Project Grant FA95501110216

This $217,000 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences supports research on computational structures in equivariant chromatic homotopy theory, with a focus on developing new techniques to advance computations related to Lubin-Tate theories and the study of homotopy groups of spheres. The award funds a range of projects that leverage recent discoveries in equivariant homotopy theory to drive progress in chromatic homotopy theory and...

This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $194,902 to Texas A&M University under the Mathematical and Physical Sciences program (CFDA 47.049) to study the quantum symmetries of topological phases of matter. The investigator will classify and distinguish topological phases through their mathematical symmetries, probe their properties, and understand relationships between phases through transitions. Some emphasis will be placed on...

This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) project grant award of $106,619 to Case Western Reserve University supports fundamental research in classical and motivic stable homotopy theory, a field of algebraic topology. The key projects involve computing homotopy groups of spheres, including leveraging computer calculations to overcome technical challenges, as well as exploring analogues of these groups in algebraic geometry through motivic homotopy...

Federal Grant Award Summary The Division of Mathematical Sciences (DMS) of the National Science Foundation awarded Stony Brook University a Project Grant totaling $209,999 (Award Date: August 1, 2025; Completion Date: July 31, 2027) under the Mathematical and Physical Sciences program (CFDA 47.049). This research project, titled "Varieties with Trivial Canonical Class and Hodge Theory," focuses on advancing fundamental knowledge in algebraic geometry through the classification and...

This $256,573 National Science Foundation Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) will support research exploring algebraic aspects of chaotic dynamical systems with hyperbolic behavior at Texas A&M University from July 2022 through June 2025. Specifically, the award will fund investigations into the connections between hyperbolic dynamical systems and group theory, automata theory, and other branches of algebra. The research aims to clarify whether...

This $145,000 Project Grant awarded by the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports collaborative research on the fundamental theory of wave turbulence. The research at Texas A&M University will tackle challenging problems at the intersection of physics and mathematical analysis, including the rigorous derivation of wave kinetic equations, analysis of the kinetic equation for the Fermi-Pasta-Ulam-Tsingou chain, and well-posedness...

This National Science Foundation (NSF) Project Grant, awarded under the Mathematical and Physical Sciences program (CFDA 47.049), provides $172,247 to support collaborative research on small quantum groups, their categorifications, and topological applications. The research aims to bridge the gap between 3D topological quantum field theories and our 4D universe, with a focus on developing homological invariants of 3D and 4D manifolds. The project will involve students and postdocs,...

This three-year project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $378,158 to Carnegie Mellon University to develop mathematical tools for data science and signal processing applications. Specifically, the awardee will investigate transportation-based geometries and gradient flows to provide sampling methods that leverage data geometry and can be accurately approximated in high dimensions. They will study ensemble methods...

This National Science Foundation Project Grant award in the amount of $349,981 provides funding from August 1, 2022 to July 31, 2025 to support research at Stony Brook University concerning Floer theory, arc spaces, and singularities. Specifically, the principal investigator will utilize arc spaces to compute various Floer algebras and investigate the relationship between Floer theory, symplectic geometry, and algebraic geometry. Key activities include developing computational techniques using...

Federal Grant Award Summary The National Science Foundation's Division of Mathematical Sciences awarded Texas A&M University $150,000.00 under the Mathematical and Physical Sciences program (CFDA 47.049) for a two-year project grant effective August 1, 2025 through July 31, 2027. This project centers on developing 3-manifold invariants from Virasoro Topological Quantum Field Theory (TQFT) and studying their asymptotic behavior at the interface of geometric topology and quantum topology....