Project Grant 2202363
- This $174,000 federal Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences supports research on the Langlands program, a foundational area of mathematics with connections to physics and computer science. The principal investigator (PI) will explore the representation theory of reductive groups and the theory of automorphic forms, with the primary objectives of studying the multiplicity problem for spherical varieties and using the relative trace...
- This National Science Foundation Project Grant of $180,000 supports research into geometric methods in the p-adic Langlands program under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). Specifically, the University of Utah will apply ideas from calculus to the study of perfectoid spaces and diamonds in order to uncover new structural properties of the Langlands correspondence and help understand basic questions about integers and prime numbers. The awardee will...
- This $100,000 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) aims to develop a deeper understanding of the topology and geometry of four-dimensional spaces. The research will explore similarities and differences among these spaces when equipped with additional geometric structures, such as smooth, symplectic, and complex structures, using a mix of mathematical methods. Key goals include constructing exotic...
- This $299,996 Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental mathematical research by a team at Utah State University. The project aims to develop new algebraic and geometric tools to formalize and advance the mathematical theory underlying quantum physics, particularly in low-dimensional topology and the theory of quantum invariants. The key products and...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a 3-year, $250,000 Project Grant to the University of Wisconsin - Madison under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate moduli spaces of surfaces with additional geometric structure. The grant will fund research to solve long-standing conjectures about the geometry and topology of these moduli spaces, which are mathematical spaces that parameterize the shapes an object can take....
- This $200,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on the Langlands and relative Langlands programs, which describe subtle relationships between different spaces of automorphic forms. The principal investigators (PIs) will work jointly to study these programs and extend them to new situations, focusing on functoriality and the study of periods. This will generate new insights into...
- This $210,000 Project Grant was awarded on July 15, 2025 by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The grant will support research by the University of Chicago to investigate the p-adic aspects of the Langlands program, a connection between number theory and harmonic analysis. Key focus areas include constructing a categorical p-adic local Langlands correspondence by combining methods from representation theory, the...
- This $200,000 National Science Foundation project grant supports mathematical and physical sciences research at Michigan State University from September 2022 through August 2025. The award falls under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and address national problems through basic research and education in these fields. Specifically, the principal investigator and their team will investigate Floer and Khovanov theories...
- The National Science Foundation (NSF) awarded a $285,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Utah to conduct research on hyperbolic geometry in two- and three-dimensional spaces. The project, running from August 1, 2024 to July 31, 2027, will focus on studying the geometry of hyperbolic 3-manifolds, including investigating the renormalized volume of such manifolds and the connection to the Weil-Petersson gradient flow. The...
- This $200,000 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in topology and group theory at Louisiana State University (LSU). The primary goal of the 3-year research program is to study the growth of homology in a residual tower of finite regular covers of aspherical manifolds, with potential connections to the high-dimensional analogue of Agol's virtual fibering theorem. The research will...
This $280,444 National Science Foundation project grant supports research and education activities advancing the Langlands program for 3-manifolds at Montana State University from June 2022 through May 2025. Funded through the Integrative Activities program under the National Science Foundation's Division of Mathematical Sciences, the grant supports defining and studying the space of states associated with a 3-manifold in the family of geometric Langlands topological quantum field theories. Specific research goals include formulating a duality conjecture for skein module dimensions and tools to verify it in important cases; proving the Betti and de Rham geometric Langlands conjecture for elliptic curves at generic level; refining the B-model state space construction using derived algebraic geometry; and computing gauge group homology of 3-manifolds in terms of Langlands dual spectral Whittaker theory. The award also provides research and training opportunities for students, advancing the NSF's mission to stimulate competitive STEM research and education through its Integrative Activities program.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $140.2k | 6/7/22 |