Project Grant 2501507
- 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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into analytical problems involving automorphic forms and L-functions, which are important tools for understanding the distribution of prime numbers. The $152,334 award to Rutgers, The State University will fund work to develop properties of new families of L-functions, study high moments of L-functions, and establish large sieve inequalities for...
- 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 $246,000 Project Grant under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) to Princeton University. The grant, with a period of performance from July 1, 2025 to June 30, 2027, supports fundamental research in number theory. The principal investigator will develop new probabilistic models and multiple Dirichlet series to advance the understanding of Galois groups and L-functions, which have applications to prime number...
- 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 $140,000 project grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) will develop new techniques in the study of harmonics and their applications to the structure of prime numbers. The research will focus on improving the understanding of p-adic geometry and its connections to automorphic forms, which have important applications in signal processing and cryptography. The project will provide training opportunities for...
- This Project Grant award of $205,000.00 from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on the Kudla program, an important area of modern number theory. The principal investigator will continue their work on understanding the deep connections between arithmetic and analysis on Shimura varieties, with a focus on CM values of higher Green functions, the construction of Green currents for Kudla special...
- This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) is focused on three distinct problems in number theory, combinatorics, and ergodic theory. The $184,738 award will support research on generalizations of Szemerédi's Theorem, which concerns the existence of long arithmetic progressions in sufficiently large sets of integers. The investigator will also study the size and structure of integer distance sets. Additionally, the...
- 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 $119,000 Project Grant award from the National Science Foundation's (CFDA 47.049) Mathematical and Physical Sciences program concerns research in number theory. The principal investigator will seek to advance the boundaries of "large sieve inequalities" - an important mathematical tool used to study arithmetic sequences over prime numbers and the values of L-functions. The research aims to make progress on fundamental problems in number theory, including predictions about...
This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program will support research by the principal investigator on p-adic L-functions and Selmer groups in number theory. The $125,986 award, with a performance period from August 15, 2025 to July 31, 2027, will fund investigations into connections between the arithmetic properties of polynomial equations and the behavior of their associated L-functions. The research will focus on developing new techniques for studying p-adic properties of algebraic automorphic forms, which can provide a bridge between Selmer groups and L-functions for Galois representations arising from automorphic representations. The award will also support the mentoring of undergraduate and graduate students, the organization of seminars, and outreach activities.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $126.0k | 8/5/25 |