The National Science Foundation awarded Indiana University a $142,059 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research investigating ways to characterize, describe, and study spaces with many symmetries in various dynamical, geometric, and topological settings. The grant will support research exploiting connections between a wide range of mathematical areas to further understand fundamental structures related to lattices in Lie groups. Key...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $320,000 Project Grant to the University of Illinois, Urbana-Champaign under the Mathematical and Physical Sciences program (CFDA 47.049). The three-year grant, effective September 1, 2023 through August 31, 2026, supports fundamental research on symplectic groupoids and the quantization of Poisson manifolds. Key objectives include developing a novel non-formal deformation quantization approach, advancing the...
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...
The National Science Foundation awarded a $361,306 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to the University of Maryland, College Park for research titled "Geometries of Topological Groups." The three-year award beginning September 1, 2023 will support the university's efforts to solve open questions regarding the geometrization of topological groups through mathematical problems combining logic, analysis and metric geometry. As part of the...
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...
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 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 Division of Mathematical Sciences awarded Indiana University a $203,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to support research titled "COLLABORATIVE RESEARCH: ALGEBRAIC K-THEORY, ARITHMETIC, AND EQUIVARIANT STABLE HOMOTOPY THEORY" from August 1, 2021 through July 31, 2024. The grant funding will support collaborative research in algebraic K-theory, arithmetic, and equivariant stable homotopy theory being...
The National Science Foundation (NSF) awarded Purdue University a $185,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program. The grant supports research to investigate the hypothetical mod p and p-adic Langlands correspondences that relate Galois representations and modular and integral representations of p-adic reductive groups. The research aims to construct local models for stacks of Galois representations in order to analyze these conjectural sheaves and...
This Project Grant award of $299,999.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research by the Trustees of Indiana University (Indiana University) on the rigidity and bounded cohomology of groups acting on nonpositively curved spaces. The award will fund three main projects: investigating the relationship between the geometry of nonpositively curved closed Riemannian manifolds and the bounded cohomology of their...