This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research into the dynamic interactions between operator theory, linear algebra, combinatorics, and probability theory. The 3-year, $285,236 award to Pomona College will fund investigations into new frontiers in these interconnected mathematical domains, with a focus on engaging undergraduate students in the research. Key areas of exploration...
Pomona College was awarded a $548,786 Project Grant from the National Science Foundation Directorate for Mathematical and Physical Sciences. The grant is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to strengthen the nation's scientific enterprise through increased understanding of major problems. Under the two-year award running from June 2022 to May 2024, Pomona College will deliver a research experience program in mathematics. The college will utilize...
This $204,372 federal Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports research on the potential theoretic aspects of complex geometry. The principal investigator will employ methods from potential theory, infinite-dimensional geometry, and geometric analysis to investigate a cluster of interconnected questions and conjectures in complex geometry. The project aims to advance scientific knowledge in this...
This $200,000 National Science Foundation Division of Mathematical Sciences Project Grant will support research and training in noncommutative algebra and geometry at the University of California Irvine from July 1, 2022 to June 30, 2025. The award will advance fundamental understanding of noncommutative algebraic structures that arise in geometry and physics. Researchers will develop new techniques to deduce good algebraic properties for geometrically constructed noncommutative algebras and...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $290,813 to The Washington University in St. Louis to support a research project in noncommutative geometry and its applications. The primary objectives are to: Introduce new numerical invariants to distinguish noncommutative spaces and refine known invariants such as the Connes-Chern character. Apply cyclic theory to study an analytic version of the Milnor...
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 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on the geometry of mapping class groups and surface bundles, as well as related educational initiatives. The $117,892 award to the Regents of the University of California at Riverside, effective July 1, 2025 through June 30, 2030, aims to develop combinatorial techniques for studying the geometry of mapping class groups and Teichmüller spaces,...
This $299,996 Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental mathematical research by a team at Utah State University. The project aims to develop new algebraic and geometric tools to formalize and advance the mathematical theory underlying quantum physics, particularly in low-dimensional topology and the theory of quantum invariants. The key products and...
This federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in differential equations and the geometry of manifolds. The award, totaling $223,343, will fund the principal investigator's work in three main areas: classification of gravitational instantons in 4 dimensions, understanding Gromov-Hausdorff limits of Einstein metrics in the collapsing case, and the study of higher-dimensional...
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...