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 $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...
The National Science Foundation (NSF) awarded a 3-year, $118,501 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to Yale University to conduct research on geometric Langlands and automorphic functions. The project will study the arithmetic properties and connections between geometry, topology, and number theory, with a focus on developing new mathematical theories and methods. The award will provide research training opportunities for graduate students and result...
This $280,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research in birational geometry at New York University from April 2022 through March 2025. Specifically, the principal investigator will use methods from Galois cohomology of function fields, properties of algebraic cycles over non-algebraically closed fields, K-theory, and degeneration techniques to advance understanding of rationality and stable...
This $106,185 federal Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) supports research at The Johns Hopkins University to advance the Langlands Functoriality Conjecture. The project aims to use quantization methods to construct novel ways of comparing relative trace formulas, which have important applications in number theory. Key expected products include new mathematical techniques for proving functoriality conjectures, as well as...
The National Science Foundation (NSF) awarded a $220,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to Duke University. The funding will support research by the principal investigator to develop generalized Poisson summation formulae, which are expected to establish the properties of certain L-functions critical to advancing the Langlands functoriality conjecture - a central problem in mathematics with broad implications across fields ranging from number...
This $152,334 federal Project Grant award, provided by the National Science Foundation (NSF) through its Mathematical and Physical Sciences program (CFDA 47.049), supports research by Rutgers, The State University to advance understanding of automorphic forms and L-functions. The project aims to develop new properties of families of L-functions, which are mathematical constructions that combine information about prime numbers, and study their moments and large sieve inequalities. This work...
This $193,010 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports a research project at the University of Minnesota to develop connections between number theory and physics. The project focuses on using quantum groups and their representation theory to bridge the theory of special functions in number theory with statistical mechanics models in physics. Key objectives include providing research training opportunities...
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 $300,000 National Science Foundation award under the Mathematical and Physical Sciences program (CFDA 47.049) supports research and education activities in the area of automorphic forms and exceptional algebraic structures at the University of California, San Diego from July 1, 2022 to June 30, 2027. The principal investigator will conduct three related research projects investigating half-integral weight modular forms on exceptional groups, modular forms on the exceptional group G2 with...