From d5fd03c3f976a461f2cc11ec92ede2c41945e51f Mon Sep 17 00:00:00 2001 From: Yimin Zhong Date: Wed, 10 Apr 2024 06:33:40 +0000 Subject: [PATCH] Update Awards --- .../Awards-Algebra-and-Number-Theory-2024.csv | 5 ++++ Analysis/Awards-Analysis-2024.csv | 30 ++++++++++--------- Foundations/Awards-Foundations-2024.csv | 25 ++++++++-------- Topology/Awards-Topology-2024.csv | 19 ++++++------ 4 files changed, 44 insertions(+), 35 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 cfd9da0..32fc020 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 @@ -1,4 +1,6 @@ "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" +"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." "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." "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." @@ -15,6 +17,9 @@ "2401117","Arithmetic Structure in Dense Sets","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/04/2024","Sarah Peluse","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Andrew Pollington","05/31/2027","$117,039.00","","speluse@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126400","9251","$0.00","This project focuses primarily on three different problems in number theory, combinatorics, and ergodic theory. This includes work in additive combinatorics concerning generalizations of Szemerédi's theorem on arithmetic progressions (sequences of numbers that are all equally spaced, like 4, 6, 8, and 10), which, informally, says that any sufficiently large collection of whole numbers contains a long arithmetic progression. It is a central problem in additive combinatorics to determine how large ""sufficiently large"" is. The investigator will study versions of this question involving more complicated patterns than arithmetic progressions, and then use the results and techniques developed to make progress on a related problem in ergodic theory. The investigator will also study the size and structure of integer distance sets, which are sets of points whose pairwise distances are all whole numbers. This award will support undergraduate summer research on representation theory and additive combinatorics, and also support the training of graduate students.

More specifically, the investigator will build on her previous work on quantitative bounds for subsets of the integers lacking polynomial progressions of distinct degrees and for subsets of vector spaces over finite fields lacking a certain four-point configuration to tackle more general polynomial, multidimensional, and multidimensional polynomial configurations. The results for multidimensional polynomial configurations of distinct degree will then be used to make progress on the Furstenberg--Bergelson--Leibman conjecture in ergodic theory, which concerns the pointwise almost everywhere convergence of certain nonconventional ergodic averages. She will also investigate the size and structure of integer distance sets, in both the Euclidean plane and in higher dimensions, by encoding them as subsets of rational points on certain families of varieties and then studying these varieties. With her undergraduate students, the investigator will study the distribution of entries in the character tables of symmetric groups and some algorithmic problems in higher-order Fourier 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." "2401106","Analytic Number Theory at the Interface","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/04/2024","Maksym Radziwill","IL","Northwestern University","Continuing Grant","Andrew Pollington","04/30/2029","$75,520.00","","maksym.radziwill@northwestern.edu","633 CLARK ST","EVANSTON","IL","602080001","3125037955","MPS","126400","","$0.00","The main objective of this award is to develop connections between analytic number theory and other areas of mathematics, specifically dynamics and probability theory. A basic problem in dynamics is to understand how quickly a deterministic process, for example particles in a gas sampled at regularly spaced intervals, randomizes. The regular spacing amounts to sampling the system at the integers. Answering the subtler questions in this area often requires a non-trivial understanding of the properties of the integers. Conversely, a basic problem in number theory is to show that fundamental properties of the integers (e.g their prime factorization) randomize, and here techniques from dynamics can be useful. As for probability, questions from mathematical physics led to the development of techniques for the study of interacting systems, for example the macroscopic properties of a gas of electrons constrained to a surface. It has been recently understood that these techniques are applicable in a number theoretic context, for example in the study of the Riemann zeta-function, a basic function governing the finer properties of the integers. A second objective of this proposal is to develop such techniques further in a number theoretic context. The PI will continue training graduate students and mentor postdocs on topics related to this research.

In dynamics the focus of this project is to understand the convergence of dynamical systems over sparse sets (primes, squares) at every point in the space, with a particular focus on horocycle flow. A second goal is to reexamine the work of Elkies-McMullen on the gap distribution of square-roots of integers modulo one from the perspective of the circle method. In probability theory, the focus is on developing further connections with branching random walks and statistical mechanics, specifically by focusing on the Fyodorov-Hiary-Keating conjecture and its other avatars. A final goal of the project is to develop our understanding of automorphic forms of fractional weight, with applications to concrete number theoretic problems (e.g the equidistribution of Kummer sums).

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

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "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." "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." diff --git a/Analysis/Awards-Analysis-2024.csv b/Analysis/Awards-Analysis-2024.csv index 90bcef3..9c880fe 100644 --- a/Analysis/Awards-Analysis-2024.csv +++ b/Analysis/Awards-Analysis-2024.csv @@ -1,40 +1,42 @@ "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" "2350079","RUI: Nonuniformly Hyperbolic and Extended Dynamical Systems","DMS","ANALYSIS PROGRAM","09/01/2024","04/08/2024","Mark Demers","CT","Fairfield University","Standard Grant","Jan Cameron","08/31/2027","$242,456.00","","mdemers@fairfield.edu","1073 N BENSON RD","FAIRFIELD","CT","068245171","2032544000","MPS","128100","9229","$0.00","The PI will investigate the properties of chaotic dynamical systems that are out of equilibrium due to the influence of either external forces or interconnected components. Research in dynamical systems is often focused on closed systems in which the dynamics are self-contained. In many modeling situations, however, such a global view is not possible, and it becomes necessary to study local systems influenced by external dynamics, possibly on different spatial or temporal scales. To better understand these phenomena, the PI will study open systems in which mass or energy may enter or exit through deterministic or random mechanisms, as well as large-scale systems of smaller interacting components that exchange mass or energy. These problems are strongly motivated by connections with statistical mechanics and seek to advance our understanding of fundamental questions related to energy transport and diffusion. This award will also support the involvement of undergraduates in mathematics research. The highly visual nature and physical motivation of the problems will enable the investigator to recruit undergraduate students to participate in related research projects. Special emphasis will be given to recruiting students from underrepresented groups in research mathematics. Students will disseminate results of their research via poster sessions, conference presentations and publications in peer-reviewed journals. By stimulating interest in research careers in mathematics and creating a peer community supportive of that interest, this award will contribute to the important goal of integrating research and education.

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348996","Variable Coefficient Fourier Analysis","DMS","ANALYSIS PROGRAM","07/01/2024","04/05/2024","Christopher Sogge","MD","Johns Hopkins University","Continuing Grant","Wing Suet Li","06/30/2027","$129,987.00","","sogge@jhu.edu","3400 N CHARLES ST","BALTIMORE","MD","212182608","4439971898","MPS","128100","","$0.00","The PI will study several problems in Geometric Harmonic Analysis. The settings for these problems involve geometric manifolds of dimension two or more. Associated with a given manifold are fundamental objects called eigenfunctions. These are the fundamental modes of vibration of the manifold, and they are the higher dimensional analogs of the familiar trigonometric functions for the circle. Designers of musical instruments are well aware that the shape of, say, a drum or the soundboard of stringed instrument affects the basic tones that it omits, as well as the sound volume. Similar phenomena arise for manifolds, and the PI will study precisely how their shapes, such as how they are curved, affect the properties properties of eigenfunctions. Just as in music, one particularly expects different shapes and geometries to become more apparent in the behavior of the fundamental modes of vibration as the frequency becomes larger and larger. These eigenfunctions are solutions of a differential equation that is similar to the wave equation, and the PI will study similar problems involving it. The general theme is to study how solutions of wave equations are affected by their physical backgrounds, such as whether or not black holes are present or whether the background becomes very close to a vacuum near infinity. This project provides research training opportunities for graduate students.

Among the specific problems the PI shall study, they wish to obtain improved estimates that measure the size and concentration of eigenfunctions. In order to do this, they will develop what is called ``global harmonic analysis??, which is a mixture of classical harmonic analysis, microlocal analysis, and techniques from geometry. The basic estimates are Lp-estimates for eigenfunctions and quasimodes and related highly localized L2 estimates that are sensitive to concentration. The main questions center around how the geometry and the global dynamics of the geodesic flow affect the estimates and the kinds of functions that saturate them. The latter issue is closely related to the much-studied (but still not well-understood) questions of concentration, oscillation, and size properties of modes and quasimodes in spectral asymptotics. These questions are also naturally linked to the long-time properties of the solution operator for the wave equation, Schrodinger equation, and resolvent estimates coming from the metric Laplacian. High frequency solutions and obtaining sharp results under geometric assumptions are particularly interesting. They will also study functions that saturate the estimates in different ways depending on the sign of the sectional curvatures of the 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." -"2409251","Conference: Maryland Dynamics Conference","DMS","ANALYSIS PROGRAM","04/15/2024","04/04/2024","Adam Kanigowski","MD","University of Maryland, College Park","Standard Grant","Jeremy Tyson","03/31/2027","$49,800.00","Giovanni Forni, Rodrigo Trevino, Bassam Fayad","adkanigowski@gmail.com","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","128100","7556","$0.00","This award provides funding for three years for an annual workshop, to be held in the spring, on dynamical systems and related topics. The workshop will take place on the campus of the University of Maryland at College Park. The event provides a forum for both early career and established researchers to exchange ideas with each other and with their counterparts from around the world. Conference proceedings will be produced at the conclusion of each workshop; these publications will help early career mathematicians to gain familiarity with the presented material. Funding from the award will be prioritized for the reimbursement of travel expenses incurred by junior participants and participants without access to other sources of support.

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2400332","NSF-BSF: C*-algebras and Dynamics Beyond the Elliott Program","DMS","ANALYSIS PROGRAM","08/01/2024","04/08/2024","Norman Phillips","OR","University of Oregon Eugene","Standard Grant","Jan Cameron","07/31/2027","$343,286.00","","ncp@uoregon.edu","1776 E 13TH AVE","EUGENE","OR","974031905","5413465131","MPS","128100","","$0.00","A C*-algebra is a kind of mathematical object which, for example, appears in quantum mechanics. Simple C*-algebras are those that cannot be broken apart into smaller (""simpler"") C*-algebras. The largest part of this project is about when a simple C*-algebra is isomorphic to its opposite algebra, that is, mathematically the same as what might be thought of as its mirror image. For an example from everyday life, an ordinary sock is the same as its mirror image, since a sock which fits on a right foot will fit equally well on the left foot. A glove isn't like that: whatever one does, a right glove will not fit on a left hand. A nonsimple C*-algebra can be made of very elementary parts, but put together in a tricky way, so as to not be isomorphic to its opposite. Simple C*-algebras which are not separable or not nuclear (""too large"", but in different senses) can also fail to be isomorphic to their opposites. On the other hand, simple C*-algebras covered by the Elliott classification program are isomorphic to their opposites. A long-term goal of the project is to exhibit a simple separable nuclear C*-algebra which is not isomorphic to its opposite. Such an algebra could not be covered even by any proposed expansion of the Elliott program. The project will also contribute to US workforce development through the training of graduate and undergraduate students.

The intended example is a simple unital AH algebra with fast dimension growth. The intended proof that it is not isomorphic to its opposite depends on nonexistence theorems for certain homomorphisms from one matrix algebra over the algebra of continuous functions on a compact space to a different matrix algebra over the continuous functions on a different compact space. When the second matrix size is large enough, all homomorphisms not ruled out for fairly obvious reasons actually exist. When it is small, known obstructions rule out most homomorphisms. The application requires information about an intermediate range. Here, even the simplest case, asked by Blackadar over 30 years ago, remains open; understanding this case is a necessary preliminary step. This case can almost certainly be settled by computations in rational homotopy theory, a new use of algebraic topology in C*-algebras.

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


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

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

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

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

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

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

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

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


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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2350128","Conference: PDE in Moab: Advances in Theory and Application","DMS","ANALYSIS PROGRAM","04/15/2024","04/05/2024","Mark Allen","UT","Brigham Young University","Standard Grant","Jan Cameron","03/31/2025","$35,875.00","Blair Davey, Mariana Smit Vega Garcia","mkallen2@gmail.com","A-153 ASB","PROVO","UT","846021128","8014223360","MPS","128100","7556","$0.00","The purpose of this award is to fund a research conference on Partial Differential Equations (PDE) to take place on June 3-7, 2024, at the Utah State University (USU) building located in Moab, Utah. The conference, called ""PDE in Moab: Advances in Theory and Application"" will feature 14 invited talks, along with 9 contributed talks from early career mathematicians, with a total of approximately 40 participants. Funding attached to this grant will be used to support travel and lodging expenses for participants in the conference, with priority for junior participants who do not have access to other sources of travel funding. The conference website is https://pdemoab.byu.edu

This conference aims to explore the tools and methods of partial differential equations (PDE), and their applications in related fields such as geometric measure theory (GMT), harmonic analysis, and free boundary problems. Historically, these areas of mathematics have benefited from many fruitful interconnections. Indeed, pioneering advancements in free boundary problems adapted techniques from regularity theory in both PDE and GMT. Moreover, recent advances in both nonlinear and nonlocal PDE have enlarged the intersection of the aforementioned fields, thereby increasing interactions, collaborations, and the overall advancement of these areas. This conference will bring together experts from the areas of PDE, GMT, harmonic analysis, and free boundary problems to explore and build on recent progress. The list of speakers is comprised of a dynamic group of mathematicians specializing in complementary fields, many of whom already have intersecting interests. It is expected that by bringing these researchers together, there will be further interaction between research areas, leading to the cross-pollination of techniques and novel research results.

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349846","Parabolic and elliptic boundary value and free boundary problems","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Steven Hofmann","MO","University of Missouri-Columbia","Standard Grant","Wing Suet Li","06/30/2027","$247,227.00","","hofmanns@missouri.edu","121 UNIVERSITY HALL","COLUMBIA","MO","652113020","5738827560","MPS","128100","","$0.00","This project is concerned with the theory of boundary value problems and free boundary problems for elliptic and parabolic partial differential equations. Such equations arise, for example, in the mathematical theory of heat conduction: an equation of elliptic type describes steady state (equilibrium) temperature distributions and a related parabolic equation governs heat conduction in the time-evolutive case. In a boundary value problem, one uses mathematical knowledge of either 1) the temperature distribution on the boundary (i.e., perimeter) of some region in space (or of some evolving region in space-time) or 2) the heat flux (the rate at which heat flows across the boundary), to deduce information about the internal temperature distribution inside the region. In free boundary problems, one uses simultaneous knowledge of both the boundary temperature distribution and the heat flux to deduce information about the geometry of the region and its boundary. A central goal of this project is to understand the interplay between analytic information and geometry. This project provides research training opportunities for graduate students.

The project has three main areas of focus: 1) to find a geometric characterization of the space-time domains for which the Dirichlet (or initial-Dirichlet) problem is solvable for the heat equation with singular (p-integrable) data, and to study related free boundary problems. The PI and coauthors have previously treated such problems in the steady state (elliptic) setting; in the present project, the PI seeks to treat the more difficult time-evolutive case. 2) to solve the Kato square root problem for elliptic equations in non-divergence form. The solution of the Kato problem for divergence form elliptic operators has led to significant progress in the theory of boundary value problems for divergence form equations. As a first step towards opening up the analogous theory in the nondivergence setting, the PI plans to treat the Kato problem for non-divergence elliptic operators. 3) to solve the Dirichlet problem in Lipschitz domains for non-symmetric divergence from elliptic equations with periodic coefficients. A primary motivation for the study of operators with periodic coefficients is their applicability to the theory of homogenization, which in turn provides a mathematical model for materials with periodic microstructure.

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2337630","CAREER: Isoperimetric and Minkowski Problems in Convex Geometric Analysis","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","06/01/2024","12/28/2023","Yiming Zhao","NY","Syracuse University","Continuing Grant","Eriko Hironaka","05/31/2029","$69,246.00","","yzhao197@syr.edu","900 S CROUSE AVE","SYRACUSE","NY","132444407","3154432807","MPS","126500, 128100","1045","$0.00","Isoperimetric problems and Minkowski problems are two central ingredients in Convex Geometric Analysis. The former compares geometric measurements (such as volume and surface area) while the latter recovers the shape of geometric figures using local versions of these measurements. The two types of problems are inherently connected. This project will exploit this connection to seek answers to either isoperimetric problems or Minkowski problems in various settings when answers to one exist while answers to the other remain elusive. Although these problems originate from a geometric background, their applications extend beyond mathematics into engineering and design, including areas like antenna reflector design and urban planning. The principal investigator will organize a series of events and workshops at local science museums, community centers, and schools, involving high school teachers and students as well as undergraduate and graduate students. These events and workshops aim to expose the fun and exploratory side of the principal investigator?s research and mathematics in general to students early in their educational careers, raise society's awareness and interest in mathematics, and promote mathematics among historically underrepresented populations.

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2404675","Conference: Young Mathematicians in C*-Algebras 2024","DMS","ANALYSIS PROGRAM","04/15/2024","04/09/2024","Adam Fuller","OH","Ohio University","Standard Grant","Jan Cameron","03/31/2025","$49,665.00","Priyanga Ganesan","fullera@ohio.edu","1 OHIO UNIVERSITY","ATHENS","OH","457012942","7405932857","MPS","128100","7556","$0.00","This award provides funding for U.S.-based participants, including members of underrepresented groups in the mathematical sciences, to participate in the conference Young Mathematicians in C*-Algebras (YMC*A), to be held August 5 -9, 2024 at The University of Glasgow, United Kingdom. This meeting is organized for and by graduate students and postdoctoral researchers in operator algebras and related areas, with the goal of fostering scientific and social interaction among early-career researchers. In each of its previous seven editions, YMC*A has provided an excellent opportunity for over one hundred early-career operator algebraists from around the world to attend mini-courses on current research topics in operator algebras. This grant significantly boosts the participation of U.S.-based researchers and their institutions at this conference, exemplifying U.S. research and furnishing opportunities for researchers to expand their professional networks.

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348996","Variable Coefficient Fourier Analysis","DMS","ANALYSIS PROGRAM","07/01/2024","04/05/2024","Christopher Sogge","MD","Johns Hopkins University","Continuing Grant","Wing Suet Li","06/30/2027","$129,987.00","","sogge@jhu.edu","3400 N CHARLES ST","BALTIMORE","MD","212182608","4439971898","MPS","128100","","$0.00","The PI will study several problems in Geometric Harmonic Analysis. The settings for these problems involve geometric manifolds of dimension two or more. Associated with a given manifold are fundamental objects called eigenfunctions. These are the fundamental modes of vibration of the manifold, and they are the higher dimensional analogs of the familiar trigonometric functions for the circle. Designers of musical instruments are well aware that the shape of, say, a drum or the soundboard of stringed instrument affects the basic tones that it omits, as well as the sound volume. Similar phenomena arise for manifolds, and the PI will study precisely how their shapes, such as how they are curved, affect the properties properties of eigenfunctions. Just as in music, one particularly expects different shapes and geometries to become more apparent in the behavior of the fundamental modes of vibration as the frequency becomes larger and larger. These eigenfunctions are solutions of a differential equation that is similar to the wave equation, and the PI will study similar problems involving it. The general theme is to study how solutions of wave equations are affected by their physical backgrounds, such as whether or not black holes are present or whether the background becomes very close to a vacuum near infinity. This project provides research training opportunities for graduate students.

Among the specific problems the PI shall study, they wish to obtain improved estimates that measure the size and concentration of eigenfunctions. In order to do this, they will develop what is called ``global harmonic analysis??, which is a mixture of classical harmonic analysis, microlocal analysis, and techniques from geometry. The basic estimates are Lp-estimates for eigenfunctions and quasimodes and related highly localized L2 estimates that are sensitive to concentration. The main questions center around how the geometry and the global dynamics of the geodesic flow affect the estimates and the kinds of functions that saturate them. The latter issue is closely related to the much-studied (but still not well-understood) questions of concentration, oscillation, and size properties of modes and quasimodes in spectral asymptotics. These questions are also naturally linked to the long-time properties of the solution operator for the wave equation, Schrodinger equation, and resolvent estimates coming from the metric Laplacian. High frequency solutions and obtaining sharp results under geometric assumptions are particularly interesting. They will also study functions that saturate the estimates in different ways depending on the sign of the sectional curvatures of the 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." +"2409251","Conference: Maryland Dynamics Conference","DMS","ANALYSIS PROGRAM","04/15/2024","04/04/2024","Adam Kanigowski","MD","University of Maryland, College Park","Standard Grant","Jeremy Tyson","03/31/2027","$49,800.00","Giovanni Forni, Rodrigo Trevino, Bassam Fayad","adkanigowski@gmail.com","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","128100","7556","$0.00","This award provides funding for three years for an annual workshop, to be held in the spring, on dynamical systems and related topics. The workshop will take place on the campus of the University of Maryland at College Park. The event provides a forum for both early career and established researchers to exchange ideas with each other and with their counterparts from around the world. Conference proceedings will be produced at the conclusion of each workshop; these publications will help early career mathematicians to gain familiarity with the presented material. Funding from the award will be prioritized for the reimbursement of travel expenses incurred by junior participants and participants without access to other sources of support.

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2349575","Geometric Techniques for Studying Singular Solutions to Hyperbolic Partial Differential Equations in Physics","DMS","ANALYSIS PROGRAM","06/15/2024","04/09/2024","Jared Speck","TN","Vanderbilt University","Standard Grant","Marian Bocea","05/31/2027","$330,901.00","","jared.speck@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","128100","","$0.00","The Principal Investigator (PI) will study evolution equations that arise in several physical models of nature, including Einstein?s equations of general relativity, Maxwell?s equations of electromagnetism, Euler?s equations of compressible fluid mechanics, and new, modified versions of Euler?s equations that account for viscous effects that were experimentally discovered in the study of the Quark-Gluon Plasma and neutron stars. While these equations have been studied for many decades, much remains to be understood about the dynamics of solutions. This project will focus on deriving theoretical results in one of the most exciting and rapidly advancing areas of study: singularity formation. Roughly, singularities are infinities that can develop in solutions, making the equations exceptionally challenging to study. Such infinities lie at the crux of some of the most fascinating physical phenomena. Outstanding examples include Big Bangs in general relativity, where the curvature of spacetime becomes infinite, and shock waves in compressible fluids, where pressure gradients become infinitely large. The results of the project will shed deep new insights into the laws of nature. The PI will integrate education, research, and scientific training by incorporating undergraduates, Master?s degree students, PhD students, and postdoctoral scholars into the research program.

The PI aims to prove novel stable blowup-results in multidimensions for solutions to the Cauchy problem for the PDE systems mentioned above, which are quasilinear and hyperbolic in character. For compressible Euler flow, the goal is to prove shock-formation, with an eye towards understanding the global structure of the largest possible classical solution, i.e, the Maximal Globally Hyperbolic Development (MGHD). There are currently no results on the global structure of the MGHD, and such results are essential for proving the uniqueness of classical solutions with shocks. For the viscous fluid models, there are currently no constructive blowup-results, so any constructive singularity-formation result would be the first of its kind. For Einstein?s equations (coupled to various matter models), the goal is to understand the structure and stability of spacetime singularities, with a focus on techniques that are localizable and robust, thus allowing one to probe new solution regimes. In all of the problems, gauge choices motivated by geometric and analytical considerations lie at the heart of the 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." +"2400332","NSF-BSF: C*-algebras and Dynamics Beyond the Elliott Program","DMS","ANALYSIS PROGRAM","08/01/2024","04/08/2024","Norman Phillips","OR","University of Oregon Eugene","Standard Grant","Jan Cameron","07/31/2027","$343,286.00","","ncp@uoregon.edu","1776 E 13TH AVE","EUGENE","OR","974031905","5413465131","MPS","128100","","$0.00","A C*-algebra is a kind of mathematical object which, for example, appears in quantum mechanics. Simple C*-algebras are those that cannot be broken apart into smaller (""simpler"") C*-algebras. The largest part of this project is about when a simple C*-algebra is isomorphic to its opposite algebra, that is, mathematically the same as what might be thought of as its mirror image. For an example from everyday life, an ordinary sock is the same as its mirror image, since a sock which fits on a right foot will fit equally well on the left foot. A glove isn't like that: whatever one does, a right glove will not fit on a left hand. A nonsimple C*-algebra can be made of very elementary parts, but put together in a tricky way, so as to not be isomorphic to its opposite. Simple C*-algebras which are not separable or not nuclear (""too large"", but in different senses) can also fail to be isomorphic to their opposites. On the other hand, simple C*-algebras covered by the Elliott classification program are isomorphic to their opposites. A long-term goal of the project is to exhibit a simple separable nuclear C*-algebra which is not isomorphic to its opposite. Such an algebra could not be covered even by any proposed expansion of the Elliott program. The project will also contribute to US workforce development through the training of graduate and undergraduate students.

The intended example is a simple unital AH algebra with fast dimension growth. The intended proof that it is not isomorphic to its opposite depends on nonexistence theorems for certain homomorphisms from one matrix algebra over the algebra of continuous functions on a compact space to a different matrix algebra over the continuous functions on a different compact space. When the second matrix size is large enough, all homomorphisms not ruled out for fairly obvious reasons actually exist. When it is small, known obstructions rule out most homomorphisms. The application requires information about an intermediate range. Here, even the simplest case, asked by Blackadar over 30 years ago, remains open; understanding this case is a necessary preliminary step. This case can almost certainly be settled by computations in rational homotopy theory, a new use of algebraic topology in C*-algebras.

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


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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2350128","Conference: PDE in Moab: Advances in Theory and Application","DMS","ANALYSIS PROGRAM","04/15/2024","04/05/2024","Mark Allen","UT","Brigham Young University","Standard Grant","Jan Cameron","03/31/2025","$35,875.00","Blair Davey, Mariana Smit Vega Garcia","mkallen2@gmail.com","A-153 ASB","PROVO","UT","846021128","8014223360","MPS","128100","7556","$0.00","The purpose of this award is to fund a research conference on Partial Differential Equations (PDE) to take place on June 3-7, 2024, at the Utah State University (USU) building located in Moab, Utah. The conference, called ""PDE in Moab: Advances in Theory and Application"" will feature 14 invited talks, along with 9 contributed talks from early career mathematicians, with a total of approximately 40 participants. Funding attached to this grant will be used to support travel and lodging expenses for participants in the conference, with priority for junior participants who do not have access to other sources of travel funding. The conference website is https://pdemoab.byu.edu

This conference aims to explore the tools and methods of partial differential equations (PDE), and their applications in related fields such as geometric measure theory (GMT), harmonic analysis, and free boundary problems. Historically, these areas of mathematics have benefited from many fruitful interconnections. Indeed, pioneering advancements in free boundary problems adapted techniques from regularity theory in both PDE and GMT. Moreover, recent advances in both nonlinear and nonlocal PDE have enlarged the intersection of the aforementioned fields, thereby increasing interactions, collaborations, and the overall advancement of these areas. This conference will bring together experts from the areas of PDE, GMT, harmonic analysis, and free boundary problems to explore and build on recent progress. The list of speakers is comprised of a dynamic group of mathematicians specializing in complementary fields, many of whom already have intersecting interests. It is expected that by bringing these researchers together, there will be further interaction between research areas, leading to the cross-pollination of techniques and novel research results.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350129","Problems in Regularity Theory of Partial Differential Equations","DMS","ANALYSIS PROGRAM, EPSCoR Co-Funding","07/01/2024","04/02/2024","Hongjie Dong","RI","Brown University","Standard Grant","Marian Bocea","06/30/2027","$351,235.00","","Hongjie_Dong@brown.edu","1 PROSPECT ST","PROVIDENCE","RI","029129100","4018632777","MPS","128100, 915000","9150","$0.00","This project focuses on understanding certain types of partial differential equations (PDE) commonly encountered in physics and engineering, such as those governing elasticity and conductivity. When we study how materials deform under stress or conduct electricity, we often use equations to describe these phenomena. However, some equations don't behave smoothly, especially when dealing with high contrast materials or complex shapes. These situations can lead to equations that are much harder to analyze, and traditional methods may not work. Another area of study is equations from fluid dynamics. Understanding these questions is crucial for practical applications like designing airplanes or predicting weather patterns, and it also inspires new ideas in mathematics and statistics. Finally, the Principal Investigator (PI) is interested in kinetic equations, which describe how particles move and interact in systems like nuclear fusion experiments. By studying these equations, scientists hope to improve our understanding of how plasmas behave in extreme conditions, such as inside a tokamak. The project provides research training opportunities for graduate students.

As part of this project, the PI will carry out research closely related to the aforementioned topics and will attempt to address some of the open problems in these areas. The focus will be on several projects that can be gathered into three main topical areas. First, the project will develop new methods to study elliptic equations arising in composite materials (e.g., elasticity problems, conductivity problems). The PI is particularly interested in the blowup behaviors of solutions to PDE in domains with Lipschitz inclusions, equations involving the p-Laplacian, and the insulated problem for the Lamé system. Second, the project will explore the free boundary problem involving an incompressible fluid permeating a porous medium, often referred to as the one-phase Muskat problem. The focus will be on investigating the regularity of solutions to the two- and three-dimensional one-phase Muskat problem in the whole space, as well as on exploring the short-term and long-term smoothing effects of these solutions. Finally, the project will investigate boundary regularity of linear kinetic equations as well as the stability and global well-posedness of nonlinear kinetic equations, including the relativistic Vlasov-Maxwell-Landau system and the spatially inhomogeneous Boltzmann equations in general domains.

This project is jointly funded by the Analysis Program in the Division of Mathematical Sciences (DMS) 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." "2350101","Some problems in harmonic analysis","DMS","ANALYSIS PROGRAM","07/01/2024","04/02/2024","Xiaochun Li","IL","University of Illinois at Urbana-Champaign","Standard Grant","Wing Suet Li","06/30/2027","$327,441.00","","xcli@math.uiuc.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","128100","","$0.00","The principal investigator (PI) intends to delve into challenges situated at the junction of harmonic analysis, number theory, and dispersive equations. In addition to focusing on classical Fourier analysis, the PI aims to establish connections with diverse fields, including number theory, combinatorics, dispersive equations on tori, and Ergodic theory. Furthermore, the PI plans to mentor students, disseminate their findings through talks, and foster collaborations, thereby generating broader impacts.


The PI plans to continue the research efforts in several areas. Firstly, the PI and his collaborators will delve into the rapidly advancing field of modern mathematics, particularly focusing on additive combinatorics alongside Fourier analysis. Within this realm, they aim to further explore Roth's theorem, a fundamental result that determines the minimum subset size required for the existence of arithmetic progressions within {1, ..., N}. Their work will extend their previous investigations into the polynomial Roth theorem on rings and/or finite fields. Secondly, in classical harmonic analysis, the PI is dedicated to investigating the conjectured pointwise convergence of the Bochner-Riesz mean on the plane, as proposed by Sogge and Tao. Thirdly, in collaboration with Yang, the PI has made strides in improving both Gauss's circle problem and Dirichlet's divisor problem. They believe there is still room for additional progress in these areas. Finally, the PI will continue his study of the Waring problem, which can be approached as a decoupling problem for a function whose Fourier transform is confined to a broken line.

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348748","Exploring Large-Scale Geometry via Local and Nonlocal Potential Theory","DMS","ANALYSIS PROGRAM","09/01/2024","04/02/2024","Nageswari Shanmugalingam","OH","University of Cincinnati Main Campus","Standard Grant","Jan Cameron","08/31/2027","$343,850.00","","shanmun@uc.edu","2600 CLIFTON AVE","CINCINNATI","OH","452202872","5135564358","MPS","128100","","$0.00","This project will develop new mathematical tools for the analysis of metric measure spaces ? that is, spaces equipped (like Euclidean space) with notions of distance and volume ? with a focus on metric measure spaces that (unlike Euclidean space) lack smooth structure. The analysis of non-smooth spaces is a vital area of research with diverse applications across the mathematical and physical sciences, including fluid mechanics, neurophysiology, and fractal geometry. The PI will investigate the large-scale geometric behavior of objects in these spaces using the mathematical tools of local and nonlocal energies. Given a function measuring a physical phenomenon, such as temperature or momentum, local energies measure the function?s nearby or small-scale oscillations, while nonlocal energies measure its variations over long distances. A primary goal of this work is to develop much-needed mathematical tools for analyzing nonlocal energies. The project will also enhance the professional training of graduate students and postdoctoral scholars, through collaborative research projects, instruction in effective mathematical communication, and opportunities for research interactions with undergraduate students.


The primary objects of study in this project are represented as metric measure spaces that lack smooth structure. The finite dimensionality of the ambient space is represented by the property of supporting a doubling Radon measure. In such a setting, nearby or asymptotic oscillation of a function is measured using upper gradients, which are viable substitutes for the derivative of a function, and the local energy is associated with the collection of functions on the object, called Sobolev functions. The large-scale variation energy is associated with the collection called Besov space of functions. Recent research has uncovered a connection between local energies on a region in a metric measure space and nonlocal energies on the boundary of the region. The project will leverage this connection to explore the large-scale geometry of nonlocal energies on the boundary of the region by linking them with small-scale behavior of local energies on the region itself. In particular, connections between Dirichlet-type boundary value problems and Neumann-type boundary value problems will 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." "2348315","Structural Properties of Measurable and Topological Dynamical Systems","DMS","ANALYSIS PROGRAM","06/01/2024","04/02/2024","Bryna Kra","IL","Northwestern University","Standard Grant","Jan Cameron","05/31/2027","$349,929.00","","kra@math.northwestern.edu","633 CLARK ST","EVANSTON","IL","602080001","3125037955","MPS","128100","","$0.00","The investigator proposes a program of research, education, and outreach in dynamics. The research is focused on structural questions in dynamics that lie at the heart of understanding many different types of abstract systems, focused on gaining a deeper understanding of connections among different dynamical properties. The education and outreach portions of the project aim to broaden the cohort of researchers working in these areas.

The proposed research problems have a combinatorial flavor, and the methods used to approach them are dynamical. Using structural results in ergodic theory and topological dynamics, the PI proposes studying the types of infinite configurations that must arise in any sufficiently large set of integers. To gain a better understanding of the interactions of topological measurable structures, the PI proposes studying a newly defined class of systems that gives rise to a type of rigidity. A symbolic viewpoint underlines the approaches, and the PI plans to study the interactions of algebraic, measurable, and dynamical properties of these systems. This includes gaining a better understanding of how the automorphism group of the system reflects the underlying dynamics and the system supports a measure invariant under this group of symmetries.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2350242","Hilbert's Sixth Problem: From Particles to Waves","DMS","ANALYSIS PROGRAM","06/01/2024","04/03/2024","Zaher Hani","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Marian Bocea","05/31/2027","$130,000.00","","zhani@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","128100","","$0.00","Hilbert?s sixth problem, posed in 1900, asks for a rigorous mathematical derivation of the macroscopic laws of statistical physics, formulated by Maxwell and Boltzmann in the nineteenth century, starting from the microscopic laws of dynamics (aka first principles). The classical setting of this problem pertains to particle systems which collide according to the laws of classical mechanics. The same problem emerges in more modern theories of statistical physics, where particles are replaced by waves that interact according to some Hamiltonian wave-type partial differential equation. Such theories of statistical physics for waves often go by the name of ?wave turbulence theory?, because they play a central role in understanding turbulent behaviors in wave systems. This has applications in many areas of science such as quantum mechanics, oceanography, climate science, etc. Broadly speaking, the goal of this project is to advance the mathematical, and hence scientific, understanding of such turbulence theories, and settle some longstanding conjectures in mathematical physics on the foundations of statistical mechanics. The project provides research training opportunities for graduate students.

Even in its classical setting, Hilbert?s sixth problem remains a formidable task, that has only been resolved for short times. The project seeks to provide its long-time resolution, thus giving a final answer to this longstanding open problem. This amounts to giving the rigorous derivation of Boltzmann?s kinetic equation starting from Newton?s laws, followed by the derivation of the macroscopic fluid models (Euler?s and Navier-Stokes equations). In parallel, the project proposes similar justifications in the setting of wave turbulence theory. There too, the Principal Investigator (PI) seeks to provide the long-time derivation of the corresponding ?wave kinetic equations? for various wave systems of scientific interest. Starting with the nonlinear Schrödinger equation as a prime model for nonlinear wave systems, this will be followed by similar investigations for other wave systems, like many-particle quantum systems and some models coming from ocean and climate science. Finally, the project will investigate mathematical problems related to the turbulence aspects of wave turbulence theory. There, the PI intends to use the above rigorous derivation of the wave kinetic equations, combined with an analysis of solutions to those equations, to understand turbulence phenomena for wave systems, such as energy cascades and growth of Sobolev norms.

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

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2350242","Hilbert's Sixth Problem: From Particles to Waves","DMS","ANALYSIS PROGRAM","06/01/2024","04/03/2024","Zaher Hani","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Marian Bocea","05/31/2027","$130,000.00","","zhani@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","128100","","$0.00","Hilbert?s sixth problem, posed in 1900, asks for a rigorous mathematical derivation of the macroscopic laws of statistical physics, formulated by Maxwell and Boltzmann in the nineteenth century, starting from the microscopic laws of dynamics (aka first principles). The classical setting of this problem pertains to particle systems which collide according to the laws of classical mechanics. The same problem emerges in more modern theories of statistical physics, where particles are replaced by waves that interact according to some Hamiltonian wave-type partial differential equation. Such theories of statistical physics for waves often go by the name of ?wave turbulence theory?, because they play a central role in understanding turbulent behaviors in wave systems. This has applications in many areas of science such as quantum mechanics, oceanography, climate science, etc. Broadly speaking, the goal of this project is to advance the mathematical, and hence scientific, understanding of such turbulence theories, and settle some longstanding conjectures in mathematical physics on the foundations of statistical mechanics. The project provides research training opportunities for graduate students.

Even in its classical setting, Hilbert?s sixth problem remains a formidable task, that has only been resolved for short times. The project seeks to provide its long-time resolution, thus giving a final answer to this longstanding open problem. This amounts to giving the rigorous derivation of Boltzmann?s kinetic equation starting from Newton?s laws, followed by the derivation of the macroscopic fluid models (Euler?s and Navier-Stokes equations). In parallel, the project proposes similar justifications in the setting of wave turbulence theory. There too, the Principal Investigator (PI) seeks to provide the long-time derivation of the corresponding ?wave kinetic equations? for various wave systems of scientific interest. Starting with the nonlinear Schrödinger equation as a prime model for nonlinear wave systems, this will be followed by similar investigations for other wave systems, like many-particle quantum systems and some models coming from ocean and climate science. Finally, the project will investigate mathematical problems related to the turbulence aspects of wave turbulence theory. There, the PI intends to use the above rigorous derivation of the wave kinetic equations, combined with an analysis of solutions to those equations, to understand turbulence phenomena for wave systems, such as energy cascades and growth of Sobolev norms.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2400036","New Challenges in the Study of Propagation of Randomness for Nonlinear Evolution Equations","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Andrea Nahmod","MA","University of Massachusetts Amherst","Standard Grant","Marian Bocea","06/30/2027","$388,536.00","","nahmod@math.umass.edu","101 COMMONWEALTH AVE","AMHERST","MA","010039252","4135450698","MPS","128100","","$0.00","Waves are everywhere in nature. We observe them when we look at the ripples that form when we throw a pebble in a lake, the expanding ring called a wave-packet; or when we look at a rainbow that is formed when light wave passes through a prism or water droplet and note the spatial separation of white light into different colors. Partial differential equations (PDE) modeling wave propagation phenomena have played a fundamental role in understanding such physical and natural events as well as quantum mechanics, fiber optics, ferromagnetism, atmospheric and water waves, and many other physical models. In these cases, wave phenomena are never too smooth or too simple, and in fact the byproduct of nonlinear wave interactions as they propagate in time. Being able to understand and describe the dynamical behavior of such models under certain noisy conditions or given an initial statistical ensemble and have a precise description of how the inherent randomness built in these models propagates, is fundamental to accurately predict wave phenomena when studying the natural world. This project is aimed at answering several central questions about long-time dynamics and the propagation of randomness in this context using analytical and probabilistic methodologies. The work of the project, and its connections to science, promotes interdisciplinary interactions and fosters the training of graduate students and junior researchers in the United States thus fundamentally contributing to its STEM workforce.

The interplay of deterministic methods in nonlinear PDE and probabilistic ones naturally feed off each other and when combined contribute to a deep understanding of wave phenomena, which opens the door to new paradigms that move research forward in various directions. The Principal Investigator studies several projects at the forefront of current research. The problems, grouped in two interrelated directions, aim broadly at: (1) studying the out of equilibrium long-time dynamics of dispersive flows from a probabilistic viewpoint in energy subcritical regimes by means of suitable quantitative quasi-invariance, modified energies and stability theory of random structures; (2) establishing the invariance of Gibbs measures for the probabilistically critical three-dimensional nonlinear Schrödinger equation (also known as a model in constructive quantum field theory) in the context of equilibrium statistical mechanics; (3) establishing a suitable probabilistic local theory of the hyperbolic sine-Gordon equation on 2D tori and the invariance of its associated Gibbs measure; and (4) the development of the random tensor theory for the nonlinear wave equations and for non-Gaussian data. The research bridges between the dispersive and wave equations communities that specialize in stochastic equations and contributes to understanding in a fundamental way propagation of randomness in nonlinear wave phenomena.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2349868","Testing Theorems in Analytic Function Theory, Harmonic Analysis and Operator Theory","DMS","ANALYSIS PROGRAM","07/01/2024","04/02/2024","Brett Wick","MO","Washington University","Standard Grant","Wing Suet Li","06/30/2027","$310,000.00","","wick@math.wustl.edu","ONE BROOKINGS DR","SAINT LOUIS","MO","63110","3147474134","MPS","128100","","$0.00","This proposal involves basic fundamental mathematical research at the intersection of analytic function theory, harmonic analysis, and operator theory. Motivation to study these questions can be found in partial differential equations, which are fundamental to the study of science and engineering. The solution to a partial differential equation is frequently given by an integral operator, a Calderon-Zygmund operator, whose related properties can be used to deduce related properties of these partial differential equations. In general, studying these Calderon-Zygmund operators is challenging and one seeks to study their action on certain spaces of functions, by checking the behavior only on a simpler class of test functions. In analogy, this can be seen as attempting to understand a complicated musical score by simply understanding a simpler finite collection of pure frequencies. The proposed research is based on recent contributions made by the PI, leveraging the skills and knowledge developed through prior National Science Foundation awards. Through this proposal the PI will address open and important questions at the interface of analytic function theory, harmonic analysis, and operator theory. Resolution of questions in these areas will provide for additional lines of inquiry. Funds from this award will support a diverse group of graduate students whom the PI advises; helping to increase the national pipeline of well-trained STEM students for careers in academia, government, or industry.

The research program of this proposal couples important open questions with the PI's past work. The general theme will be to use methods around ``testing theorems,'' called ``T1 theorems'' in harmonic analysis or the ``reproducing kernel thesis'' in analytic function theory and operator theory, to study questions that arise in analytic function theory, harmonic analysis, and operator theory. In particular, applications of the proof strategy of testing theorems will: (1) be used to characterize when Calderon-Zygmund operators are bounded between weighted spaces both for continuous and dyadic variants of these operators; (2) serve as motivation for a class of questions related to operators on the Fock space of analytic functions that are intimately connected to Calderon-Zygmund operators; and, (3) be leveraged to provide a method to study Carleson measures in reproducing kernel Hilbert spaces of analytic functions. Results obtained will open the door to other lines of 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." "2350351","Unique continuation and the regularity of elliptic PDEs and generalized minimal submanifolds","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","06/01/2024","03/27/2024","Zihui Zhao","MD","Johns Hopkins University","Standard Grant","Jeremy Tyson","05/31/2027","$253,734.00","","zhaozh@jhu.edu","3400 N CHARLES ST","BALTIMORE","MD","212182608","4439971898","MPS","126500, 128100","5920, 5936, 5946, 5950","$0.00","This award supports research on the regularity of solutions to elliptic partial differential equations and regularity of generalized minimal submanifolds. Elliptic differential equations govern the equilibrium configurations of various physical phenomena, for instance, those arising from minimization problems for natural energy functionals. Examples include the shape of free-hanging bridges, the shape of soap bubbles, and the sound of drums. Elliptic differential equations are also used to quantify the degree to which physical objects are bent or distorted, with far-reaching implications and applications in geometry and topology. The proposed research focuses on the regularity of solutions to such equations. Questions to be addressed include the following: Do non-smooth points (singularities) exist? How large can the set of singularities be? What is the behavior of the solution near a singularity? Is it possible to perturb the underlying environment in order to eliminate the singularity? The project will also provide opportunities for the professional development of graduate students, both via individual mentoring and via the organization of a directed learning seminar on geometric analysis and geometric measure theory.

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2400036","New Challenges in the Study of Propagation of Randomness for Nonlinear Evolution Equations","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Andrea Nahmod","MA","University of Massachusetts Amherst","Standard Grant","Marian Bocea","06/30/2027","$388,536.00","","nahmod@math.umass.edu","101 COMMONWEALTH AVE","AMHERST","MA","010039252","4135450698","MPS","128100","","$0.00","Waves are everywhere in nature. We observe them when we look at the ripples that form when we throw a pebble in a lake, the expanding ring called a wave-packet; or when we look at a rainbow that is formed when light wave passes through a prism or water droplet and note the spatial separation of white light into different colors. Partial differential equations (PDE) modeling wave propagation phenomena have played a fundamental role in understanding such physical and natural events as well as quantum mechanics, fiber optics, ferromagnetism, atmospheric and water waves, and many other physical models. In these cases, wave phenomena are never too smooth or too simple, and in fact the byproduct of nonlinear wave interactions as they propagate in time. Being able to understand and describe the dynamical behavior of such models under certain noisy conditions or given an initial statistical ensemble and have a precise description of how the inherent randomness built in these models propagates, is fundamental to accurately predict wave phenomena when studying the natural world. This project is aimed at answering several central questions about long-time dynamics and the propagation of randomness in this context using analytical and probabilistic methodologies. The work of the project, and its connections to science, promotes interdisciplinary interactions and fosters the training of graduate students and junior researchers in the United States thus fundamentally contributing to its STEM workforce.

The interplay of deterministic methods in nonlinear PDE and probabilistic ones naturally feed off each other and when combined contribute to a deep understanding of wave phenomena, which opens the door to new paradigms that move research forward in various directions. The Principal Investigator studies several projects at the forefront of current research. The problems, grouped in two interrelated directions, aim broadly at: (1) studying the out of equilibrium long-time dynamics of dispersive flows from a probabilistic viewpoint in energy subcritical regimes by means of suitable quantitative quasi-invariance, modified energies and stability theory of random structures; (2) establishing the invariance of Gibbs measures for the probabilistically critical three-dimensional nonlinear Schrödinger equation (also known as a model in constructive quantum field theory) in the context of equilibrium statistical mechanics; (3) establishing a suitable probabilistic local theory of the hyperbolic sine-Gordon equation on 2D tori and the invariance of its associated Gibbs measure; and (4) the development of the random tensor theory for the nonlinear wave equations and for non-Gaussian data. The research bridges between the dispersive and wave equations communities that specialize in stochastic equations and contributes to understanding in a fundamental way propagation of randomness in nonlinear wave phenomena.

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2337630","CAREER: Isoperimetric and Minkowski Problems in Convex Geometric Analysis","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","06/01/2024","12/28/2023","Yiming Zhao","NY","Syracuse University","Continuing Grant","Eriko Hironaka","05/31/2029","$69,246.00","","yzhao197@syr.edu","900 S CROUSE AVE","SYRACUSE","NY","132444407","3154432807","MPS","126500, 128100","1045","$0.00","Isoperimetric problems and Minkowski problems are two central ingredients in Convex Geometric Analysis. The former compares geometric measurements (such as volume and surface area) while the latter recovers the shape of geometric figures using local versions of these measurements. The two types of problems are inherently connected. This project will exploit this connection to seek answers to either isoperimetric problems or Minkowski problems in various settings when answers to one exist while answers to the other remain elusive. Although these problems originate from a geometric background, their applications extend beyond mathematics into engineering and design, including areas like antenna reflector design and urban planning. The principal investigator will organize a series of events and workshops at local science museums, community centers, and schools, involving high school teachers and students as well as undergraduate and graduate students. These events and workshops aim to expose the fun and exploratory side of the principal investigator?s research and mathematics in general to students early in their educational careers, raise society's awareness and interest in mathematics, and promote mathematics among historically underrepresented populations.

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2349868","Testing Theorems in Analytic Function Theory, Harmonic Analysis and Operator Theory","DMS","ANALYSIS PROGRAM","07/01/2024","04/02/2024","Brett Wick","MO","Washington University","Standard Grant","Wing Suet Li","06/30/2027","$310,000.00","","wick@math.wustl.edu","ONE BROOKINGS DR","SAINT LOUIS","MO","63110","3147474134","MPS","128100","","$0.00","This proposal involves basic fundamental mathematical research at the intersection of analytic function theory, harmonic analysis, and operator theory. Motivation to study these questions can be found in partial differential equations, which are fundamental to the study of science and engineering. The solution to a partial differential equation is frequently given by an integral operator, a Calderon-Zygmund operator, whose related properties can be used to deduce related properties of these partial differential equations. In general, studying these Calderon-Zygmund operators is challenging and one seeks to study their action on certain spaces of functions, by checking the behavior only on a simpler class of test functions. In analogy, this can be seen as attempting to understand a complicated musical score by simply understanding a simpler finite collection of pure frequencies. The proposed research is based on recent contributions made by the PI, leveraging the skills and knowledge developed through prior National Science Foundation awards. Through this proposal the PI will address open and important questions at the interface of analytic function theory, harmonic analysis, and operator theory. Resolution of questions in these areas will provide for additional lines of inquiry. Funds from this award will support a diverse group of graduate students whom the PI advises; helping to increase the national pipeline of well-trained STEM students for careers in academia, government, or industry.

The research program of this proposal couples important open questions with the PI's past work. The general theme will be to use methods around ``testing theorems,'' called ``T1 theorems'' in harmonic analysis or the ``reproducing kernel thesis'' in analytic function theory and operator theory, to study questions that arise in analytic function theory, harmonic analysis, and operator theory. In particular, applications of the proof strategy of testing theorems will: (1) be used to characterize when Calderon-Zygmund operators are bounded between weighted spaces both for continuous and dyadic variants of these operators; (2) serve as motivation for a class of questions related to operators on the Fock space of analytic functions that are intimately connected to Calderon-Zygmund operators; and, (3) be leveraged to provide a method to study Carleson measures in reproducing kernel Hilbert spaces of analytic functions. Results obtained will open the door to other lines of 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." "2349828","Spatial restriction of exponential sums to thin sets and beyond","DMS","ANALYSIS PROGRAM","06/01/2024","04/01/2024","Ciprian Demeter","IN","Indiana University","Standard Grant","Wing Suet Li","05/31/2027","$299,999.00","","demeterc@indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","128100","","$0.00","In recent years, the PI has developed a new tool called decoupling that measures the extent to which waves traveling in different directions interact with each other. While this tool was initially intended to analyze differential equations that describe wave cancellations, it has also led to important breakthroughs in number theory. For example, Diophantine equations are potentially complicated systems of equations involving whole numbers. They are used to generate scrambling and diffusion keys, which are instrumental in encrypting data. Mathematicians are interested in counting the number of solutions to such systems. Unlike waves, numbers do not oscillate, at least not in an obvious manner. But we can think of numbers as frequencies and thus associate them with waves. In this way, problems related to counting the number of solutions to Diophantine systems can be rephrased in the language of quantifying wave interferences. This was the case with PI's breakthrough resolution of the Main Conjecture in Vinogradov's Mean Value Theorem. The PI plans to further extend the scope of decoupling toward the resolution of fundamental problems in harmonic analysis, geometric measure theory, and number theory. He will seek to make the new tools accessible and useful to a large part of the mathematical community. This project provides research training opportunities for graduate students.


Part of this project is aimed at developing the methodology to analyze the Schrödinger maximal function in the periodic setting. Building on his recent progress, the PI aims to incorporate Fourier analysis and more delicate number theory into the existing combinatorial framework. Decouplings have proved successful in addressing a wide range of problems in such diverse areas as number theory, partial differential equations, and harmonic analysis. The current project seeks to further expand the applicability of this method in new directions. One of them is concerned with finding sharp estimates for the Fourier transforms of fractal measures supported on curved manifolds. The PI seeks to combine decoupling with sharp estimates for incidences between balls and tubes. In yet another direction, he plans to further investigate the newly introduced tight decoupling phenomenon. This has deep connections to both number theory and the Lambda(p) estimates.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348846","Interfaces, Degenerate Partial Differential Equations, and Convexity","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Benjamin Weinkove","IL","Northwestern University","Standard Grant","Marian Bocea","06/30/2027","$145,617.00","","weinkove@math.northwestern.edu","633 CLARK ST","EVANSTON","IL","602080001","3125037955","MPS","128100","9251","$0.00","Partial differential equations (PDE) are essential mathematical objects for modeling physical processes. This project aims to understand the properties of some fundamental PDE models for the diffusion of gas, the shape of liquid droplets, and electric transmission in composite materials. Many such processes exhibit an interface, where the equation becomes degenerate or singular. In the case of a model of gas diffusion through a porous medium, the interface is the set which separates the region where there is gas from the region where there is no gas. The boundary of a liquid droplet is another example of an interface. The project will investigate qualitative and quantitative properties of these interfaces, including convexity and smoothness. For a composite material, consisting of two materials with different conductivity properties, the interface is where these materials meet. The Principal Investigator (PI) will study the behavior of the electric field when one of the materials has a very thin part. This project has possible implications for material failure, an important question in Engineering. Students and postdoctoral scholars will be trained on the techniques and theory of these PDE models.

This project centers on four topics, connected by the themes of interfaces, degeneracies, and convexity/concavity. The porous medium equation is a nonlinear degenerate parabolic equation used to model the diffusion of gas. The PI will investigate questions of concavity and convexity of solutions and finding global optimal regularity estimates. Secondly, the PI will study linear PDE whose coefficients are discontinuous along two almost touching interfaces, a model for transmission problems and composite materials. In this setting, the PI will investigate new approaches to obtaining optimal gradient estimates in the thin region between the interfaces. A third project is to study linear equations which are parabolic on the interior on a fixed domain but are degenerate at the boundary. These equations arise as linearizations of the porous medium equation and the Gauss curvature flow. The PI will investigate optimal conditions for existence and uniqueness of smooth solutions. Finally, questions of concavity of solutions to the elliptic torsion problem with Dirichlet boundary conditions and the dynamic version of this equation, known as the quasi-static droplet model, will be studied. In addition, the PI will carry out summer research projects with undergraduates, exploring explicit solutions to these 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." +"2400115","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Kate Juschenko","TX","University of Texas at Austin","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","","kate.juschenko@gmail.com","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350340","Coarse-graining, Renormalization, and Fractal Homogenization","DMS","ANALYSIS PROGRAM","07/01/2024","04/02/2024","Scott Armstrong","NY","New York University","Continuing Grant","Marian Bocea","06/30/2027","$142,013.00","","sa3602@nyu.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","128100","","$0.00","This project is focused on the development of new mathematics for analyzing the statistical behavior of physical systems which exhibit complex behavior across a large number of length scales. A typical examples include turbulent fluids, such as the earth's atmosphere, which have fluctuations on the human scale (a gust of wind) and on the continental scale (weather patterns), and every scale in between. Other examples include important models in statistical mechanics and quantum field theory. Such chaotic physical systems have interesting behaviors which emerge through the interaction of these very different length scales, often called ""critical phenomena"" by physicists. Physicists have developed heuristic, non-rigorous ways of understanding and analyzing many such physical systems, some of which are called ""renormalization group"" arguments. One of the main goals of this project is to develop precise versions of these informal arguments which are mathematically rigorous. In the past decade, the work of the Principal Investigator (PI) and other mathematicians have led to a rigorous theory of ""quantitative homogenization"" of certain partial differential equations. These equations have some of the properties of the complex physical systems mentioned above, and the homogenization theory resembles renormalization group-type arguments in important ways. However, it currently works well only for problems with a small number of length scales. The project proposes to increase the level of sophistication of the homogenization methods until the theory can be deployed more flexibly on physical systems exhibiting critical behavior. This requires the development of new mathematical ideas and concepts and will require input from analysis, probability theory, partial differential equations and mathematical physics. The project provides research training opportunities for graduate students.

The project has two main goals. The first one concerns improving the quantitative homogenization theory, so that it is more explicit in its dependence on important parameters in the equation (like the ellipticity ratio) and allows for degenerate and possibly unbounded coefficient fields. This is a well-known open problem in the subfield, but the PI and his collaborator Kuusi have made recent progress on this question, and this project will continue to develop these new ideas. A second focus of the project is to use these analytic methods developed for homogenization as means of formalizing heuristic renormalization group arguments in physics. Such methods arise in a wide variety of contexts, but the project has a few specific problems in mind. One arises in fluid turbulence, and concerns proving the anomalous diffusion of a passive scalar advected by a rough vector field. The PI and his collaborator Vicol have made recent progress on this question by using homogenization to formalize a renormalization group argument. This points the way to further possibilities, including the construction of more physically realistic examples of anomalous diffusion. Another potential application lies in Euclidean field theory, following a stochastic quantization approach to study Gibbs measures.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349981","Survival Threshold for Collective Plasma Oscillations","DMS","ANALYSIS PROGRAM","06/01/2024","04/01/2024","Toan Nguyen","PA","Pennsylvania State Univ University Park","Continuing Grant","Marian Bocea","05/31/2027","$127,987.00","","nguyen@math.psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","128100","","$0.00","The main objective of this project is to investigate questions about the final states of matter consisting of a sufficiently large number of interacting particles such as plasmas in plasma physics and condensates in quantum mechanics. The research will advance the understanding of turbulence in plasma physics and quantum mechanics, provide foundational mathematics to tackle unsolved problems in physics, and push the boundaries of current mathematical techniques. The research will contribute new techniques to the theory of partial differential equations, mathematical physics, dynamical systems, and applied mathematics. The project includes activities aimed at training graduate students and young researchers.

The project will prove longstanding conjectures concerning the large time behavior of solutions to the mathematical mean field models that are used in plasma physics and quantum mechanics. The primary mathematical models under investigation include the relativistic Vlasov-Maxwell system and the Hartree equations used to model the nonlinear collective effects of infinitely many interacting particles. The research will rigorously validate nonlinear physical phenomena including plasma oscillations, phase transition, phase mixing, Landau damping, and the formation of coherent structures. The scattering theory as well as the formation of periodic structures for the Vlasov and Hartree equations near nontrivial translation-invariant equilibria will be established. The work of the project involves mathematical techniques from spectral theory, resolvent analysis, Fourier analysis, dispersive PDEs, probability, and statistical physics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348018","Well-posedness and Long-time Behavior of Dispersive Integrable Systems","DMS","ANALYSIS PROGRAM","07/01/2024","04/01/2024","Monica Visan","CA","University of California-Los Angeles","Continuing Grant","Marian Bocea","06/30/2027","$130,679.00","","visan@math.ucla.edu","10889 WILSHIRE BLVD STE 700","LOS ANGELES","CA","900244200","3107940102","MPS","128100","","$0.00","Integrable systems have long served as guides in the study of Hamiltonian partial differential equations. They arise as effective models of real physical systems, including in optics and many-body quantum mechanics. It is in the setting of completely integrable systems that solitons and multisolitons were first discovered. These structures have since found numerous applications in the applied sciences: for example, in fiber optics, solitons have been employed in the transmission of digital signals over long distances, while in biology, they are used to describe signal propagation in the nervous system and low-frequency collective motion in proteins. This project seeks to investigate both longstanding and newly introduced integrable models. Specifically, we seek to find the minimal conditions on the initial state under which one can construct global-in-time dynamics, investigate the (in)stability of special structures (such as solitons and multisolitons), and elucidate the long-time behavior of general solutions. The project provides significant research training opportunities for graduate students, who are integrated into the main objectives of the project.

The project investigates the following specific questions for the newly introduced continuum Calogero-Moser equations: (1) large data well-posedness in the scaling-invariant space, (2) scattering for both the defocusing model and the focusing equation for initial data with mass less than that of the ground state soliton, and (3) the determination of the blowup threshold in the focusing case. Further objectives include orbital and asymptotic stability of multisoliton solutions to the Benjamin-Ono equation in optimal well-posedness spaces, dispersive decay away from the soliton component for large solutions to this equation, and the construction of Gibbs dynamics for the Landau-Lifshitz model.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -45,8 +47,8 @@ "2400114","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Jose Carrion Muniz","TX","Texas Christian University","Standard Grant","Wing Suet Li","03/31/2027","$17,250.00","Travis Russell","j.carrion@tcu.edu","3101 BELLAIRE DRIVE NORTH","FORT WORTH","TX","761290001","8172577516","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400113","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Tao Mei","TX","Baylor University","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","Sheng Yin","tao_mei@baylor.edu","700 S UNIVERSITY PARKS DR","WACO","TX","767061003","2547103817","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

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

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

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

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

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

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

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337344","Conference: Madison Lectures in Harmonic Analysis","DMS","ANALYSIS PROGRAM","02/01/2024","01/23/2024","Brian Street","WI","University of Wisconsin-Madison","Standard Grant","Wing Suet Li","01/31/2025","$50,000.00","Andreas Seeger, Betsy Stovall","street@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","128100","7556","$0.00","The Madison Lectures in Harmonic Analysis, a two-week program encompassing a week-long international conference, followed by a week-long summer school on Fourier analysis and related topics, will take place on the campus of the University of Wisconsin-Madison, May 13-23, 2024.

The conference, to take place during the first week, May 13-17, 2024, is devoted to recent developments in the field of harmonic analysis, and will also encompass its many applications to other mathematical areas. The conference will bring 26 internationally-recognized mathematicians to each give a 50-minute talk and participate throughout the week. It will also support the participation of a number of early career researchers. All participants will have the opportunity to present their research in a poster session running throughout the week, and an open problem session will focus on future directions of research. The Spring School will take place during the second week, May 19-23, 2024. It will be led by two young experts, Drs. Durcik and Roos, with 10 to 15 participants at the graduate student or postdoctoral level. The participants will prepare presentations from a list of important papers in the field in advance and during the Spring School, they will study the papers together under the guidance of Drs. Durcik and Roos which will introduce these junior researchers to important recent developments in the field and gain a broad understanding of this every active area of mathematics. These two events are connected for synergistic purposes; junior researchers will be invited to the conference to learn more from more senior researchers, where they can present their own work in a poster session, and they can stay for the summer school for a more in-depth study. Thus, organizing the two events consecutively will provide enhanced opportunities for junior researchers to network, share their results, and learn from their peers and more senior researchers. The organizers have dedicated a substantial portion of the conference budget to the participation of early-career mathematicians. They will make special efforts to invite and encourage the participation of women and members of other underrepresented groups.

The topics to be discussed at the conference will include, but will not be limited to, the following important developments in harmonic analysis in recent years: the Fourier restriction and Bochner?Riesz problems; decoupling inequalities and local smoothing problems in Fourier analysis and their applications, applications to geometric measure theory; inequalities of Brascamp-Lieb type; sparse domination inequalities and their application to weighted norm theory; analysis problems for the Hamming cube; subelliptic partial differential equations and generalized pseudo-differential operators. The spring school will focus on the exciting and active area of multilinear singular integrals with applications to ergodic theory.

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Foundations/Awards-Foundations-2024.csv b/Foundations/Awards-Foundations-2024.csv index 1f80295..ab3505d 100644 --- a/Foundations/Awards-Foundations-2024.csv +++ b/Foundations/Awards-Foundations-2024.csv @@ -1,13 +1,14 @@ "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" -"2348208","Descriptive Set Theory and Computability","DMS","FOUNDATIONS","04/01/2024","04/04/2024","Andrew Marks","CA","University of California-Berkeley","Continuing Grant","Tomek Bartoszynski","06/30/2024","$118,647.00","","marks@math.berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","1268","","$0.00","An important problem encountered throughout mathematics is to completely classify some type of mathematical object by invariants. The field of descriptive set theory gives a general framework for studying these types of classification problems and comparing their relative difficulties. The PI proposes research in descriptive set theory and its connections with other mathematical fields including computability, operator algebras, topological dynamics, and ergodic theory. The PI will continue facilitating connections with these mathematical communities, and engaging with graduate students and young researchers. The project will support the training of graduate students at UCLA.

The PI proposes research on Weiss's question on amenability and hyperfiniteness using tools from Gromov's theory of asymptotic dimension. This approach to Weiss's question has already greatly extended and simplified prior results on the problem and clarified their proofs. This investigation has applications to topological dynamics and operator algebras. The PI also proposes research on classical geometrical paradoxes such as the Banach-Tarski paradox and Tarski's circle squaring problem. Recent advances in measurable combinatorics have led to new theorems giving measurable solutions to these problems using combinatorial techniques from the study of flows and matching problems on Borel graphs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2404023","Conference: 17th International Conference on Computability, Complexity and Randomness (CCR 2024)","DMS","FOUNDATIONS","01/15/2024","01/11/2024","Johanna Franklin","NY","Hofstra University","Standard Grant","Tomek Bartoszynski","12/31/2024","$32,630.00","","johanna.n.franklin@hofstra.edu","128 HOFSTRA UNIVERSITY","HEMPSTEAD","NY","115491280","5164636810","MPS","1268","7556","$0.00","This award supports the participation of early-career researchers and graduate students from the US at the 17th International Conference on Computability, Complexity and Randomness (CCR 2024), taking place March 11-15, 2024 at Nagoya University in Nagoya, Japan. The conferences in this series have as their central theme the study of randomness at the intersection of mathematics and computer science. Randomness is a natural informal notion in our lives and a formal, mathematical notion in probability theory, but here we seek to use different types of algorithms to quantify the levels of randomness that a mathematical object (such as an infinite binary string) can possess. Since the pandemic has made it far more difficult for American early-career researchers and graduate students to form international professional networks, it is extremely important for them to be able to travel, share their work, and build in-person collaborations with their colleagues abroad now.

The Computability, Complexity and Randomness conference series has been ongoing since 2004 and promotes research in algorithmic randomness, complexity theory, and computability theory as well as applications of algorithmic randomness to areas of mathematics such as ergodic theory and geometric measure theory and other areas of computability theory such as computable structure theory and reverse mathematics. This year, we are seeking to extend the focus of this conference and welcome researchers in related areas such as effective set theory and continuous combinatorics. It is a common venue for early-career researchers and graduate students to present their own work in contributed talks and encounter areas of research that are new to them, accelerating their professional development and enhancing their research networks. The conference website can be found at https://sites.google.com/view/ccr2024/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." -"2401789","Generalizations of the Ultrapower Axiom","DMS","FOUNDATIONS","07/01/2024","03/26/2024","Gabriel Goldberg","CA","University of California-Berkeley","Continuing Grant","Tomek Bartoszynski","06/30/2029","$80,000.00","","ggoldberg@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","1268","","$0.00","At the turn of the 20th century, mathematicians discovered a series of logical paradoxes that forced them to reevaluate the very foundation of the subject. The Zermelo-Frankel axioms of set theory (ZFC) emerged in the decades that followed as an answer to the question: what are the basic assumptions of mathematics? From the nine postulates of ZFC, one can derive all known theorems of mathematics. Despite this triumph of logic, a
major problem remains: there are mathematical problems that cannot be solved assuming the ZFC axioms alone. Most famously, Godel and Cohen showed that starting with these axioms, it is impossible to prove or refute Cantor's Continuum Hypothesis. One of the main goals of modern set theory is to analyze and classify axiomatic systems beyond ZFC that are strong enough to answer these undecidable questions. This project studies a framework for generating set-theoretic axioms by mining the structure of large cardinals in inner models of set theory. This project involves student training and conference organization and will have an impact on the philosophy of mathematics.

ZFC can be seen as an attempt to axiomatize the structure of the class of all sets. It is incomplete because our mathematical intuitions about arbitrary sets do not suffice to determine all their properties. To get around this problem, one can restrict attention to smaller subclasses of sets that are somehow canonical. Gödel discovered that there are subclasses that are rich enough to satisfy the ZFC axioms yet constrained enough that all their properties can be determined. Such a subclass is called a canonical inner model. For example, in canonical inner models, the Continuum Hypothesis is true. One obtains extensions of ZFC by considering the statements that hold in canonical inner models. One such statement is the Ultrapower Axiom, identified and studied by the PI in his dissertation. The axiom imposes a rich structure on the upper reaches of the hierarchy of infinite cardinals, or large cardinals, one of the central objects of study in set theory. Taking advantage of a recent breakthrough of Woodin, the PI was able to formulate strong generalizations of the Ultrapower Axiom, which this project proposes to study in hopes that they will shed further light on major open problems in inner model theory and large cardinals.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2414907","Conference: Travel Awards to Attend the Twentieth Latin American Symposium on Mathematical Logic","DMS","FOUNDATIONS","06/01/2024","03/26/2024","Russell Miller","CT","Association For Symbolic Logic","Standard Grant","Tomek Bartoszynski","05/31/2025","$40,000.00","Antonio Montalban","Russell.Miller@qc.cuny.edu","341 MANSFIELD RD","STORRS MANSFIELD","CT","062691009","8604863989","MPS","1268","7556","$0.00","This award supports up to sixteen US-based researchers in mathematical logic to attend the Twentieth Simposio Latino Americano de Logica Matematica, which will take place in Piriapolis, Uruguay, on July 1-5, 2024. These logicians, all based at universities in the USA, will include doctoral students, early-career researchers, and senior scholars in the discipline of logic. Many of them will give presentations about their own original research in this area, and all will have the opportunity to attend many other talks and to learn what progress is being made in research in logic across the Americas. The SLALM, which is held every two to three years, is the pre-eminent conference in logic in Latin America, which has proven over recent decades to be a region of great productivity in this field.

Logic in Latin America does not always focus on the same areas as it does in the US. There is a heavy concentration of non-classical logicians, especially in South American nations, making it important for external researchers to come to the SLALM in order to keep current on progress in this area. In contrast, computability theory is much more prominent in the US than in Latin America, and US-based researchers who attend the SLALM will be able to detail and explain recent advances in this area. Model theory is well represented in Colombia and Costa Rica in particular, as well as in the US, while set theorists are scattered all over the Americas, both North and South. There have often been fruitful collaborations between US and Latin American scholars in these fields, and we confidently expect this SLALM to produce many more.

Further information is available at https://xxslalm.cmat.edu.uy/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348371","Choiceless set theory","DMS","FOUNDATIONS","05/01/2024","03/27/2024","Jindrich Zapletal","FL","University of Florida","Continuing Grant","Tomek Bartoszynski","04/30/2027","$57,819.00","","zapletal@math.ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","1268","","$0.00","The project studies set theory (ZF) without the axiom of choice. The axiom of choice is known for providing objects which are central to mathematical theory yet are impossible to directly construct, such as ultrafilters on natural numbers. The PI recently developed a method which makes it possible to stratify such objects by intuitive complexity in detail regardless of which field of mathematics they originate. The result of the chart will be an extensive chart of such objects organized by this method. The project involves graduate students.

This project sets out to study choiceless set theory (ZF) at the level of sets of reals. The axiom of choice implies the existence of numerous such sets with useful combinatorial or algebraic properties, such as bases for vector spaces or fields, ultrafilters, or complicated partitions of Euclidean spaces. The PI recently developed a method which makes it possible to prove detailed ZF independence results regarding the existence of such sets, in effect stratifying them by intuitive complexity regardless of the field of mathematics they originate in. The result of the project will be an extensive chart of such objects organized by this method.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2400200","NSF-BSF Combinatorial Set Theory and PCF","DMS","FOUNDATIONS","07/01/2024","03/26/2024","Erick Eisworth","OH","Ohio University","Standard Grant","Tomek Bartoszynski","06/30/2027","$184,844.00","","eisworth@ohio.edu","1 OHIO UNIVERSITY","ATHENS","OH","457012942","7405932857","MPS","1268","","$0.00","This project supports advanced mathematical research and training in an underserved area of the United States (Appalachia) by leveraging funding from the NSF-BSF program to build an international partnership between the PI and a colleague at Ben-Gurion University in Israel. We will develop a horizontal collaborative structure bridging the two institutions to allow us to combine our expertise. Using a pedagogical model we pioneered during the pandemic, we will involve students in both countries in collaborative research centered on the mathematical research of the senior personnel in the grant.

The research component of the project is centered on PCF(Possible CoFinality) theory, a body of work developed by Shelah to analyze cardinal arithmetic in set theory. Shelah obtained fantastic results in set theory and other fields by using these techniques, but even after three decades, the full implications of PCF theory at singular fixed points are not fully understood. Our project addresses this gap by continuing the recent work of the PI and his Israeli counterpart, with a focus on mapping out the extent to which PCF theory imposes constraints in cardinal arithmetic and infinitary Ramsey 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." -"2348792","Computable model theory and invariant descriptive computability theory","DMS","FOUNDATIONS","07/01/2024","03/22/2024","Uri Andrews","WI","University of Wisconsin-Madison","Standard Grant","Tomek Bartoszynski","06/30/2027","$290,000.00","","andrews@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","1268","","$0.00","Mathematical logic grew out of a need to develop rigorous foundations for mathematics. Within mathematical logic, three major subfields are studied. Model theory understands mathematical objects by considering them through the lens of a formal language. Computability theory understands mathematical objects by considering them through the lens of computational complexity. Set theory understands mathematical objects through the foundational axioms of mathematics and how those axioms imply the object?s existence. This project focuses on some connections between computability theory and the other two subfields of logic. Regarding model theory, the project involves exploring the phenomenon when two mathematical objects look the same in terms of their formal languages, but one can be computed while the other cannot. In set theory, there is a rich theory exploring the complexity of 2-dimensional sets in terms of constructively embedding one into another. These embeddings are constructible in terms of the basic set-theoretic operations of unions and complements, but they may not be computable. The project will explore an analogous theory where one considers embeddings that must be computable. This project involves work with undergraduate and graduate students.

The computable spectrum of a first-order theory asks which dimensions of models of that theory are computable. The spectrum problem in computable model theory, which has been a major open problem since the 70s, asks for which sets may be computable spectra of uncountably categorical theories, with a focus on strongly minimal theories. In this project, the aim is to give a reduction of the problem from a fully general framework down to the locally modular strongly minimal theories, which are geometrically tame and are closely related to groups. From there, the hope is to be able to give concrete answers as to which sets are spectra. Separately, this project will examine computable reduction on equivalence relations. One major direction is to use this complexity notion to examine algebraic decision problems in detail. In the past, the Turing degrees have been used to analyze algebraic decision problems, but these form a coarse yardstick, so all computably enumerable degrees seem to contain all natural algebraic decision problems. Using computable reductions on equivalence relations, there should be a much more interesting structure emerging.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348881","Applied Abstract Elementary Classes","DMS","FOUNDATIONS","07/01/2024","03/21/2024","Marcos Mazari Armida","TX","Baylor University","Standard Grant","Tomek Bartoszynski","06/30/2027","$130,000.00","","marcos_mazari@baylor.edu","700 S UNIVERSITY PARKS DR","WACO","TX","767061003","2547103817","MPS","1268","","$0.00","Model theory is a branch of mathematical logic that studies and classifies classes of mathematical structures, such as the class of vector spaces, graphs, and groups. Classical model theory focuses on studying classes of structures that can be defined by sets of finite sentences (first-order logic). Although many classes are defined by sets of finite sentences, there are many that can only be defined using sets of infinite sentences (infinitary logic). The setting of this project is that of abstract elementary classes (AECs for short) which is a setting where one can study classes defined by sets of infinite sentences. AECs have been studied since the late seventies, and recently, the theory has developed very rapidly. The objective of this project is to continue the PI's work on finding interactions and applications of AECs to algebra.

More precisely, the project focuses on finding interactions and applications of AECs to module theory and acts (polygons, G-sets) theory. The first part of the project focuses on continuing the development of AECs of modules. A key problem is to determine the stability behavior of AECs of modules with pure embeddings. The second part of the project focuses on developing a parallel theory for acts to what the PI has been able to accomplish for modules. A fundamental notion that will be studied on AECs of acts is independence relations (non-forking for AECs). The PI expects that these studies will help him better understand the strengths and limitations of independence relations, so he can apply them in other settings in the future.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348891","Computability and the absolute Galois group of the rational numbers","DMS","FOUNDATIONS","09/01/2024","03/21/2024","Russell Miller","NY","CUNY Queens College","Continuing Grant","Tomek Bartoszynski","08/31/2027","$124,676.00","","Russell.Miller@qc.cuny.edu","6530 KISSENA BLVD","FLUSHING","NY","113671575","7189975400","MPS","1268","","$0.00","The absolute Galois group Gal(Q) is well-known throughout mathematics. Its elements are precisely the symmetries of the algebraic closure of the rational numbers. In practice, though, this group is particularly difficult to study. There are continuum-many of these symmetries, most of which cannot be computed by any computer (or Turing machine) running any finite-length program whatsoever. However, the symmetries that mathematicians encounter on a regular basis are essentially always computable -- perhaps because these are fundamental to the group, or perhaps just because noncomputable symmetries are naturally more difficult to examine and work with. This project aims to determine just how much difference there is between the computable symmetries (as a group) and the larger group of all symmetries. The research work lies at the interface of logic and number theory and is likely to attract the interest of both communities. Graduate students from CUNY Graduate Center will participate in this project.

An analogous situation exists with the field of all real numbers: only countably many real numbers have computable decimal expansions, so the vast majority of real numbers are noncomputable, yet the computable ones are the only ones ever encountered in daily life. Here, it is known that the computable real numbers form a subfield extremely similar to the full field of all real numbers, an elementary subfield with exactly the same first-order properties. This grant will fund research to attempt to determine whether Gal(Q) is analogous in this way: do the computable symmetries form an elementary subgroup of the full group? (Or, at a minimum, are the two elementarily equivalent?) If so, then mathematicians should be able to determine many results about the full group just by examining the computable symmetries, which are far more accessible. If not, that would suggest that the absolute Galois group is a thornier object than the field of real numbers, with its noncomputable symmetries somehow essential to its character. However, even then, it is possible that the subgroup might be elementary for relatively simple properties (e.g., purely existential statements about the group), in which case this project will attempt to find the first level at which the subgroup stops imitating the full group.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401437","Conference: Southeastern Logic Symposium","DMS","FOUNDATIONS","02/15/2024","02/02/2024","Jindrich Zapletal","FL","University of Florida","Continuing Grant","Tomek Bartoszynski","01/31/2027","$30,000.00","Robin Tucker-Drob, Dana Bartosova","zapletal@math.ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","1268","7556","$0.00","The proposal is used to support the Southeastern Logic Symposium (SEALS), an annual series of weekend conferences in mathematical logic held at University of Florida during the first weekend of March. In each installment of the series, the conference brings together researchers in two selected subfields of mathematical logic to foster cooperation and exchange of information. Each installment will host three senior plenary speakers and about 35 participants in the early stages of their career giving talks in two special sessions. There are satellite colloquium talks on the shoulders of the conference weekend as well, encouraging the participants to stay longer and cooperate on their research projects.

The proposal is used to support the Southeastern Logic Symposium (SEALS), an annual series of weekend conferences in mathematical logic held at University of Florida. In each installment of the series, the conference brings together researchers in two selected subfields of mathematical logic to foster cooperation and exchange of information. The paired subfields may include model theory/set theoretic dynamics, or descriptive set theory/computability, or choiceless set theory/Polish group actions. The target audience for the conference includes mainly researchers from advanced graduate students to postdocs to early career professors without personal travel grants. The website for the 2024 edition is https://people.clas.ufl.edu/r-tuckerdrob/seals-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." -"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","1267, 1268","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." -"2339018","CAREER: Compactness in Incompact Worlds","DMS","FOUNDATIONS","07/01/2024","02/02/2024","William Boney","TX","Texas State University - San Marcos","Continuing Grant","Tomek Bartoszynski","06/30/2029","$100,847.00","","wb1011@txstate.edu","601 UNIVERSITY DR","SAN MARCOS","TX","786664684","5122452314","MPS","1268","1045","$0.00","The field of model theory studies classes of structures: groups, fields, graphs. This is a broad field to study, so important distinctions are made based on how the class of structures is described (or axiomatized). If the class is describable in first-order logic, it is called an elementary class. First-order logic has many powerful properties, especially the property of compactness. Compactness allows model theorists to build structures with exotic properties and has driven much of the model theory of elementary classes, most notably classification theory. However, many classes of structures are not describable in first-order logic (these are called nonelementary classes). Lacking compactness, the development of nonelementary model theory and classification theory has proceeded much slower than its elementary counterpart. Recent work in nonelementary classes has shown that various fragments of compactness can still hold in some nonelementary classes and are still powerful enough to prove various results of elementary classification theory. The PI will develop more of these fragments in nonelementary classes. Additionally, the PI will run a program to build research infrastructure at their home institution (an R2 institution and HSI). This program will support undergraduates conducting research in logic, supported by a speaker series that will build connections between expert logicians and faculty and students.

This research will develop fragments of compactness in a variety of ways. From category theory, methods from accessible categories and from topoi will be used to find compactness principles in certain nonelementary classes. Drawing on model theory and set theory, generalized indiscernibles and generalizations of the Erdos-Rado theorem will find compactness principles that hold in all nonelementary classes. Further drawing on set theory, the connections between large cardinals and compactness principles (along with other model-theoretic ideas) will be extended. The connections formed in categorical logic will be extended to higher category theory to open new areas for model 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." +"2401789","Generalizations of the Ultrapower Axiom","DMS","FOUNDATIONS","07/01/2024","03/26/2024","Gabriel Goldberg","CA","University of California-Berkeley","Continuing Grant","Tomek Bartoszynski","06/30/2029","$80,000.00","","ggoldberg@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126800","","$0.00","At the turn of the 20th century, mathematicians discovered a series of logical paradoxes that forced them to reevaluate the very foundation of the subject. The Zermelo-Frankel axioms of set theory (ZFC) emerged in the decades that followed as an answer to the question: what are the basic assumptions of mathematics? From the nine postulates of ZFC, one can derive all known theorems of mathematics. Despite this triumph of logic, a
major problem remains: there are mathematical problems that cannot be solved assuming the ZFC axioms alone. Most famously, Godel and Cohen showed that starting with these axioms, it is impossible to prove or refute Cantor's Continuum Hypothesis. One of the main goals of modern set theory is to analyze and classify axiomatic systems beyond ZFC that are strong enough to answer these undecidable questions. This project studies a framework for generating set-theoretic axioms by mining the structure of large cardinals in inner models of set theory. This project involves student training and conference organization and will have an impact on the philosophy of mathematics.

ZFC can be seen as an attempt to axiomatize the structure of the class of all sets. It is incomplete because our mathematical intuitions about arbitrary sets do not suffice to determine all their properties. To get around this problem, one can restrict attention to smaller subclasses of sets that are somehow canonical. Gödel discovered that there are subclasses that are rich enough to satisfy the ZFC axioms yet constrained enough that all their properties can be determined. Such a subclass is called a canonical inner model. For example, in canonical inner models, the Continuum Hypothesis is true. One obtains extensions of ZFC by considering the statements that hold in canonical inner models. One such statement is the Ultrapower Axiom, identified and studied by the PI in his dissertation. The axiom imposes a rich structure on the upper reaches of the hierarchy of infinite cardinals, or large cardinals, one of the central objects of study in set theory. Taking advantage of a recent breakthrough of Woodin, the PI was able to formulate strong generalizations of the Ultrapower Axiom, which this project proposes to study in hopes that they will shed further light on major open problems in inner model theory and large cardinals.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2416669","Conference: School and Workshop on Univalent Mathematics","DMS","FOUNDATIONS","07/01/2024","04/09/2024","Kuen-Bang Hou","MN","University of Minnesota-Twin Cities","Standard Grant","Tomek Bartoszynski","06/30/2025","$49,959.00","","kbh@umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","126800","7556","$0.00","This award supports participants of the Fourth School and Workshop on Univalent Mathematics during 2024/7/28-8/2 at the University of Minnesota. The ""Univalent Foundations,"" devised by Fields Medalist Vladimir Voevodsky, is an alternative foundation for mathematics that is particularly amenable to formal computer verification. Mathematical proofs formulated in the Univalent Foundations can thus be checked by computers automatically. This workshop will be the first one in the series in the United States, and aims to train the participants in the theory and practice of the Univalent Foundations and foster research activities in related areas.

The Univalent Foundations offers certain novel features:
1. It is based on type theory, a formal language that arguably matches everyday mathematics better and supports effective computer checking.
2. Traditional sets from set theory can still be represented as particular types.
3. Equalities between elements can have richer structures suitable for representing, for example, different isomorphisms between two isomorphic sets.
4. The univalence principle is built-in, which formally asserts that isomorphic structures must be treated as equal, and thus, all definitions automatically respect isomorphisms.

Participants will learn how to express mathematical ideas using the Univalent Foundations in a computer system (proof assistant) that can offer immediate feedback. More information about the event is available at https://unimath.github.io/minneapolis2024/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348208","Descriptive Set Theory and Computability","DMS","FOUNDATIONS","04/01/2024","04/04/2024","Andrew Marks","CA","University of California-Berkeley","Continuing Grant","Tomek Bartoszynski","06/30/2024","$118,647.00","","marks@math.berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126800","","$0.00","An important problem encountered throughout mathematics is to completely classify some type of mathematical object by invariants. The field of descriptive set theory gives a general framework for studying these types of classification problems and comparing their relative difficulties. The PI proposes research in descriptive set theory and its connections with other mathematical fields including computability, operator algebras, topological dynamics, and ergodic theory. The PI will continue facilitating connections with these mathematical communities, and engaging with graduate students and young researchers. The project will support the training of graduate students at UCLA.

The PI proposes research on Weiss's question on amenability and hyperfiniteness using tools from Gromov's theory of asymptotic dimension. This approach to Weiss's question has already greatly extended and simplified prior results on the problem and clarified their proofs. This investigation has applications to topological dynamics and operator algebras. The PI also proposes research on classical geometrical paradoxes such as the Banach-Tarski paradox and Tarski's circle squaring problem. Recent advances in measurable combinatorics have led to new theorems giving measurable solutions to these problems using combinatorial techniques from the study of flows and matching problems on Borel graphs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2414907","Conference: Travel Awards to Attend the Twentieth Latin American Symposium on Mathematical Logic","DMS","FOUNDATIONS","06/01/2024","03/26/2024","Russell Miller","CT","Association For Symbolic Logic","Standard Grant","Tomek Bartoszynski","05/31/2025","$40,000.00","Antonio Montalban","Russell.Miller@qc.cuny.edu","341 MANSFIELD RD","STORRS MANSFIELD","CT","062691009","8604863989","MPS","126800","7556","$0.00","This award supports up to sixteen US-based researchers in mathematical logic to attend the Twentieth Simposio Latino Americano de Logica Matematica, which will take place in Piriapolis, Uruguay, on July 1-5, 2024. These logicians, all based at universities in the USA, will include doctoral students, early-career researchers, and senior scholars in the discipline of logic. Many of them will give presentations about their own original research in this area, and all will have the opportunity to attend many other talks and to learn what progress is being made in research in logic across the Americas. The SLALM, which is held every two to three years, is the pre-eminent conference in logic in Latin America, which has proven over recent decades to be a region of great productivity in this field.

Logic in Latin America does not always focus on the same areas as it does in the US. There is a heavy concentration of non-classical logicians, especially in South American nations, making it important for external researchers to come to the SLALM in order to keep current on progress in this area. In contrast, computability theory is much more prominent in the US than in Latin America, and US-based researchers who attend the SLALM will be able to detail and explain recent advances in this area. Model theory is well represented in Colombia and Costa Rica in particular, as well as in the US, while set theorists are scattered all over the Americas, both North and South. There have often been fruitful collaborations between US and Latin American scholars in these fields, and we confidently expect this SLALM to produce many more.

Further information is available at https://xxslalm.cmat.edu.uy/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348792","Computable model theory and invariant descriptive computability theory","DMS","FOUNDATIONS","07/01/2024","03/22/2024","Uri Andrews","WI","University of Wisconsin-Madison","Standard Grant","Tomek Bartoszynski","06/30/2027","$290,000.00","","andrews@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","126800","","$0.00","Mathematical logic grew out of a need to develop rigorous foundations for mathematics. Within mathematical logic, three major subfields are studied. Model theory understands mathematical objects by considering them through the lens of a formal language. Computability theory understands mathematical objects by considering them through the lens of computational complexity. Set theory understands mathematical objects through the foundational axioms of mathematics and how those axioms imply the object?s existence. This project focuses on some connections between computability theory and the other two subfields of logic. Regarding model theory, the project involves exploring the phenomenon when two mathematical objects look the same in terms of their formal languages, but one can be computed while the other cannot. In set theory, there is a rich theory exploring the complexity of 2-dimensional sets in terms of constructively embedding one into another. These embeddings are constructible in terms of the basic set-theoretic operations of unions and complements, but they may not be computable. The project will explore an analogous theory where one considers embeddings that must be computable. This project involves work with undergraduate and graduate students.

The computable spectrum of a first-order theory asks which dimensions of models of that theory are computable. The spectrum problem in computable model theory, which has been a major open problem since the 70s, asks for which sets may be computable spectra of uncountably categorical theories, with a focus on strongly minimal theories. In this project, the aim is to give a reduction of the problem from a fully general framework down to the locally modular strongly minimal theories, which are geometrically tame and are closely related to groups. From there, the hope is to be able to give concrete answers as to which sets are spectra. Separately, this project will examine computable reduction on equivalence relations. One major direction is to use this complexity notion to examine algebraic decision problems in detail. In the past, the Turing degrees have been used to analyze algebraic decision problems, but these form a coarse yardstick, so all computably enumerable degrees seem to contain all natural algebraic decision problems. Using computable reductions on equivalence relations, there should be a much more interesting structure emerging.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2404023","Conference: 17th International Conference on Computability, Complexity and Randomness (CCR 2024)","DMS","FOUNDATIONS","01/15/2024","01/11/2024","Johanna Franklin","NY","Hofstra University","Standard Grant","Tomek Bartoszynski","12/31/2024","$32,630.00","","johanna.n.franklin@hofstra.edu","128 HOFSTRA UNIVERSITY","HEMPSTEAD","NY","115491280","5164636810","MPS","126800","7556","$0.00","This award supports the participation of early-career researchers and graduate students from the US at the 17th International Conference on Computability, Complexity and Randomness (CCR 2024), taking place March 11-15, 2024 at Nagoya University in Nagoya, Japan. The conferences in this series have as their central theme the study of randomness at the intersection of mathematics and computer science. Randomness is a natural informal notion in our lives and a formal, mathematical notion in probability theory, but here we seek to use different types of algorithms to quantify the levels of randomness that a mathematical object (such as an infinite binary string) can possess. Since the pandemic has made it far more difficult for American early-career researchers and graduate students to form international professional networks, it is extremely important for them to be able to travel, share their work, and build in-person collaborations with their colleagues abroad now.

The Computability, Complexity and Randomness conference series has been ongoing since 2004 and promotes research in algorithmic randomness, complexity theory, and computability theory as well as applications of algorithmic randomness to areas of mathematics such as ergodic theory and geometric measure theory and other areas of computability theory such as computable structure theory and reverse mathematics. This year, we are seeking to extend the focus of this conference and welcome researchers in related areas such as effective set theory and continuous combinatorics. It is a common venue for early-career researchers and graduate students to present their own work in contributed talks and encounter areas of research that are new to them, accelerating their professional development and enhancing their research networks. The conference website can be found at https://sites.google.com/view/ccr2024/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." +"2400200","NSF-BSF Combinatorial Set Theory and PCF","DMS","FOUNDATIONS","07/01/2024","03/26/2024","Erick Eisworth","OH","Ohio University","Standard Grant","Tomek Bartoszynski","06/30/2027","$184,844.00","","eisworth@ohio.edu","1 OHIO UNIVERSITY","ATHENS","OH","457012942","7405932857","MPS","126800","","$0.00","This project supports advanced mathematical research and training in an underserved area of the United States (Appalachia) by leveraging funding from the NSF-BSF program to build an international partnership between the PI and a colleague at Ben-Gurion University in Israel. We will develop a horizontal collaborative structure bridging the two institutions to allow us to combine our expertise. Using a pedagogical model we pioneered during the pandemic, we will involve students in both countries in collaborative research centered on the mathematical research of the senior personnel in the grant.

The research component of the project is centered on PCF(Possible CoFinality) theory, a body of work developed by Shelah to analyze cardinal arithmetic in set theory. Shelah obtained fantastic results in set theory and other fields by using these techniques, but even after three decades, the full implications of PCF theory at singular fixed points are not fully understood. Our project addresses this gap by continuing the recent work of the PI and his Israeli counterpart, with a focus on mapping out the extent to which PCF theory imposes constraints in cardinal arithmetic and infinitary Ramsey 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." +"2348371","Choiceless set theory","DMS","FOUNDATIONS","05/01/2024","03/27/2024","Jindrich Zapletal","FL","University of Florida","Continuing Grant","Tomek Bartoszynski","04/30/2027","$57,819.00","","zapletal@math.ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","126800","","$0.00","The project studies set theory (ZF) without the axiom of choice. The axiom of choice is known for providing objects which are central to mathematical theory yet are impossible to directly construct, such as ultrafilters on natural numbers. The PI recently developed a method which makes it possible to stratify such objects by intuitive complexity in detail regardless of which field of mathematics they originate. The result of the chart will be an extensive chart of such objects organized by this method. The project involves graduate students.

This project sets out to study choiceless set theory (ZF) at the level of sets of reals. The axiom of choice implies the existence of numerous such sets with useful combinatorial or algebraic properties, such as bases for vector spaces or fields, ultrafilters, or complicated partitions of Euclidean spaces. The PI recently developed a method which makes it possible to prove detailed ZF independence results regarding the existence of such sets, in effect stratifying them by intuitive complexity regardless of the field of mathematics they originate in. The result of the project will be an extensive chart of such objects organized by this method.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348881","Applied Abstract Elementary Classes","DMS","FOUNDATIONS","07/01/2024","03/21/2024","Marcos Mazari Armida","TX","Baylor University","Standard Grant","Tomek Bartoszynski","06/30/2027","$130,000.00","","marcos_mazari@baylor.edu","700 S UNIVERSITY PARKS DR","WACO","TX","767061003","2547103817","MPS","126800","","$0.00","Model theory is a branch of mathematical logic that studies and classifies classes of mathematical structures, such as the class of vector spaces, graphs, and groups. Classical model theory focuses on studying classes of structures that can be defined by sets of finite sentences (first-order logic). Although many classes are defined by sets of finite sentences, there are many that can only be defined using sets of infinite sentences (infinitary logic). The setting of this project is that of abstract elementary classes (AECs for short) which is a setting where one can study classes defined by sets of infinite sentences. AECs have been studied since the late seventies, and recently, the theory has developed very rapidly. The objective of this project is to continue the PI's work on finding interactions and applications of AECs to algebra.

More precisely, the project focuses on finding interactions and applications of AECs to module theory and acts (polygons, G-sets) theory. The first part of the project focuses on continuing the development of AECs of modules. A key problem is to determine the stability behavior of AECs of modules with pure embeddings. The second part of the project focuses on developing a parallel theory for acts to what the PI has been able to accomplish for modules. A fundamental notion that will be studied on AECs of acts is independence relations (non-forking for AECs). The PI expects that these studies will help him better understand the strengths and limitations of independence relations, so he can apply them in other settings in the future.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348891","Computability and the absolute Galois group of the rational numbers","DMS","FOUNDATIONS","09/01/2024","03/21/2024","Russell Miller","NY","CUNY Queens College","Continuing Grant","Tomek Bartoszynski","08/31/2027","$124,676.00","","Russell.Miller@qc.cuny.edu","6530 KISSENA BLVD","FLUSHING","NY","113671575","7189975400","MPS","126800","","$0.00","The absolute Galois group Gal(Q) is well-known throughout mathematics. Its elements are precisely the symmetries of the algebraic closure of the rational numbers. In practice, though, this group is particularly difficult to study. There are continuum-many of these symmetries, most of which cannot be computed by any computer (or Turing machine) running any finite-length program whatsoever. However, the symmetries that mathematicians encounter on a regular basis are essentially always computable -- perhaps because these are fundamental to the group, or perhaps just because noncomputable symmetries are naturally more difficult to examine and work with. This project aims to determine just how much difference there is between the computable symmetries (as a group) and the larger group of all symmetries. The research work lies at the interface of logic and number theory and is likely to attract the interest of both communities. Graduate students from CUNY Graduate Center will participate in this project.

An analogous situation exists with the field of all real numbers: only countably many real numbers have computable decimal expansions, so the vast majority of real numbers are noncomputable, yet the computable ones are the only ones ever encountered in daily life. Here, it is known that the computable real numbers form a subfield extremely similar to the full field of all real numbers, an elementary subfield with exactly the same first-order properties. This grant will fund research to attempt to determine whether Gal(Q) is analogous in this way: do the computable symmetries form an elementary subgroup of the full group? (Or, at a minimum, are the two elementarily equivalent?) If so, then mathematicians should be able to determine many results about the full group just by examining the computable symmetries, which are far more accessible. If not, that would suggest that the absolute Galois group is a thornier object than the field of real numbers, with its noncomputable symmetries somehow essential to its character. However, even then, it is possible that the subgroup might be elementary for relatively simple properties (e.g., purely existential statements about the group), in which case this project will attempt to find the first level at which the subgroup stops imitating the full group.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401437","Conference: Southeastern Logic Symposium","DMS","FOUNDATIONS","02/15/2024","02/02/2024","Jindrich Zapletal","FL","University of Florida","Continuing Grant","Tomek Bartoszynski","01/31/2027","$30,000.00","Robin Tucker-Drob, Dana Bartosova","zapletal@math.ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","126800","7556","$0.00","The proposal is used to support the Southeastern Logic Symposium (SEALS), an annual series of weekend conferences in mathematical logic held at University of Florida during the first weekend of March. In each installment of the series, the conference brings together researchers in two selected subfields of mathematical logic to foster cooperation and exchange of information. Each installment will host three senior plenary speakers and about 35 participants in the early stages of their career giving talks in two special sessions. There are satellite colloquium talks on the shoulders of the conference weekend as well, encouraging the participants to stay longer and cooperate on their research projects.

The proposal is used to support the Southeastern Logic Symposium (SEALS), an annual series of weekend conferences in mathematical logic held at University of Florida. In each installment of the series, the conference brings together researchers in two selected subfields of mathematical logic to foster cooperation and exchange of information. The paired subfields may include model theory/set theoretic dynamics, or descriptive set theory/computability, or choiceless set theory/Polish group actions. The target audience for the conference includes mainly researchers from advanced graduate students to postdocs to early career professors without personal travel grants. The website for the 2024 edition is https://people.clas.ufl.edu/r-tuckerdrob/seals-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." +"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." +"2339018","CAREER: Compactness in Incompact Worlds","DMS","FOUNDATIONS","07/01/2024","02/02/2024","William Boney","TX","Texas State University - San Marcos","Continuing Grant","Tomek Bartoszynski","06/30/2029","$100,847.00","","wb1011@txstate.edu","601 UNIVERSITY DR","SAN MARCOS","TX","786664684","5122452314","MPS","126800","1045","$0.00","The field of model theory studies classes of structures: groups, fields, graphs. This is a broad field to study, so important distinctions are made based on how the class of structures is described (or axiomatized). If the class is describable in first-order logic, it is called an elementary class. First-order logic has many powerful properties, especially the property of compactness. Compactness allows model theorists to build structures with exotic properties and has driven much of the model theory of elementary classes, most notably classification theory. However, many classes of structures are not describable in first-order logic (these are called nonelementary classes). Lacking compactness, the development of nonelementary model theory and classification theory has proceeded much slower than its elementary counterpart. Recent work in nonelementary classes has shown that various fragments of compactness can still hold in some nonelementary classes and are still powerful enough to prove various results of elementary classification theory. The PI will develop more of these fragments in nonelementary classes. Additionally, the PI will run a program to build research infrastructure at their home institution (an R2 institution and HSI). This program will support undergraduates conducting research in logic, supported by a speaker series that will build connections between expert logicians and faculty and students.

This research will develop fragments of compactness in a variety of ways. From category theory, methods from accessible categories and from topoi will be used to find compactness principles in certain nonelementary classes. Drawing on model theory and set theory, generalized indiscernibles and generalizations of the Erdos-Rado theorem will find compactness principles that hold in all nonelementary classes. Further drawing on set theory, the connections between large cardinals and compactness principles (along with other model-theoretic ideas) will be extended. The connections formed in categorical logic will be extended to higher category theory to open new areas for model 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." diff --git a/Topology/Awards-Topology-2024.csv b/Topology/Awards-Topology-2024.csv index 2dd1ed7..077e849 100644 --- a/Topology/Awards-Topology-2024.csv +++ b/Topology/Awards-Topology-2024.csv @@ -1,33 +1,34 @@ "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" "2404322","Conference: Young Geometric Group Theory XII","DMS","TOPOLOGY","04/15/2024","04/05/2024","Rylee Lyman","NJ","Rutgers University Newark","Standard Grant","Swatee Naik","03/31/2025","$35,000.00","","rylee.lyman@rutgers.edu","123 WASHINGTON ST","NEWARK","NJ","071023026","9739720283","MPS","126700","7556","$0.00","This award will provide partial support for U.S.-based participants in ?Young Geometric Group Theory XII?, a conference which will be held in Bristol, U.K. from April 8 to April 12, 2024. The Young Geometric Group Theory conference series is the largest annual conference in geometric group theory, and unique among similar events for being primarily aimed at graduate students and early career researchers. The purpose of the conference is to expose early career researchers to cutting edge research in the field, provide them opportunities to share their work, and to facilitate new collaborations. The conference includes mini-courses by established experts, plenary talks by selected senior and early career researchers, lighting talks and a poster session for participants, small-group informal discussions, and panel discussions, which will focus on career opportunities as well as equity, diversity and inclusion. Participating in a conference in this series may be transformative for a young researcher?s career, and NSF support makes attendance accessible for U.S.-based participants.

The mini-courses for this conference are Cubical Geometry by Mark Hagen, Convergence Groups, Three-Manifolds and Anosov-Like Actions by Kathryn Mann, and Analytic/Topological Obstructions to Coarse Embeddings by Romain Tessera. Each of these lectures, along with four senior plenary talks will present an overview of the topic and expose participants to tools and recent developments in the field. Additionally, four plenary talks by early career researchers will broaden the scope of the conference and present new developments in the field from researchers closer to the participants in career stage. More information can be found on the conference?s website: https://sites.google.com/view/yggt2024

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2349755","Conference: Mid-Atlantic Topology Conference 2024","DMS","TOPOLOGY","03/01/2024","02/22/2024","Benjamin Knudsen","MA","Northeastern University","Standard Grant","Swatee Naik","02/28/2025","$30,000.00","Jose Perea, Iva Halacheva, Thomas Brazelton","b.knudsen@northeastern.edu","360 HUNTINGTON AVE","BOSTON","MA","021155005","6173733004","MPS","126700","7556","$0.00","This National Science Foundation award provides funding for participants of the Mid-Atlantic Topology Conference, which will take place March 23 and 24, 2024 at Northeastern University in Boston. The conference will focus on a broad overview of trends in topology currently at the forefront of research, including geometric group theory, geometric and topological data analysis, applied and computational topology, higher category theory, and motivic homotopy theory. This conference will further advance the growing diversity within algebraic topology, as well as the strength and coherence of the East Coast topology community. It is the latest iteration in a series of recurring conferences aimed at uniting the increasingly active topology groups in this geographical area.

The conference will feature nine 45-minute talks spread over two days. Speakers have been chosen with particular emphasis on gender representation. They are predominantly early career researchers and hail from public and private institutions alike. Advertising and funding will be targeted to prioritize inclusion of participants from underrepresented populations, continuing a strategy proven to be successful in the last iteration of the conference. The conference will provide graduate students and postdoctoral researchers with invaluable networking and community building opportunities and will strengthen the regional fabric of the field of topology. Further
information is available at https://sites.google.com/northeastern.edu/matc2024/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." -"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." +"2427220","Computations in Classical and Motivic Stable Homotopy Theory","DMS","TOPOLOGY","04/01/2024","04/09/2024","Eva Belmont","OH","Case Western Reserve University","Standard Grant","Swatee Naik","06/30/2025","$106,619.00","","eva.belmont@case.edu","10900 EUCLID AVE","CLEVELAND","OH","441061712","2163684510","MPS","126700","","$0.00","Algebraic topology is a field of mathematics that involves using algebra and category theory to study properties of geometric objects that do not change when those objects are deformed. A central challenge is to classify all maps from spheres to other spheres, where two maps are considered equivalent if one can be deformed to the other. The equivalence classes of these maps are called the homotopy groups of spheres, and collectively they form one of the deepest and most central objects in the field. Historically, much important theory has arisen out of attempts to compute more homotopy groups of spheres and understand patterns within them. This project involves furthering knowledge of the homotopy groups of spheres, using old and new techniques as well as computer calculations. The project also involves studying an analogue of these groups in algebraic geometry; this falls under a relatively new and actively developed area called motivic homotopy theory, which applies techniques in algebraic topology to study algebraic geometry. The broader impacts of this project center around supporting the local mathematics community through mentoring and promoting diversity. The principal investigator will help build the nascent homotopy theory community at the university and promote women and minorities in the subject through seminar organization and mentoring.

One of the main planned projects is a large-scale effort to compute the homotopy groups of spheres at the prime 3 in a range, using old and new techniques such as the Adams-Novikov spectral sequence as well as infinite descent machinery. This work will be aided by computer calculations, which short-circuits some of the technical difficulties encountered in previous attempts. Another main group of projects concerns computing the analogue of the stable homotopy groups of spheres in the world of R-motivic homotopy theory. This represents a continuation of prior work of the PI and collaborator; the plan is to supplement the techniques used in that work with computer calculations and a new tool, the slice spectral sequence. A third project concerns theory and spectral sequence computations aimed at computing the cohomology of profinite groups such as special linear groups and Morava stabilizer 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." "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." -"2341618","Conference: Lloyd Roeling Conference in Topology at UL Lafayette","DMS","TOPOLOGY","01/01/2024","12/18/2023","Robin Koytcheff","LA","University of Louisiana at Lafayette","Standard Grant","Swatee Naik","12/31/2024","$14,931.00","Daniel Davis, Philip Hackney","koytcheff@louisiana.edu","104 E UNIVERSITY AVE","LAFAYETTE","LA","705032014","3374825811","MPS","126700","7556, 9150","$0.00","This award provides support for the Lloyd Roeling Conference in Topology to be held March 15-17, 2024 at the University of Louisiana at Lafayette. The Lloyd Roeling Conference is an annual tradition since 1970 and rotates among four subfields in mathematics and statistics. This iteration will provide a forum for algebraic topology in the South and will support the mathematical and professional development of graduate students and postdoctoral fellows in the EPSCoR state of Louisiana as well as nearby regions.

The topic of the conference will be algebraic topology, broadly interpreted, including topics in chromatic homotopy theory, configuration spaces, equivariant homotopy theory, higher category theory, loop spaces and string topology, and tropical geometry. The conference will feature eight plenary lectures as well as short contributed talks. Accessible talks across a variety of areas will encourage cross-pollination between subfields. The conference web page is https://userweb.ucs.louisiana.edu/~c00424469/lr2024/

This award reflects 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." +"2341618","Conference: Lloyd Roeling Conference in Topology at UL Lafayette","DMS","TOPOLOGY","01/01/2024","12/18/2023","Robin Koytcheff","LA","University of Louisiana at Lafayette","Standard Grant","Swatee Naik","12/31/2024","$14,931.00","Philip Hackney, Daniel Davis","koytcheff@louisiana.edu","104 E UNIVERSITY AVE","LAFAYETTE","LA","705032014","3374825811","MPS","126700","7556, 9150","$0.00","This award provides support for the Lloyd Roeling Conference in Topology to be held March 15-17, 2024 at the University of Louisiana at Lafayette. The Lloyd Roeling Conference is an annual tradition since 1970 and rotates among four subfields in mathematics and statistics. This iteration will provide a forum for algebraic topology in the South and will support the mathematical and professional development of graduate students and postdoctoral fellows in the EPSCoR state of Louisiana as well as nearby regions.

The topic of the conference will be algebraic topology, broadly interpreted, including topics in chromatic homotopy theory, configuration spaces, equivariant homotopy theory, higher category theory, loop spaces and string topology, and tropical geometry. The conference will feature eight plenary lectures as well as short contributed talks. Accessible talks across a variety of areas will encourage cross-pollination between subfields. The conference web page is https://userweb.ucs.louisiana.edu/~c00424469/lr2024/

This award reflects 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." +"2349755","Conference: Mid-Atlantic Topology Conference 2024","DMS","TOPOLOGY","03/01/2024","02/22/2024","Benjamin Knudsen","MA","Northeastern University","Standard Grant","Swatee Naik","02/28/2025","$30,000.00","Jose Perea, Iva Halacheva, Thomas Brazelton","b.knudsen@northeastern.edu","360 HUNTINGTON AVE","BOSTON","MA","021155005","6173733004","MPS","126700","7556","$0.00","This National Science Foundation award provides funding for participants of the Mid-Atlantic Topology Conference, which will take place March 23 and 24, 2024 at Northeastern University in Boston. The conference will focus on a broad overview of trends in topology currently at the forefront of research, including geometric group theory, geometric and topological data analysis, applied and computational topology, higher category theory, and motivic homotopy theory. This conference will further advance the growing diversity within algebraic topology, as well as the strength and coherence of the East Coast topology community. It is the latest iteration in a series of recurring conferences aimed at uniting the increasingly active topology groups in this geographical area.

The conference will feature nine 45-minute talks spread over two days. Speakers have been chosen with particular emphasis on gender representation. They are predominantly early career researchers and hail from public and private institutions alike. Advertising and funding will be targeted to prioritize inclusion of participants from underrepresented populations, continuing a strategy proven to be successful in the last iteration of the conference. The conference will provide graduate students and postdoctoral researchers with invaluable networking and community building opportunities and will strengthen the regional fabric of the field of topology. Further
information is available at https://sites.google.com/northeastern.edu/matc2024/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." "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." "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","Allison Moore, Marco Aldi","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." -"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." "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." +"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." "2403833","Conference: Geometric and Asymptotic Group Theory with Applications 2024","DMS","TOPOLOGY","01/01/2024","12/18/2023","Jingyin Huang","OH","Ohio State University","Standard Grant","Swatee Naik","12/31/2024","$22,100.00","","huang.929@osu.edu","1960 KENNY RD","COLUMBUS","OH","432101016","6146888735","MPS","126700","7556","$0.00","The conference ?Geometric and Asymptotic Group Theory with Applications? will be held in Luminy, France February 5 - 9, 2024. This award provides partial travel support for a group of early career US based mathematicians to attend this conference. The conference has an interdisciplinarity nature, focusing on topics in the intersection of mathematics and computer science. A variety of leading experts working in the relevant fields will present their work. Early career US based participants will also be given the opportunity to give talks and thereby enhance their international profile. The exposure to recent developments in the field and the opportunities to communicate with their colleagues from all over the world is expected to initiate new research collaborations. Conference organizers will devote special efforts to recruit and encourage members of under-represented groups in mathematics.

The study of infinite groups is a very active area in modern mathematics. A major trend in this area is geometric group theory, which aims at understanding the asymptotic geometry of finitely generated groups. On the other hand, this seemingly geometric approach to infinite groups also has deep connections to the more classical theme of decidability, logic, and algorithmic aspects of group theory, which lie in the intersection of computer science and mathematics. This conference will bring together prominent researchers interested in group theory, but from different sub-fields and viewpoints, some on the geometric side, while others on the algorithmic/computation side, to present their work. The speakers are carefully chosen in order to emphasize connections between different aspects, and to stimulate further collaboration. A wide range of infinite groups of great importance will be discussed during the conference, including cubical groups, hyperbolic groups, automaton groups, automatic groups, Artin groups, Coxeter groups, self-similar groups, non-positively curved groups etc. More information is available on the webpage of the conference at https://conferences.cirm-math.fr/3149.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." "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." +"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." "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." -"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." "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","Daniel Isaksen, Vesna Stojanoska, Manuel Rivera, Carmen Rovi","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." "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." -"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." "2405684","Conference: 2024 Redbud Topology Conference","DMS","TOPOLOGY","03/01/2024","02/26/2024","Henry Segerman","OK","Oklahoma State University","Standard Grant","Swatee Naik","02/28/2025","$28,869.00","Jonathan Johnson, Neil Hoffman","henry@segerman.org","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","126700","7556, 9150","$0.00","This award provides funding for the 2024 Spring and Fall Redbud Geometry/Topology Conferences, the first of which is to be held April 12-14, 2024, at Oklahoma State University. These conferences are part of an ongoing series of conferences held at universities in Arkansas and Oklahoma, intended to increase interaction and collaboration among early career and established mathematicians in the area. The Spring meeting will feature talks by prominent speakers from across North America, as well as a graduate student workshop. The Fall meeting will take place at the University of Oklahoma, and it will predominantly consist of talks by early-career mathematicians from the EPSCoR regions of Arkansas, Oklahoma, and surrounding states.

Many interesting results have linked low-dimensional topology and group orderability. These results have provided evidence for a prominent conjecture addressing which three-manifold groups are left-orderable, and have made progress towards a classification of bi-orderable three-manifold groups. The 2024 Spring Redbud Geometry/Topology Conference will bring together leading researchers to discuss these developments. The invited speakers are: Idrissa Ba (University of Manitoba), Adam Clay (University of Manitoba), Nathan Dunfield (University of Illinois Urbana-Champaign), Cameron Gordon (University of Texas at Austin), Ying Hu (University of Nebraska, Omaha), Tao Li (Boston College), Rachel Roberts (Washington University in St. Louis), Dale Rolfsen (University of British Columbia), and Hannah Turner (Georgia Institute of Technology). The conference begins with a workshop designed to enhance the experience of graduate students and junior researchers. The workshop will feature expository talks by Clay, Gordon, and Rolfsen. More information is available at the conference website: https://math.okstate.edu/conferences/redbud/

This award reflects 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","05/31/2024","$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." "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." "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." +"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." "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." -"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." "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." +"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." "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." "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." "2350373","Collaborative Research: Conference: Workshops in Geometric Topology","DMS","TOPOLOGY","05/01/2024","01/23/2024","Nathan Sunukjian","MI","Calvin University","Standard Grant","Swatee Naik","04/30/2027","$40,000.00","Molly Moran, Greg Friedman, Craig Guilbault","nss9@calvin.edu","3201 BURTON ST SE","GRAND RAPIDS","MI","495464301","6165266000","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." "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." -"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." +"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." +"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." "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." +"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."