topology, and topological data analysis and will be given by leading experts in these fields. By bringing together a diverse cohort of mathematicians working on different sub-fields, the organizers aim to foster new ideas and perspectives. The public lectures will discuss research in theoretical mathematics, and its relevance to society, science, and technology, with examples coming from topology.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409099","Conference: 2024-2026 Graduate Student Conference in Geometry, Topology, and Algebra","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","05/15/2024","05/15/2024","Matthew Stover","PA","Temple University","Standard Grant","Swatee Naik","04/30/2027","$90,000.00","David Futer, Jaclyn Lang","mstover@temple.edu","1805 N BROAD ST","PHILADELPHIA","PA","191226104","2157077547","MPS","126400, 126700","7556","$0.00","This award supports the next three events in the Annual Graduate Student Conference series in Algebra, Geometry, and Topology (GTA Philadelphia). The next conference will be held on May 31-June 2, 2024 at Temple University. The conference will bring together over 80 graduate students at all levels and from a variety of backgrounds and universities, along with four distinguished plenary speakers that work at the interface of algebra, geometry, and topology. Supplementing lectures by faculty and students, the conference features a professional development panel focused on career building and social responsibility. The conference provides a rare opportunity for a large number of early career mathematicians with similar research interests to come together and develop mathematical relationships. In addition, it strongly supports interactions between graduate students from different schools, different backgrounds, and different research areas.

The large majority of lectures will be given by graduate students, supplying them with opportunities to practice presenting their research ideas and interests to fellow students. The conference strives to include a wide range of topics and a broad diversity of speakers. In addition, talks by distinguished plenary speakers will provide insights into how different parts of algebra, geometry, and topology are connected, open research questions of interest, and recent techniques used in groundbreaking work in these fields. For further information, see https://math.temple.edu/events/conferences/gscagt/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2405301","The Topology of 3- and 4-Manifolds","DMS","OFFICE OF MULTIDISCIPLINARY AC, TOPOLOGY","07/01/2024","05/15/2024","Alexander Zupan","NE","University of Nebraska-Lincoln","Standard Grant","Swatee Naik","06/30/2027","$317,407.00","","zupan@unl.edu","2200 VINE ST","LINCOLN","NE","685032427","4024723171","MPS","125300, 126700","9150","$0.00","The field of topology involves understanding properties of abstract shapes that are unchanged by twisting, stretching, and bending (but not breaking or tearing). A n-dimensional manifold is a space that locally resembles n-dimensional real space. For example, the surface of a donut is a two-dimensional manifold, because under very high magnification, this surface looks like a two-dimensional plane. Three-dimensional objects arise naturally in our physical world, and four-dimensional objects can be motivated by thinking about the evolution of three-dimensional objects over time. Notably, low-dimensional topology has a number of interesting applications to biology, chemistry, physics, and quantum computing. This project focuses on the search for deep connections between manifold theory in dimensions three and four. In addition, the project includes funding for graduate and undergraduate student research, and it will support the Great Plains Alliance, a program that pairs graduate students with speaking opportunities at other institutions for the purpose of broadening the impact of their work and promoting graduate school in mathematics to the undergraduate attendees. The project will also fund the Distinguished Women in Mathematics colloquium series at the University of Nebraska-Lincoln, the PI?s home institution. This series connects UNL faculty and graduate students with prominent women mathematicians and their research.

Topology in dimension three has seen an explosion of activity over the last several decades, and a number of important open problems have now been resolved. In contrast, the topology of four-dimensional manifolds has become an increasingly active area of research, motivated by fundamental conjectures that have stubbornly resisted progress. Two of the most famous examples include the smooth four-dimensional Poincaré conjecture (SPC4) and the slice-ribbon conjecture. Recently, the PI has shown that a substantial family of four-manifolds satisfies the SPC4 in joint work with Jeffrey Meier. The work connects four-dimensional handle calculus with results about Dehn surgery on knots and links in three-manifolds; it brings together a wide range of tools and techniques; and it subsumes several historically important results. The collection of manifolds can be characterized by families of links, including some of the most promising potential counterexamples to the slice-ribbon conjecture. This project describes a varied set of problems stemming from past work and interweaving ideas from knot theory, three-manifolds, and smooth four-manifold topology. Specific objectives include proving additional cases of the SPC4, finding new relationships between the topology of certain homotopy four-spheres and the Andrews-Curtis conjecture in combinatorial group theory, developing connections between three- and four-dimensional knot invariants, and utilizing bridge trisections in new constructions of surfaces in four-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." "2405029","Collaborative Research: Algebraic K-theory and Equivariant Stable Homotopy Theory: Applications to Geometry and Arithmetic","DMS","TOPOLOGY","08/01/2024","05/14/2024","Andrew Blumberg","NY","Columbia University","Continuing Grant","Swatee Naik","07/31/2027","$21,883.00","","andrew.blumberg@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126700","","$0.00","Algebraic topology began as the study of those algebraic invariants of geometric objects which are preserved under certain smooth deformations. Gradually, it was realized that the algebraic invariants called cohomology theories could themselves be represented by geometric objects, known as spectra. A central triumph of modern homotopy theory has been the construction of categories of ring spectra (representing objects for multiplicative cohomology theories) which are suitable for performing constructions directly analogous to those of classical algebra. This move has turned out to be incredibly fruitful, both by providing invariants which shed new light on old questions as well as by raising new questions which have unexpected connections to other areas of mathematics and physics. This research proposal studies such constructions in algebraic K-theory, the newly emerging field of Floer homotopy theory, and the foundations of equivariant stable homotopy theory. Broader impacts include workforce development in the form of graduate student advising, undergraduate and postdoc mentorship, high school mathematical science project mentorship, conference organization, and development of new education and training programs.

This proposal describes a broad research program to study a wide variety of problems in homotopy theory, geometry, and arithmetic. The PIs' prior work gives a complete description of the homotopy groups of algebraic K-theory of the sphere spectral at odd primes and a canonical identification of the fiber of the cyclotomic trace via a spectral lift of Tate-Poitou duality. In this proposal, the PIs describe a vast expansion of that argument to study the fiber of the cyclotomic trace on more general rings and schemes over algebraic p-integers in number fields and a related K-theory question more generally for other kinds of Artin duality. The prior work also leads to a new approach to the Kummer-Vandiver conjecture based on Bökstedt-Hsiang-Madsen's geometric Soule embedding that the PIs propose to study. The PIs' recent work with Yuan established a theory of topological cyclic homology (TC) relative to MU-algebras, where there are many interesting computations to explore. Prior work of PI Blumberg with Abouzaid building a Morava K-theory Floer homotopy type has opened new lines of research in Floer homotopy theory; this already has been used to resolve old conjectures in symplectic geometry. The PIs propose to extend this construction to its natural generality, building the homotopy type over MUP and KU and rigidifying the multiplication. They propose to obtain spectral models of deformed operations on quantum cohomology (i.e., quantum Steenrod operations). This work will have myriad applications in symplectic geometry and potentially have transformative impact on the Floer homotopy theory program. The PIs propose to resolve the longstanding confusion about the role of multiplicative norm maps in equivariant stable homotopy theory for positive dimensional compact Lie groups. This requires a new foundation for factorization homology and will lead to genuine equivariant factorization homology for positive dimensional compact Lie groups. In prior work, the PIs identified previously unknown multiplicative transfers on geometric fixed points of G-commutative ring spectra. The PIs propose to study how these fit into the foundations of G-symmetric monoidal categories; a first step is to establish new multiplicative splittings that have the feel of multiplicative versions of the tom Dieck splitting.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2415445","CAREER: Machine learning, Mapping Spaces, and Obstruction Theoretic Methods in Topological Data Analysis","DMS","TOPOLOGY, CDS&E-MSS","04/01/2024","04/02/2024","Jose Perea","MA","Northeastern University","Continuing Grant","Jodi Mead","04/30/2025","$336,550.00","","j.pereabenitez@northeastern.edu","360 HUNTINGTON AVE","BOSTON","MA","021155005","6173733004","MPS","126700, 806900","079Z, 1045","$0.00","Data analysis can be described as the dual process of extracting information from observations, and of understanding patterns in a principled manner. This process and the deployment of data-centric technologies have recently brought unprecedented advances in many scientific fields, as well as increased global prosperity with the advent of knowledge-based economies and systems. At a high level, this revolution is driven by two thrusts: the modern technologies which allow for the collection of complex data sets, and the theories and algorithms we use to make sense of them. That said, and for all its benefits, extracting actionable knowledge from data is difficult. Observations gathered in uncontrolled environments are often high-dimensional, complex and noisy; and even when controlled experiments are used, the intricate systems that underlie them --- like those from meteorology, chemistry, medicine and biology --- can yield data sets with highly nontrivial underlying topology. This refers to properties such as the number of disconnected pieces (i.e., clusters), the existence of holes or the orientability of the data space. The research funded through this CAREER award will leverage ideas from algebraic topology to address data science questions like visualization and representation of complex data sets, as well as the challenges posed by nontrivial topology when designing learning systems for prediction and classification. This work will be integrated into the educational program of the PI through the creation of an online TDA (Topological Data Analysis) academy, with the dual purpose of lowering the barrier of entry into the field for data scientists and academics, as well as increasing the representation of underserved communities in the field of computational mathematics. The project provides research training opportunities for graduate students.

Understanding the set of maps between topological spaces has led to rich and sophisticated mathematics, for it subsumes algebraic invariants like homotopy groups and generalized (co)homology theories. And while several data science questions are discrete versions of mapping space problems --- including nonlinear dimensionality reduction and supervised learning --- the corresponding theoretical and algorithm treatment is currently lacking. This CAREER award will contribute towards remedying this situation. The research program articulated here seeks to launch a novel research program addressing the theory and algorithms of how the underlying topology of a data set can be leveraged for data modeling (e.g., in dimensionality reduction) as well as when learning maps between complex data spaces (e.g., in supervised learning). This work will yield methodologies for the computation of topology-aware and robust multiscale coordinatizations for data via classifying spaces, a computational theory of topological obstructions to the robust extension of maps between data sets, as well as the introduction of modern deep learning paradigms in order to learn maps between non-Euclidean data sets.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405030","Collaborative Research: Algebraic K-theory and Equivariant Stable Homotopy Theory: Applications to Geometry and Arithmetic","DMS","TOPOLOGY","08/01/2024","05/14/2024","Michael Mandell","IN","Indiana University","Continuing Grant","Swatee Naik","07/31/2027","$69,737.00","","mmandell@indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","126700","","$0.00","Algebraic topology began as the study of those algebraic invariants of geometric objects which are preserved under certain smooth deformations. Gradually, it was realized that the algebraic invariants called cohomology theories could themselves be represented by geometric objects, known as spectra. A central triumph of modern homotopy theory has been the construction of categories of ring spectra (representing objects for multiplicative cohomology theories) which are suitable for performing constructions directly analogous to those of classical algebra. This move has turned out to be incredibly fruitful, both by providing invariants which shed new light on old questions as well as by raising new questions which have unexpected connections to other areas of mathematics and physics. This research proposal studies such constructions in algebraic K-theory, the newly emerging field of Floer homotopy theory, and the foundations of equivariant stable homotopy theory. Broader impacts include workforce development in the form of graduate student advising, undergraduate and postdoc mentorship, high school mathematical science project mentorship, conference organization, and development of new education and training programs.

This proposal describes a broad research program to study a wide variety of problems in homotopy theory, geometry, and arithmetic. The PIs' prior work gives a complete description of the homotopy groups of algebraic K-theory of the sphere spectral at odd primes and a canonical identification of the fiber of the cyclotomic trace via a spectral lift of Tate-Poitou duality. In this proposal, the PIs describe a vast expansion of that argument to study the fiber of the cyclotomic trace on more general rings and schemes over algebraic p-integers in number fields and a related K-theory question more generally for other kinds of Artin duality. The prior work also leads to a new approach to the Kummer-Vandiver conjecture based on Bökstedt-Hsiang-Madsen's geometric Soule embedding that the PIs propose to study. The PIs' recent work with Yuan established a theory of topological cyclic homology (TC) relative to MU-algebras, where there are many interesting computations to explore. Prior work of PI Blumberg with Abouzaid building a Morava K-theory Floer homotopy type has opened new lines of research in Floer homotopy theory; this already has been used to resolve old conjectures in symplectic geometry. The PIs propose to extend this construction to its natural generality, building the homotopy type over MUP and KU and rigidifying the multiplication. They propose to obtain spectral models of deformed operations on quantum cohomology (i.e., quantum Steenrod operations). This work will have myriad applications in symplectic geometry and potentially have transformative impact on the Floer homotopy theory program. The PIs propose to resolve the longstanding confusion about the role of multiplicative norm maps in equivariant stable homotopy theory for positive dimensional compact Lie groups. This requires a new foundation for factorization homology and will lead to genuine equivariant factorization homology for positive dimensional compact Lie groups. In prior work, the PIs identified previously unknown multiplicative transfers on geometric fixed points of G-commutative ring spectra. The PIs propose to study how these fit into the foundations of G-symmetric monoidal categories; a first step is to establish new multiplicative splittings that have the feel of multiplicative versions of the tom Dieck splitting.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -15,22 +18,19 @@ "2349814","Algebraic and Syntactic Invariants for Homeomorphism Groups of Manifolds","DMS","TOPOLOGY","09/01/2024","05/01/2024","Thomas Koberda","VA","University of Virginia Main Campus","Continuing Grant","Eriko Hironaka","08/31/2027","$150,756.00","","tmk5a@virginia.edu","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126700","","$0.00","The PI will investigate fundamental problems in geometry and topology, applying ideas from mathematical logic. The research will introduce new tools for studying manifolds, which are central objects in mathematics and physics, and will shed light on some basic unanswered questions about manifolds while simultaneously building bridges between topology and logic. Beyond the scientific investigation and attendant international collaborations, the PI will continue to promote access to education. Activities include organizing a Research Experiences for Undergraduates (REU) both in the United States and in Vietnam, with the goal of attracting global talent to US educational institutions and fostering academic pipelines between Vietnam and the US. The PI will also engage in initiatives to make higher mathematical education accessible to under-served populations within the US and will write a textbook making geometric group theory accessible to a wider range of students.

The PI's research involves synthesizing ideas from model theory and applying them to the theory of groups acting on compact manifolds. This work builds on a theory of critical regularity of group actions in one dimension, as developed by the PI and Kim, and on more recent results about first order rigidity of homeomorphism groups of manifolds. One motivating goal is to prove the existence of finitely generated groups with prescribed critical regularities for compact manifolds of dimension two and higher. The methods to be applied here are two-fold: one is dynamical, concerning smooth group actions on manifolds, which has for example been successfully applied to finding groups of critical regularity 1 acting on compact two-manifolds. The second is to understand the interplay between mathematical logic and homeomorphism groups of compact manifolds, in particular the expressivity of first order logic in homeomorphism and diffeomorphism groups, and in countable groups that are elementarily equivalent to homeomorphism and diffeomorphism groups of manifolds. Potential payoffs include examples of torsion-free countable groups that cannot act on given compact manifolds, insight into the smooth Poincare conjecture, and potentially a proof that Gromov random groups cannot act nontrivially on compact 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." "2407438","Problems in Non-Positive Curvature","DMS","TOPOLOGY","05/01/2024","05/01/2024","Jean-Francois Lafont","OH","Ohio State University","Standard Grant","Eriko Hironaka","04/30/2027","$332,834.00","","jlafont@math.ohio-state.edu","1960 KENNY RD","COLUMBUS","OH","432101016","6146888735","MPS","126700","","$0.00","Geometry is concerned with quantitative features of a space, while topology studies qualitative aspects of a space. As an example, a teacup and a donut are topologically the same (they both have a single hole), but geometrically different. Non-positive curvature is a geometric property of spaces, which roughly corresponds to the space being expansive at every point and in every direction. Spaces with this property are pervasive, both in mathematics and in nature. As a result, there are numerous different viewpoints and approaches to their study. This proposal is focused on a variety of problems that are loosely centered around non-positively curved spaces. The approaches are highly interdisciplinary, drawing on tools and techniques from various distinct areas of mathematics. This project also provides opportunities for graduate student and postdoc research and training.


The Principal Investigator (PI) will work on various projects in non-positive curvature that fall into four broad categories. (1) Projects on Coxeter groups: the PI will construct high-dimensional right-angled Coxeter groups that virtually algebraically fiber, will construct some new examples of negatively curved manifolds that fiber over the circle, and will construct new Davis manifolds that are CAT(0) but do not support Riemannian non-positive curvature smoothing. (2) Projects on simplicial volume: the PI will study which 4-dimensional Davis manifolds have positive simplicial volume, and will study how Anasov diffeomorphims constrain the simplicial volume. (3) Construtions of new aspherical manifolds: the PI will construct some new non-arithmetic hyperbolic manifolds, some new negatively curved Riemannian manifolds, and will study the commensurability problem for these manifolds. (4) Geodesic flows: the PI will study the decay of correlations for geodesic flows on locally CAT(-1) spaces, and will construct a version of the Sinai-Ruelle-Bowen measures for these 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." "2403798","Motivic to C2-Equivariant Homotopy and Beyond","DMS","TOPOLOGY, EPSCoR Co-Funding","08/15/2024","04/26/2024","Bertrand Guillou","KY","University of Kentucky Research Foundation","Standard Grant","Eriko Hironaka","07/31/2027","$245,299.00","","bertguillou@uky.edu","500 S LIMESTONE","LEXINGTON","KY","405260001","8592579420","MPS","126700, 915000","9150","$0.00","The problem of classifying mappings of a high-dimensional sphere onto a sphere of lower dimension is a central problem in algebraic topology and has repercussions in geometry and physics. The PI will focus on the context of mappings that preserve special symmetries of the spheres. The research will use recent theoretical developments to advance computational knowledge in this area. This research will be integrated with mentoring activities in the electronic Computational Homotopy Theory (eCHT) community and will be involved in recruiting for activities run by eCHT such as seminars, courses, and networking events for graduate students and postdocs. As an online community, the eCHT increases access to the research community, for example for people with geographical restrictions as well as for those with physical disabilities.

The PI and collaborators will leverage motivic/synthetic homotopy theory to perform computations of equivariant stable homotopy groups for the (cyclic) group of order 2, the Klein four group, and the quaternion group of order 8. The main tools to be used are the Bockstein, Adams, and slice spectral sequences. Various techniques will be employed to run these spectral sequences, including the use of Massey products. The PI and collaborators will also work to establish the height 1 Telescope Conjecture in the R-motivic and cyclic-2-equivariant settings, giving a description of certain periodic elements in the corresponding stable homotopy groups.

This project is jointly funded by the Topology & Geometric Analysis 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." -"2422651","Topology Students Workshop","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","02/15/2024","02/27/2024","Dan Margalit","TN","Vanderbilt University","Standard Grant","Swatee Naik","12/31/2024","$4,293.00","","dan.margalit@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126000, 126700","7556","$0.00","The Topology Students Workshop (TSW) will be held at Georgia Institute of Technology during June 6-10, 2022. This conference is a 5-day research and professional development workshop for graduate students in the fields of geometric group theory, geometry, and topology. Its primary goals are to a) expose graduate students to a wide range of current research in topology, b) build their communication, networking, and problem-sharing skills, and c) give guidance on necessary but typically untaught aspects of the profession. Approximately 50 graduate students will participate, guided by 10 mentors, who come from a wide range of career stages and represent a broad array of topics within geometry and topology including contact and symplectic topology, 3-manifolds, hyperbolic geometry, group actions, and complex dynamics. The conference provides the participants, especially those from underrepresented groups, with many tools that will help them to succeed as scientists at the highest levels, in graduate school and beyond.

For many of the students, the TSW is the first conference they attend and at which they present their own results. The workshop is designed to facilitate this experience (for instance, our first professional development session is an introduction to conferences and how best to benefit from them). The goal is to build confidence and research potential among students, as well as to build community. The skills addressed here are not typically taught in grad school and can be disproportionately beneficial to students from minority groups, as indicated from responses from participants in previous iterations of the program. The professional development and research sides of the workshop run in tandem, with mentors giving guidance in both areas. The workshop includes structured sessions on networking and etiquette, the job application process, communication skills, and a panel discussion on career paths (which also involves mathematicians from organizations such as NSA, Amazon, Google, and private high schools). Mentors also give research talks, both to model good communication and introduce their research areas (deliberately chosen broadly) and relevant problems to students who are embarking on a research career. Effective communication is a major theme: two evening sessions are devoted to workshopping presentations in small groups; the final presentations are videotaped and critiqued by those in attendance. The web site for the conference is http://tsw.gatech.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." "2403817","Conference: 38th Summer Conference on Topology and Its Applications","DMS","TOPOLOGY, FOUNDATIONS","07/01/2024","04/23/2024","Will Brian","NC","University of North Carolina at Charlotte","Standard Grant","Qun Li","06/30/2025","$30,000.00","","wbrian.math@gmail.com","9201 UNIVERSITY CITY BLVD","CHARLOTTE","NC","282230001","7046871888","MPS","126700, 126800","7556","$0.00","This project supports the 38th annual Summer Topology Conference, hosted at the University of Coimbra in Coimbra, Portugal, July 8-12, 2024. This international conference encourages participation from a broad spectrum of mathematicians at different career levels and diverse backgrounds, and implements a recruitment strategy that starts with establishing a diverse cohort of session organizers. Elements of the conference provide pathways to include mathematicians into the community of topology research, such as dissemination of results through the conference affiliated journal Topology Proceedings. The funds from this grant will be used to support the participation of researchers based in the US, who wish to attend the conference but otherwise lack the funds to do so.

The conference will feature six special sessions: Set-theoretic Topology, Topological Methods in Algebra and Analysis, Topological Dynamics and Continuum Theory, Topology and Categories, Topology in Logic and Computer Science, and Topology and Order. There will be seven plenary lectures, as well as six semi-plenary lectures, one for each section. The extra plenary lecture will be delivered, per tradition, by this year's winner of the Mary Ellen Rudin Young Researcher Award. The primary goal of the conferences is to disseminate and discuss new discoveries in topology from the past few years, and to facilitate collaboration among those able to attend. Further information about the conference can be found at https://www.mat.uc.pt/~sumtopo/.

This award reflects 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." "2350370","Conference: CMND 2024 program: Field Theory and Topology","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","05/01/2024","01/18/2024","Pavel Mnev","IN","University of Notre Dame","Standard Grant","Qun Li","04/30/2025","$39,360.00","Stephan Stolz, Christopher Schommer-Pries","Pavel.N.Mnev.1@nd.edu","836 GRACE HALL","NOTRE DAME","IN","465566031","5746317432","MPS","126000, 126700","7556","$0.00","The program ?Field theory and topology? to be held at the Center for Mathematics at Notre Dame (CMND), June 3?21, 2024 will continue the line of CMND summer programs and consists of a graduate/postdoctoral summer school, a conference, and an undergraduate summer school. The program will expose a new generation of undergraduates and early-career researchers to the new ideas, developments, and open problems in the exciting meeting place between topology and quantum field theory where many surprising advances were made recently.

There is a rich interplay between quantum field theory and topology. The program ?Field theory and Topology? will focus on recent extraordinary developments in this interplay -- new invariants of manifolds and knots coming from field-theoretic constructions; new languages and paradigms for field theory coming from interaction with topology: functorial field theory, cohomological (Batalin-Vilkovisky) approach, approach via derived geometry and via factorization algebras. Among subjects discussed at the program will also be supersymmetric and extended topological field theories, holomorphic twists. Webpage of the event: https://sites.nd.edu/2024cmndthematicprogram/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349810","Conference: Richmond Geometry Meeting: Geometric Topology and Moduli","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","05/01/2024","12/07/2023","Nicola Tarasca","VA","Virginia Commonwealth University","Standard Grant","Qun Li","10/31/2025","$26,430.00","Marco Aldi, Allison Moore","tarascan@vcu.edu","910 WEST FRANKLIN ST","RICHMOND","VA","232849005","8048286772","MPS","126400, 126700","7556","$0.00","This award supports the Richmond Geometry Meeting: Geometric Topology and Moduli scheduled for August 9-11, 2024, hosted at Virginia Commonwealth University in Richmond, VA. The conference is designed to unite experts in low-dimensional topology and algebraic geometry, spanning diverse career stages and affiliations. Beyond lectures delivered by internationally recognized experts, vertically integrated participation will be fostered by a poster session showcasing the contributions of early-career researchers and a Career and Mentorship Panel.

The conference will investigate the intersection of low-dimensional topology, algebraic geometry, and mathematical physics. The roots of this interdisciplinary exploration trace back to Witten's groundbreaking work in the late 1980s and the emergence of the Jones polynomial in Chern-Simons theory. Since then, a landscape of profound connections between knot theory, moduli spaces, and string theory has emerged, due to the collective efforts of generations of mathematicians and physicists. Noteworthy developments include the deep ties between Heegaard Floer homology and the Fukaya category of surfaces, the intricate interplay revealed by Khovanov homology, and the correspondence of Gromov-Witten and Donaldson-Thomas theories. The study of moduli spaces of curves, as exemplified in Heegaard Floer homology, has played a pivotal role in several developments. The preceding three editions of the Richmond Geometry Meeting, encompassing both virtual and in-person gatherings, have showcased a wave of collaborative advancements in knot theory, algebraic geometry, and string theory. Topics such as braid varieties, Khovanov homotopy, link lattice homology, and the GW/DT correspondence in families have been explored, unveiling a nexus of interdependent breakthroughs. This award supports the fourth edition of the Richmond Geometry Meeting, providing a vital platform for the dissemination of the latest findings in this dynamic realm of research. For more information, please visit the Richmond Geometry Meeting website: https://math.vcu.edu/rgm

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348932","Conference: The 2024 Graduate Student Topology and Geometry Conference","DMS","TOPOLOGY","03/01/2024","12/04/2023","Teena Gerhardt","MI","Michigan State University","Standard Grant","Qun Li","02/28/2025","$29,996.00","Matthew Hedden","teena@math.msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","126700","7556","$0.00","This award supports the 21st annual Graduate Student Topology and Geometry Conference, to
be held at Michigan State University from April 12-14, 2024. This conference is specifically
aimed at graduate students, with many of the talks delivered by student participants. The
conference will bring together students in different stages of their graduate studies, and will
provide a venue for students from a diverse collection of institutions and geographic regions to
come together and interact. It aims to create a highly collaborative and inclusive environment
that will stimulate research and foster lasting connections between researchers at particularly
crucial moments early in their careers. The conference will also provide a venue for students to
hear about cutting edge research from established senior leaders and early-career faculty.

A principal goal for this conference is to give graduate students the opportunity to present their
research. The majority of the talks at the conference will be given by students, and there will
also be a poster session where students can present their work. Graduate students will learn
about the current frontiers of research in geometry and topology, within an inclusive and
welcoming community of scholars. Talks will range across many active subfields of topology
and geometry. There will be plenary talks by Julie Bergner (University of Virginia), Ciprian
Manolescu (Stanford University), and Gabor Szekelyhidi (Northwestern University), as well as
talks by early-career faculty members Carolyn Abbott (Brandeis University), Anthony Conway
(University of Texas at Austin), Colleen Delaney (University of California, Berkeley), Antoine
Song (California Institute of Technology), Iris Yoon (Wesleyan University), and Allen Yuan
(Institute for Advanced Study/Northwestern University). These faculty talks will also provide the
opportunity for early-career researchers to engage with experts outside of their home institution,
expanding their network of mathematical scientists. The conference URL is
https://sites.google.com/view/gstgc2024msu/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." "2405405","Algebraic Structures in String Topology","DMS","TOPOLOGY","07/01/2024","03/22/2024","Manuel Rivera","IN","Purdue University","Standard Grant","Eriko Hironaka","06/30/2027","$288,912.00","","river227@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126700","","$0.00","The goal of this project is to understand the general structure of string interactions in a background space, its significance in geometry and mathematical physics, and to carry out explicit computations using algebraic models. Interactions of strings, paths, and loops are ubiquitous throughout mathematics and science. These range from observable phenomena in fluid dynamics (vortex rings in a fluid coming together to become a new ring or self-intersecting and breaking apart into multiple rings) to patterns arising in areas of theoretical physics such as string theory and quantum field theory. String topology proposes a mathematical model to study these interactions in terms of operations defined by intersecting, reconnecting, and cutting strings (closed curves) evolving in time in a manifold. Giving a rigorous and complete description of the structure of string topology, which is one of the aims of the proposed project, will also provide solid foundations for physical theories. Furthermore, the physicially inspired theory of string topology turns out to inform theoretical questions in mathematics: probing a space through strings and studying how all possible interactions are organized also reveals intricate aspects of the background geometry. Building upon previous work of the PI, the project proposes to algebraicize string topology through tractable models obtained by decomposing, or discretizing, the underlying space into cells and using techniques from algebraic topology and homological algebra, two well developed active fields of pure mathematics. These models will be applicable to study a wide range of string interaction phenomena appearing in both pure and applied mathematics as well as in theoretical physics. The proposed project includes a broad educational component focused on fostering mathematical activity and access at multiple levels. This involves graduate student training, organization of summer workshops and conferences that bring together researchers from a wide variety of fields, and the support of periodic seminars at the PI?s institution.

In more technical detail, this project aims to study chain-level string topology with a focus on operations that are sensitive to geometric structure beyond the homotopy type of the underlying manifold. In particular, the PI proposes to construct a homotopy coherent structure lifting the Goresky-Hingston loop coalgebra (and its S^1-symmetric Lie cobracket version) originally defined on the homology of the space of free loops on a manifold relative to the constant loops. The construction of such structure will use an appropriate refinement of Poincaré duality and intersection theory at the level of chains on a finely triangulated manifold together with the theory of algebraic models for loop spaces of non-simply connected manifolds developed in previous work of the PI using techniques from Hochschild homology theory and Koszul duality theory. These models will be transparent enough to reveal the precise geometric ingredients that are necessary to construct a coherent hierarchy of higher structures for string topology. This hierarchy of chain-level operations will provide a rich source of computable and potentially new manifold invariants. Connections with symplectic geometry, homological mirror symmetry, and the theory of quantization will be explored.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348686","Conference: UnKnot V","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","06/01/2024","03/12/2024","Allison Henrich","WA","Seattle University","Standard Grant","Qun Li","11/30/2024","$40,000.00","Colin Adams, Elizabeth Denne","henricha@seattleu.edu","901 12TH AVE","SEATTLE","WA","981224411","2062966161","MPS","126000, 126700","7556","$0.00","The UnKnot V Conference will be held at Seattle University in Seattle, WA on July 13-14th, 2024. UnKnot V, like the four undergraduate knot theory conferences that preceded it, will be a gathering of students who are interested in knot theory research together with their faculty and graduate student mentors. Participants who are new to knot theory and interested to learn more are also welcome to join in this community-building event. Accessible talks at UnKnot V will be given by world-renowned knot theory experts as well as students who are just beginning their work in this field. UnKnot V will also feature a mini workshop on using machine learning in knot theory research and one on recreational topology with the aim to inspire fun math outreach projects.

Knot theory is an area of research which uses tools from and gives insight into many areas of mathematics, including topology, geometry, algebra, and combinatorics. There are important applications in knot theory to DNA knotting, synthetic chemistry, protein folding, and quantum computing as well as in anthropology, art, and materials science. Knot theory also lends itself to research by undergraduates since there are open problems that can be easily stated and explained but lead to mathematics with great depth. The focus of UnKnot V will be on research that has been done by undergraduates and on open problems amenable to research by students. Since experts will be brought together with the students and faculty who would like to do research in this field, this unique conference structure will allow for vertical integration from undergraduates and graduate students to faculty who are interested in mentoring students in knot theory research and experts in the field. Many opportunities for research projects will be presented. The conference webpage is: https://sites.google.com/view/unknot-v-conference/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." -"2342119","Conference: Riverside Workshop on Geometric Group Theory 2024","DMS","TOPOLOGY","04/01/2024","12/04/2023","Matthew Durham","CA","University of California-Riverside","Standard Grant","Qun Li","03/31/2025","$30,000.00","Thomas Koberda","mdurham@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","126700","7556","$0.00","This award provides funding for the second Riverside Workshop on Geometric Group Theory, which is to be held May 3-6, 2024, at the University of California Riverside. This workshop will feature three minicourses given by early-career mathematicians working in the field of geometric group theory. This is an active area of research lying at the interface of geometry, algebra, and dynamical systems, with many applications especially to low-dimensional topology, and which has seen many break-through results over the past decades. The topic of each minicourse will be a cutting-edge technique or idea developed by the speaker, with an audience of graduate students and postdocs in mind. Each speaker will also produce an expository paper on the topic of their minicourse, and these papers will be compiled into a book, mirroring the 2023 version of the activity.

Much of the machinery in geometric group theory is highly technical, and so graduate students looking to enter the field will benefit from careful exposition of the big ideas of the field in lecture series that elaborate extensively on background and examples. The invited minicourse speakers are: Abdalrazzaq Zalloum (University of Toronto), who will speak on the geometry of CAT(0) and injective spaces; Emily Stark (Wesleyan University), who will speak on boundaries of groups; and Inhyeok Choi (Korea Institute for Advanced Study), who will speak on random walks on groups and their applications. The website of the workshop is https://sites.google.com/view/rivggt24/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." "2348830","Conference: 57th Spring Topology and Dynamical Systems Conference","DMS","TOPOLOGY, FOUNDATIONS","02/15/2024","02/13/2024","Will Brian","NC","University of North Carolina at Charlotte","Standard Grant","Eriko Hironaka","01/31/2025","$33,000.00","Hector Barriga-Acosta","wbrian.math@gmail.com","9201 UNIVERSITY CITY BLVD","CHARLOTTE","NC","282230001","7046871888","MPS","126700, 126800","7556","$0.00","This proposal supports the 57th annual Spring Topology and Dynamical Systems conference (STDC), hosted this year at the University of North Carolina at Charlotte. The conference encourages participation from a broad spectrum of mathematicians at different career levels and diverse backgrounds and implements a recruitment strategy that starts with establishing a diverse cohort of session organizers. Elements of the conference include providing pathways to including mathematicians into the community, such as dissemination of results through the conference affiliated journal Topology Proceedings. Conference funds will be used to support graduate students and early career participants, as well as established mathematicians without other sources of travel support and invited speakers.

The 57th STDC will be the latest in an annual series that began in 1967 and will continue its tradition of bringing together researcher from the around the world and from a range of currently active areas of topology. Over the years, the conference has structured itself around a core of special sessions representing strands of topology-related fields of interest. The 57th STDC will feature sessions focused on Continuum Theory, Dynamical Systems, Geometric Group Theory, Geometric Topology, and Set-Theoretic Topology. More information about the conference is available at: https://pages.charlotte.edu/stdc2024/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2340239","CAREER: Elliptic cohomology and quantum field theory","DMS","TOPOLOGY","06/15/2024","01/10/2024","Daniel Berwick Evans","IL","University of Illinois at Urbana-Champaign","Continuing Grant","Eriko Hironaka","05/31/2029","$73,192.00","","danbe@illinois.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","126700","1045","$0.00","The research of this award lies at the interface between theoretical physics and geometry. An unsolved conjecture posits a deep connection between the geometry of supersymmetric quantum field theories and certain structures in algebraic topology. Resolving this conjecture would provide new insight into the mathematical foundations of quantum field theory, while also providing several long-anticipated applications of algebraic topology in physics. The projects the PI will work on leverage higher categorical symmetries to gain new insights into this 30-year-old conjecture. The award supports graduate students working with the PI whose research will contribute to this area. The PI will also continue his involvement in mathematics education for incarcerated people through the Education Justice Project in Illinois.

The proposed research is centered on an equivariant refinement of Stolz and Teichner?s conjectured geometric model for elliptic cohomology from 2-dimensional supersymmetric field theories. The overarching goal is to link structures in Lurie?s 2-equivariant elliptic cohomology with the geometry of supersymmetric gauge theories. Some of the projects are natural extensions of prior work at heights zero and one, focusing on height 2 generalizations of specific quantum field theories that are expected to construct elliptic Thom classes. Other projects will initiate the study of 2-equivariant geometry, interfacing with topics in string geometry, loop group representation theory, and elliptic power operations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348686","Conference: UnKnot V","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","06/01/2024","03/12/2024","Allison Henrich","WA","Seattle University","Standard Grant","Qun Li","11/30/2024","$40,000.00","Colin Adams, Elizabeth Denne","henricha@seattleu.edu","901 12TH AVE","SEATTLE","WA","981224411","2062966161","MPS","126000, 126700","7556","$0.00","The UnKnot V Conference will be held at Seattle University in Seattle, WA on July 13-14th, 2024. UnKnot V, like the four undergraduate knot theory conferences that preceded it, will be a gathering of students who are interested in knot theory research together with their faculty and graduate student mentors. Participants who are new to knot theory and interested to learn more are also welcome to join in this community-building event. Accessible talks at UnKnot V will be given by world-renowned knot theory experts as well as students who are just beginning their work in this field. UnKnot V will also feature a mini workshop on using machine learning in knot theory research and one on recreational topology with the aim to inspire fun math outreach projects.

Knot theory is an area of research which uses tools from and gives insight into many areas of mathematics, including topology, geometry, algebra, and combinatorics. There are important applications in knot theory to DNA knotting, synthetic chemistry, protein folding, and quantum computing as well as in anthropology, art, and materials science. Knot theory also lends itself to research by undergraduates since there are open problems that can be easily stated and explained but lead to mathematics with great depth. The focus of UnKnot V will be on research that has been done by undergraduates and on open problems amenable to research by students. Since experts will be brought together with the students and faculty who would like to do research in this field, this unique conference structure will allow for vertical integration from undergraduates and graduate students to faculty who are interested in mentoring students in knot theory research and experts in the field. Many opportunities for research projects will be presented. The conference webpage is: https://sites.google.com/view/unknot-v-conference/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." +"2342119","Conference: Riverside Workshop on Geometric Group Theory 2024","DMS","TOPOLOGY","04/01/2024","12/04/2023","Matthew Durham","CA","University of California-Riverside","Standard Grant","Qun Li","03/31/2025","$30,000.00","Thomas Koberda","mdurham@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","126700","7556","$0.00","This award provides funding for the second Riverside Workshop on Geometric Group Theory, which is to be held May 3-6, 2024, at the University of California Riverside. This workshop will feature three minicourses given by early-career mathematicians working in the field of geometric group theory. This is an active area of research lying at the interface of geometry, algebra, and dynamical systems, with many applications especially to low-dimensional topology, and which has seen many break-through results over the past decades. The topic of each minicourse will be a cutting-edge technique or idea developed by the speaker, with an audience of graduate students and postdocs in mind. Each speaker will also produce an expository paper on the topic of their minicourse, and these papers will be compiled into a book, mirroring the 2023 version of the activity.

Much of the machinery in geometric group theory is highly technical, and so graduate students looking to enter the field will benefit from careful exposition of the big ideas of the field in lecture series that elaborate extensively on background and examples. The invited minicourse speakers are: Abdalrazzaq Zalloum (University of Toronto), who will speak on the geometry of CAT(0) and injective spaces; Emily Stark (Wesleyan University), who will speak on boundaries of groups; and Inhyeok Choi (Korea Institute for Advanced Study), who will speak on random walks on groups and their applications. The website of the workshop is https://sites.google.com/view/rivggt24/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." "2405191","A1-Homotopy Theory and Applications to Enumerative Geometry and Number Theory","DMS","TOPOLOGY","06/01/2024","02/26/2024","Kirsten Wickelgren","NC","Duke University","Standard Grant","Eriko Hironaka","05/31/2027","$405,500.00","","kirsten.wickelgren@duke.edu","2200 W MAIN ST","DURHAM","NC","277054640","9196843030","MPS","126700","","$0.00","This award supports a research program involving an enriched form of counting to study the solutions of equations and the spaces they form. It matters if the solution to a set of equations can be expressed using the usual counting numbers, or if real numbers are required, or if one must use imaginary numbers. The enriched count detects such differences. In some cases, it is closely connected to the number of holes of dimension d in the shape of a space of real solutions to the equations. This project exploits the power of the enriched count, exposing potential applications in number theory and algebraic geometry. The award will also support a pipeline for a strong and diverse mathematical workforce. This will involve a continuing program of week-long summer math jobs for gifted high school students from diverse backgrounds. During this program, the PI will facilitate collaborative projects with high school student and teachers, providing background material as necessary. Graduates from the summer program will be encouraged to continue on to a Research Experience for Undergraduates that will provide further mathematical training and research mentorship.

The proposed research studies number-theoretic and algebro-geometric questions using cohomology theories and homotopical methods in the framework of Morel and Voevodsky's A1-homotopy theory. The project uses stable A1-homotopy theory to produce results in enumerative geometry over non-algebraically closed fields and rings of integers. New Gromov--Witten invariants defined over general fields have the potential to satisfy wall-crossing formulas, surgery formulas, and WDVV equations. For this, the project studies notions of spin over general fields. The Weil conjectures connect the number of solutions to equations over finite fields to the topology of their complex points: The zeta function of a variety over a finite field is simultaneously a generating function for the number of solutions to its defining equations and a product of characteristic polynomials of endomorphisms of cohomology groups. The ranks of these cohomology groups are the Betti numbers of the associated complex manifold. The logarithmic derivative of the zeta function is enriched to a power series with coefficients in the Grothendieck--Witt group, producing a connection with the associated real manifold. This project aims to increase our control over this logarithmic derivative of the zeta function 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." "2339110","CAREER: Rigidity in Mapping class groups and homeomorphism groups","DMS","TOPOLOGY","08/01/2024","01/10/2024","Lei Chen","MD","University of Maryland, College Park","Continuing Grant","Qun Li","07/31/2029","$95,422.00","","chenlei1991919@gmail.com","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","126700","1045","$0.00","In geometry and topology, one of the most fundamental objects is to study various geometric groups and their features. This project will investigate the rigidity problems concerning mapping class groups and homeomorphism groups of manifolds. The PI will use methods from dynamical systems, geometric group theory, low dimensional topology, and differential geometry. The educational activities include high school outreach, undergraduates research through REU projects, mentoring graduate students in the home institution, and workshops organizations.

Symmetry is a pervasive concept in mathematics. In the study of differential topology, the full symmetry group is the diffeomorphism group of a manifold. There are two sides of a diffeomorphism group: one is the mapping class group, the group of connected components of a diffeomorphism group; the other is the identity component of a diffeomorphism group, which is a connected topological group. The PI will study these groups using both geometric group theory through the study of how those groups act on certain complexes and dynamical tools through the study of how those groups act on other 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." "2350344","Collaborative Research: Conference: Trisections Workshops: Connections with Knotted Surfaces and Diffeomorphisms","DMS","TOPOLOGY","05/01/2024","02/13/2024","Maggie Miller","TX","University of Texas at Austin","Standard Grant","Eriko Hironaka","04/30/2026","$49,382.00","","maggie.miller@utexas.edu","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","126700","7556","$0.00","This proposal will fund the ?Trisections Workshop: Connections with Knotted Surfaces,? which will take place at the University of Nebraska-Lincoln from June 24-28, 2024, and the ?Trisections Workshop: Connections with Diffeomorphisms,? which will take place at the University of Texas at Austin during one week in the summer of 2025. Workshop attendees will include established experts, early-career researchers, and students, and the program will actively engage all participants. Each morning will feature plenary talks by experts and/or lightning talks highlighting the work of junior researchers. The afternoons will be devoted to working in groups on open problems. This series of regular workshops has been critical to the development of an enthusiastic community of researchers in low-dimensional topology, helping this new and growing area gain momentum and fostering numerous collaborations across career stages and demographics. The organizers take pride in the camaraderie and welcoming atmosphere they strive to create, and many in the community deeply value and appreciate these events.

A trisection splits a 4-dimensional space into three simple pieces. Since their introduction roughly a decade ago, trisections have proven to be a successful new tool with which to study smooth 4-manifolds, with numerous articles written in the interim to develop the foundations for trisection theory. An important strength of the theory of trisections is the way it interfaces with a variety of other topics in low-dimensional topology. This interface provides an opportunity to explore many classical areas of 4-manifold topology through a new lens. Such areas include, for example, the study of knotted surfaces in 4-space, diffeomorphisms of 4-manifolds, exotic smooth structures, group actions and (branched) covering spaces, and symplectic structures. The main goal of these workshops is to bring together researchers from multiple areas to propose and to work on open problems, with a particular focus on the inclusion of early career researchers. The workshops are preceded by a series of introductory virtual pre-workshop talks, which serve to bring new researchers up to speed, to facilitate the work to be done in groups, and to incorporate a broader, worldwide audience. The website for the 2024 workshop can be found here: https://sites.google.com/view/tw2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2341204","Conference: Midwest Topology Seminar","DMS","TOPOLOGY","02/01/2024","01/19/2024","Mark Behrens","IN","University of Notre Dame","Standard Grant","Eriko Hironaka","01/31/2025","$49,500.00","Vesna Stojanoska, Carmen Rovi, Manuel Rivera, Daniel Isaksen","mbehren1@nd.edu","836 GRACE HALL","NOTRE DAME","IN","465566031","5746317432","MPS","126700","7556","$0.00","This NSF award supports the Midwest Topology Seminar, from 2023 to 2026, a continuation of a previously supported regional conference series in algebraic topology that meets three times per year and rotates between universities in the Midwest and Great Lakes areas. The next two meetings are at Loyola University (March 2024) and Indiana University (Spring 2024). The Midwest Topology Seminar has been running continuously since the early 1970s, with at least one of the yearly meetings held in Chicago, the hub of the network, and is a long-standing, reliable, low-key, and low-cost way for participants to keep up with the field. The audiences are always large and diversified, drawing faculty and graduate students from a broad range of institutions. The Midwest Topology Seminar serves as a nexus for a vibrant community of research mathematicians, optimizing the distribution of new ideas through the field, especially among early career research mathematicians and mathematicians away from the traditional centers of research.

The Midwest is a traditional and continuing center of algebraic topology; hence there is a strong source of local speakers. Programs are augmented with featured speakers from around the country. Algebraic topology has always been broadly construed to include homotopy theory, algebraic K-theory, geometric group theory, and high dimensional manifolds; more recently the series has explored connections to algebraic geometry, representation theory, number theory, low dimensional manifolds, and mathematical physics. Financial support will go to graduate students and research mathematicians with limited funds from other sources. The conference web site is http://www.rrb.wayne.edu/MTS/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2350343","Collaborative Research: Conference: Trisections Workshops: Connections with Knotted Surfaces and Diffeomorphisms","DMS","TOPOLOGY","05/01/2024","02/13/2024","Alexander Zupan","NE","University of Nebraska-Lincoln","Standard Grant","Eriko Hironaka","04/30/2026","$49,910.00","","zupan@unl.edu","2200 VINE ST","LINCOLN","NE","685032427","4024723171","MPS","126700","7556, 9150","$0.00","This proposal will fund the ?Trisections Workshop: Connections with Knotted Surfaces,? which will take place at the University of Nebraska-Lincoln from June 24-28, 2024, and the ?Trisections Workshop: Connections with Diffeomorphisms,? which will take place at the University of Texas at Austin during one week in the summer of 2025. Workshop attendees will include established experts, early-career researchers, and students, and the program will actively engage all participants. Each morning will feature plenary talks by experts and/or lightning talks highlighting the work of junior researchers. The afternoons will be devoted to working in groups on open problems. This series of regular workshops has been critical to the development of an enthusiastic community of researchers in low-dimensional topology, helping this new and growing area gain momentum and fostering numerous collaborations across career stages and demographics. The organizers take pride in the camaraderie and welcoming atmosphere they strive to create, and many in the community deeply value and appreciate these events.

A trisection splits a 4-dimensional space into three simple pieces. Since their introduction roughly a decade ago, trisections have proven to be a successful new tool with which to study smooth 4-manifolds, with numerous articles written in the interim to develop the foundations for trisection theory. An important strength of the theory of trisections is the way it interfaces with a variety of other topics in low-dimensional topology. This interface provides an opportunity to explore many classical areas of 4-manifold topology through a new lens. Such areas include, for example, the study of knotted surfaces in 4-space, diffeomorphisms of 4-manifolds, exotic smooth structures, group actions and (branched) covering spaces, and symplectic structures. The main goal of these workshops is to bring together researchers from multiple areas to propose and to work on open problems, with a particular focus on the inclusion of early career researchers. The workshops are preceded by a series of introductory virtual pre-workshop talks, which serve to bring new researchers up to speed, to facilitate the work to be done in groups, and to incorporate a broader, worldwide audience. The website for the 2024 workshop can be found here: https://sites.google.com/view/tw2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350250","Conference: Quantum Topology, Quantum Information and connections to Mathematical Physics","DMS","TOPOLOGY","05/01/2024","01/29/2024","Tian Yang","TX","Texas A&M University","Standard Grant","Eriko Hironaka","04/30/2025","$40,000.00","Sherry Gong, Zhizhang Xie, Michael Willis","tianyang@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126700","7556","$0.00","This award will provide financial support for a conference on Quantum Topology, Quantum Information, and Mathematical Physics, to be held from May 27 to 31, 2024, at Texas A&M University. The conference will bring together students and researchers interested in recent advances and new connections between the fields of quantum topology and quantum information theory and their applications to several branches of mathematics and physics, including low-dimensional topology, non-commutative geometry, operator algebra, representation theory, complexity theory, and quantum statistical physics. Participants will be split evenly between early career and established mathematicians, and the former group will receive priority for funding from this grant. Leading experts in the various topics will present the state of art in the subject in a way that is accessible to researchers at various career stages and emphasize new research directions and collaborations.

Quantum topology deals with interactions between low-dimensional topology, the theory of quantum groups, category theory, C*-algebra theory, gauge theory, conformal and topological field theory and statistical mechanics, while quantum information and computation theory brings together ideas from classical information theory, quantum mechanics and computer science and explores how the quantum mechanical properties of physical systems can be harnessed to achieve efficient data storage and transmission, and rapid computations. The interplay between these ideas and potential new advances and applications will be the main focus of the conference. More information can be found at the conference website: https://sites.google.com/tamu.edu/qtqimp/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." "2340341","CAREER: Large scale geometry and negative curvature","DMS","TOPOLOGY","09/01/2024","01/25/2024","Carolyn Abbott","MA","Brandeis University","Continuing Grant","Eriko Hironaka","08/31/2029","$113,427.00","","carolynabbott@brandeis.edu","415 SOUTH ST","WALTHAM","MA","024532728","7817362121","MPS","126700","1045","$0.00","The symmetries of a space and its relation to the underlying geometric structure of the space has led researchers to deep insights into the connections between algebraic and geometric structures. This project focuses on hyperbolic spaces and the coarse geometry their structure induces on their associated symmetry groups. The project activity also includes initiatives in teaching and mentoring mathematics students at all levels, with a focus on targeting students from under-represented populations both at the department and in the region.

The funded research has three main goals: to generalize notions of coarse negative curvature, particularly acylindrical hyperbolicity, to a broad class of topological groups; to establish a strong stability result for quotients of hierarchically hyperbolic groups, a class of groups which can be completely described by their actions on hyperbolic metric spaces; and to extend combinatorial methods from cubical groups to the larger class of CAT(0) groups, with a focus on aspects of negative curvature and boundaries. Parts of this research program will be incorporated into student projects as a way to expand access to undergraduate research at the PI?s institution.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349401","Conference: Combinatorial and Analytical methods in low-dimensional topology","DMS","TOPOLOGY","04/01/2024","01/10/2024","Francesco Lin","NY","Columbia University","Standard Grant","Eriko Hironaka","03/31/2026","$26,000.00","","fl2550@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126700","7556","$0.00","This NSF award will support the participation of U.S. based participants to the conference ?Combinatorial and Gauge theoretical methods in low-dimensional topology and geometry?, to be held at Centro di Ricerca Matematica Ennio De Giorgi in Pisa (Italy) in June 3-7, 2024. The conference will bring together experts in combinatorial and analytical techniques in low-dimensional topology with the aim of exploring new interactions between the two sets of tools. In particular, the grant will fund the participation of young researchers with the concrete goal of fostering new international collaborations.

The past few decades have seen a tremendous advancement in our understanding of low-dimensional topology, and several of the most original results have come to light when the tools from analysis and combinatorics are used in combination. The conference will explore new developments in topics at this interface such as: knot theory, braid groups, and mapping class groups; constructions and obstructions in 4-dimensional topology; classification questions in contact and symplectic geometry; singularity theory and its relation with Floer theory. More details can be found on the conference website: http://www.crm.sns.it/event/519/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -44,5 +44,4 @@ "2350113","Conference: Topology Students Workshop 2024","DMS","TOPOLOGY","04/01/2024","02/22/2024","Dan Margalit","TN","Vanderbilt University","Standard Grant","Swatee Naik","03/31/2025","$34,972.00","Rebecca Winarski, Caitlin Leverson","dan.margalit@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126700","7556","$0.00","This award provides support for the 7th biennial Topology Students Workshop (TSW) that will be held at Vanderbilt University during June 10-14, 2024. This is a five-day research and professional development activity for graduate students in the fields of geometric group theory, geometry, and topology, designed to expose graduate students to a wide range of current research, and to build their communication, networking, and problem-sharing skills. Approximately forty graduate students will participate, guided by ten mentors, who come from a wide range of career stages and research backgrounds within this field. The professional development and research sides of the workshop run in tandem, with mentors giving guidance in both areas. The workshop format devotes ample time for active networking and critiquing of research presentations.

The primary goals of TSW are to a) expose graduate students to a wide range of current research in topology, b) build their communication, networking, and problem-sharing skills, and c) give guidance on necessary but typically untaught aspects of the profession. The research portion covers a broad array of topics within geometry and topology including contact and symplectic topology, 3-manifolds, hyperbolic geometry, group actions, and complex dynamics. Professional development sessions include topics such as how best to benefit from conference participation and aim to build confidence and research potential among students. The workshop includes structured sessions on networking and etiquette, the job application process, communication skills, and a panel discussion on career paths that involves mathematicians from organizations such as NSA, Amazon, Google and private high schools. Mentors will also give research talks and suggest relevant problems to students who are embarking on a research career. The web site for the conference is http://www.danmargalit.net/tsw24.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350309","Conference: St. Louis Topology Conference: Flows and Foliations in 3-Manifolds","DMS","TOPOLOGY","04/01/2024","12/18/2023","Michael Landry","MO","Saint Louis University","Standard Grant","Swatee Naik","03/31/2025","$34,920.00","Rachel Roberts, Steven Frankel","michael.landry@slu.edu","221 N GRAND BLVD","SAINT LOUIS","MO","631032006","3149773925","MPS","126700","7556","$0.00","This award provides participant support for the St. Louis Topology Conference taking place May 17-19, 2024 in St. Louis, Missouri, USA. The theme of the conference is Flows and Foliations in 3-manifolds. The mathematical concept of a dynamical system allows for any continuously time-varying physical system to be considered within a uniform framework, as a ?state space? that organizes all possible instantaneous configurations, together with a ?flow? that describes the evolution of states with time. The conference is focused on the way that the geometry and topology of a space interacts with the kinds of dynamical systems that it supports, with an eye towards applications in dynamics, geometry, and topology. The organizers are committed to broad recruitment across a diverse set of students and postdoctoral researchers. In addition to hour-long lectures by established researchers, there will be lightning talks as well as a panel discussion on issues faced by early career mathematicians.

Flows and foliations in three dimensional manifolds can be fruitfully viewed through many lenses, as they stand at the intersection of dynamics, topology, and geometry. Interest in this general area has accelerated since Agol's resolution of the Virtual Fibering Conjecture, with researchers using a variety of tools and ideas such as (pseudo-) Anosov and partially hyperbolic flows, sutured manifold hierarchies, geometric group theory, contact geometry, Floer theory, veering triangulations, and the so-called big mapping class group to study a variety of questions. These include among others the L-space conjecture, the Cannon Conjecture, the Pseudo-Anosov Finiteness Conjecture, and the classification of infinite-type mapping classes. Recent conferences have tended to focus on small subsets of these topics and techniques, and there is a need for an event at which researchers with expertise in these different topics can meet and share their knowledge. Talks will take place at Washington University. The conference website is https://sites.google.com/view/stltc/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." "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." -"2414922","Stable Homotopy Theory in Algebra, Topology, and Geometry","DMS","TOPOLOGY","01/15/2024","01/23/2024","James Quigley","VA","University of Virginia Main Campus","Standard Grant","Christopher Stark","11/30/2025","$185,923.00","","jquigley1993@gmail.com","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126700","","$0.00","Stable homotopy theory was developed throughout the twentieth century to study high-dimensional topological spaces. Since spheres are the fundamental building blocks of topological spaces, the stable stems, which encode the possible relations between high-dimensional spheres up to continuous deformation, are a central object of study. Beyond topology, the stable stems have surprisingly broad applications throughout mathematics, ranging from geometric problems, such as classifying differentiable structures on spheres, to algebraic problems, such as classifying projective modules over rings. This project will explore further applications of stable homotopy theory in algebra, topology, and geometry. Broader impacts center on online community building. The PI will continue co-organizing the Electronic Computational Homotopy Theory Online Research Community, which aims to increase inclusion at the undergraduate, graduate, and senior levels by organizing undergraduate research opportunities, graduate courses, online seminars, mini-courses, and networking events. To address inequality at the K-12 level, the PI will develop and manage a program pairing undergraduates from his home institution with students from local after-school programs for online tutoring. This program would circumvent certain barriers to participation, such as lack of access to transportation and facilities, which are common in traditional outreach.

Specific research projects include the study of the stable stems and their applications in geometric topology, algebro-geometric analogues of the stable stems and their connections to number theory, and equivariant analogues of algebraic K-theory and their applications in algebra and geometry. More specifically, building on previous work, the PI will study the stable stems using topological modular forms and the Mahowald invariant, aiming to deduce the existence of exotic spheres in new dimensions. In a related direction, the PI will use the kq-resolution introduced in previous work to study the motivic stable stems, an algebro-geometric analogues of the stable stems. The main goal is to apply the kq-resolution to relate the motivic stable stems to arithmetic invariants like Hermitian K-theory. Real algebraic K-theory, which encodes classical invariants like algebraic K-theory, Hermitian K-theory, and L-theory, will also be studied using the trace methods developed in previous work. The overarching goal is extending results from algebraic K-theory to real algebraic K-theory, thereby obtaining results for Hermitian K-theory and L-theory that will have applications in algebra and 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." "2350374","Collaborative Research: Conference: Workshops in Geometric Topology","DMS","TOPOLOGY","05/01/2024","01/23/2024","Jack Calcut","OH","Oberlin College","Standard Grant","Swatee Naik","04/30/2027","$25,350.00","","jcalcut@oberlin.edu","173 W LORAIN ST","OBERLIN","OH","440741057","4407758461","MPS","126700","7556","$0.00","This award provides support for three meetings of a well-established series of summer Workshops in Geometric Topology, with the first to be held at Calvin University in Grand Rapids, MI, June 13-15, 2024. The award will also fund workshops at Oberlin College in 2025 and University of Wisconsin-Milwaukee in 2026. These workshops provide an annual opportunity for active researchers and graduate students in the mathematical field of geometric topology to interact in a setting that provides multiple tangible benefits, including:
1) attending the lectures of a principal speaker to receive an in-depth introduction to important current streams of research being performed by nationally-recognized experts,
2) learning about a breadth of other research activities by attending shorter talks given by the other workshop participants,
3) the opportunity to share their own work by giving talks in a congenial environment, and
4) important time for informal discussion and interaction among participants and with the principal speaker.
These workshops regularly feature participation and talks by members of underrepresented groups in mathematics, and, to further broaden the impact of the workshops, the talks of the principal speaker will be recorded and posted to the internet. The workshops also provide significant benefits to graduate students by providing a serious but informal research atmosphere in which they can meet and learn from others in the field. NSF funding will be used to cover the attendance costs of workshop participants.

More specifically, the workshops provide opportunities for geometric topologists to interact and share ideas, leading to research collaborations. Furthermore, the proposed workshops will continue the tradition of inviting each year a renowned principal speaker to provide a series of three lectures on a topic of his or her choice for the purpose of expanding the interests of the participants by having a nationally-recognized expert discuss an important area of current interest. The 2024 workshop will feature Professor Maggie Miller of the University of Texas -- Austin. The web site for this workshop will be https://sites.google.com/view/workshop2024/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."