This Project Grant award of $246,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research on two central topics in number theory. The principal investigator will work on developing new probabilistic models and multiple Dirichlet series to make progress on fundamental number-theoretic problems. This includes constructing new multiple Dirichlet series with applications to moments of L-functions, developing probabilistic models...
This Project Grant award of $193,010.00 from the National Science Foundation's (NSF) Division of Mathematical Sciences under the CFDA 47.049 Mathematical and Physical Sciences program supports research to develop connections between number theory and physics. The project aims to explore the representation theory of quantum groups and their applications in explaining the bridge between special functions in number theory and statistical mechanics. The research will provide training opportunities...
The National Science Foundation (NSF) awarded a $405,500 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Duke University to support a research program in A1-homotopy theory and its applications to enumerative geometry and number theory. The award will fund research to develop enriched counting methods that can detect differences in the number of solutions to equations requiring real or imaginary numbers, with potential applications in number theory and...
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 $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 National Science Foundation Project Grant of $121,754 awarded on September 1, 2022 will support research into number theory through August 31, 2024 under the Mathematical and Physical Sciences CFDA 47.049 program. Specifically, the University of Michigan-Dearborn will extend prior work on Bianchi modular forms, elliptic Dedekind sums, and L-functions over imaginary quadratic fields. The Principal Investigator will study generalizations of Szeché's Eisenstein cocycles with applications to...
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 three-year Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $145,260 to Tufts University to investigate questions in arithmetic statistics through September 2025. Specifically, the grantee will study how arithmetic statistical objects decompose into simpler components and apply uniform bounds to number fields, class groups, and Artin L-functions. This work aims to further...
The National Science Foundation Division of Mathematical Sciences awarded a $141,400 Project Grant to the University of Illinois under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research into Galois structures and arithmetic statistics in number theory from August 15, 2022 to July 31, 2025. Specifically, the principal investigator and collaborators will modify non-abelian Cohen-Lenstra heuristics when the base field contains roots of unity;...
The National Science Foundation (NSF) awarded a $310,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to The Washington University's Office of Sponsored Research Services Division. The grant supports fundamental mathematical research at the intersection of analytic function theory, harmonic analysis, and operator theory. The proposed work aims to leverage "testing theorems" to address open questions in these areas, which have applications in...