This federal Project Grant award for $300,000.00, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program, supports research to significantly expand the investigator's work on applications of model theory to the study of geometric structures. The key objectives are to: 1) tackle major transcendence problems such as the Ax-Lindemann-Weierstrass and Ax-Schanuel conjectures for uniformizing functions of geometric structures in higher...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research on analytic problems around automorphic forms and L-functions, which are important mathematical tools for understanding the distribution of prime numbers. The $152,334 award to Rutgers, The State University, will fund the Principal Investigator's work to develop new properties of families of L-functions, particularly in ranges that have been...
This $260,000 Project Grant awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences aims to advance the understanding of algebraic points on mathematical varieties. The primary research focus is on characterizing the arithmetic and local properties of algebraic points on curves, with complementary projects exploring higher dimensional varieties such as surfaces. The award also supports mentoring and training of early career mathematicians, particularly from...
This Project Grant award of $159,995 from the National Science Foundation's (NSF) Division of Mathematical Sciences, under the CFDA program 47.049 Mathematical and Physical Sciences, will support research on algebraic cycles and normal functions. The primary goals are to: (i) produce new evidence for mathematical conjectures on special values of L-functions and provide motivic realizations of biextensions; (ii) describe variations of mixed Hodge structure and Lefschetz principles governing...
This $115,718 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports advanced research into the algebraic and geometric properties of solutions to systems of polynomial equations. The primary goals of the project are to study the algebraic aspects of these solutions using non-archimedean geometry, investigate the complexity of curves within varieties of general type, and develop new non-archimedean...
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...
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 (CFDA 47.049 - Mathematical and Physical Sciences) provided $153,842 to the Research Foundation of the City University of New York (RFCUNY) - Lehman College from September 1, 2023 to August 31, 2025. The grant supports research investigating the relationship between the geometry of curves defined by polynomial equations and the rate at which new solutions are found by augmenting beyond the rational numbers. The project also includes...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research on algebraic cycles, automorphic forms, and L-functions. The $230,000 award to The Trustees of Columbia University in the City of New York, spanning July 1, 2024 to June 30, 2027, aims to deepen the understanding of these mathematical objects and their connections, particularly in high dimensions. The research will include work on the...
This $225,000 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) will support a research project to study methods for explicitly determining the finite set of rational points on curves of genus 2 or more. The Principal Investigator (PI) will focus on leveraging Kim's nonabelian Chabauty program and the computation of Selmer sets to address this fundamental mathematical challenge. The project will also...