This federal Project Grant award in the amount of $177,469.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Grant Program (CFDA #47.049). The award will support research into the geometry of moduli spaces from low-dimensional topology and applications, with a focus on three main directions: studying higher algebraic structures in instanton Floer homology, analyzing the properties of generalized Seiberg-Witten equations, and exploring the...
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 award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program in the amount of $288,912 aims to advance the understanding of string interactions and their significance in mathematics and physics. The award to Purdue University will fund research to algebraicize string topology through tractable models, with a focus on chain-level operations sensitive to geometric structure beyond homotopy type. The project proposes to construct a...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $153,765 Project Grant to Wayne State University from August 1, 2023 to July 31, 2026. This award, funded under the Mathematical and Physical Sciences program (CFDA 47.049), supports research focused on applications of equivariant stable homotopy theory - a central part of algebraic topology involving the study of topological objects and generalized cohomology theories. The principal investigator will continue...
This Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research into the topology and dynamics of four-dimensional manifolds with symplectic structures. The $156,571 award, spanning from September 1, 2024 to August 31, 2026, will enable the principal investigator to employ advanced mathematical tools, such as surgery on Lefschetz fibrations, Gromov-Witten theory, and family...
This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $217,223 to support research investigating applications of ideas from physics to topology and vice versa under the Mathematical and Physical Sciences program (CFDA 47.049). The awardee, Washington University, will use the funding over three years from September 2022 to August 2025 to advance homology theories constructed by the Principal Investigator and collaborators. Specific activities include...
This Project Grant award, valued at $137,324.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award is focused on advancing the mathematical understanding of polytopes, which are geometric structures with universal importance in many areas of mathematics, including computer science, architecture, art, and philosophy. The principal investigator plans to attack various problems related to polytopes and...
This $304,875 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports a 5-year research program at the University of Notre Dame. The primary objectives are to: 1) develop new methods using topology and geometric group theory to study moduli spaces, specifically strata of abelian differentials and families of polynomials, with a focus on establishing "asphericality" (vanishing of higher homotopy); and 2)...
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 $186,112 project grant, awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research at the interface of algebraic geometry, string theory, and quantum field theory. The project aims to explore major open problems at this intersection, employing techniques from fields such as topology, integrable systems, and supergeometry. Specific research topics include investigating the Geometric Langlands...