This $225,000 National Science Foundation Project Grant supports research in algebraic geometry at the University of Georgia Research Foundation from July 2022 through June 2025. The Mathematical and Physical Sciences program aims to increase scientific knowledge and understanding in major problems through support of basic research. Specifically, this award will fund the principal investigator's research on degenerations of algebraic varieties and geometric compactifications of moduli spaces...
This $172,247 federal Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), funds collaborative research in the areas of small quantum groups, their categorifications, and topological applications. The primary aim is to extend existing work on Khovanov homology and develop new homological invariants of three-dimensional manifolds that could provide insights into smooth topology and have potential applications in quantum...
This $325,132 three-year Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research into symmetries and statistics in arithmetic number fields. The awardee, University of Georgia Research Foundation, Inc., will investigate distribution results for discriminants and class groups of global fields with a fixed Galois group. This includes proving new asymptotic distributions, upper and lower bounds for discriminants using...
The National Science Foundation (NSF) awarded a $155,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) Federal Grant Program to the University of Georgia Research Foundation, Inc. This funding supports research related to the representation theory of groups, which is the study of symmetry and its applications in various mathematical fields. The project aims to construct and classify pre-Tannakian categories, which are algebraic structures generalizing the...
This $105,981 project grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research at the intersection of number theory, representation theory, and geometry. The research aims to explore geometric techniques in representation theory, with a focus on connections between representations of reductive algebraic groups over local fields and geometric constructions like...
This $270,000 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research in geometric representation theory and symplectic geometry at the University of California, Berkeley. The research aims to develop new tools and solve open problems in these mathematical fields, which draw inspiration from theoretical physics. Key research themes include investigating the cocenter of the affine Hecke category,...
This National Science Foundation award under the Mathematical and Physical Sciences program (CFDA 47.049) provides $275,396 to the University of Oklahoma from August 1, 2023 through July 31, 2026. The funding supports research into the geometries and topologies of surfaces and graphs. Specifically, the award will advance understanding of how abstract algebraic groups manifest as symmetries of geometric spaces in one and two dimensions. Graduate students will gain research experience applying...
This $156,571 federal Project Grant award was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program. The grant supports fundamental research to advance the understanding of four-dimensional manifolds with symplectic structures, employing tools from topology, dynamics, and geometry. The primary objectives are to explore the properties and symmetries of four-manifolds, compare symplectic and Kähler cones, solve isotopy problems for...
The University of Georgia Research Foundation, Inc. was awarded a $232,374 Project Grant from the National Science Foundation Division of Mathematical Sciences on September 1, 2021. The grant is supporting research titled "Monoidal Triangular Categories: Representation Theory, Cohomology, and Geometry" through August 31, 2024. The grant is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these fields and strengthen the...
This $194,972 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program supports research at Emory University focused on addressing open problems in discrete geometry. The central aims are to study the covering and intersection properties of convex geometric objects and explore connections between discrete geometry and other mathematical fields. Key planned activities include mentoring undergraduate students, developing new mathematical...