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 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 $300,000 Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports research at Stanford University to develop a new framework for studying algebraic structures in topology. The key technical focus is on formulating algebraic structures geometrically at the level of underlying "flow categories" in order to extend applications of Floer homotopy theory to areas like symplectic and...
The National Science Foundation (NSF) awarded a $281,250 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) Federal Grant Program to Colorado State University (CSU) to support the 2025 Summer Research Institute in Algebraic Geometry. This large-scale, three-week conference will be held at CSU in Fort Collins, Colorado from July 14 to August 1, 2025. The grant will fund housing for 150 graduate students, postdocs, and early career researchers to attend the institute, which...
This $300,000 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on the symmetries of Floer theoretic invariants and their applications to low-dimensional topology. The research aims to use tools from Floer theory to study algebraic structures on three-dimensional spaces and address topological questions related to mathematical knots. Key focus areas include understanding versions of Floer theory...
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 $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research to develop new tools for studying the geometry and dynamics of physical systems. Key research focus areas include: Investigating the existence and properties of periodic orbits in four-dimensional phase spaces with three-dimensional energy levels Studying the geometry of phase spaces to determine when dynamical systems are equivalent...
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 National Science Foundation (NSF) Project Grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), supports research to develop new algebraic structures and invariants associated with Legendrian links in symplectic geometry. The $299,647 award to Duke University, spanning July 2025 to June 2028, will create enhanced versions of the Legendrian contact homology invariant, including combinatorial and geometric enhancements. These new algebraic structures are expected...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $170,443 Project Grant to the University of Massachusetts Boston (UMass Boston) under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research in "Critical Symplectic Geometry, Lagrangian Cobordisms, and Stable Homotopy Theory." The project aims to incorporate ideas from homotopy theory and category theory into symplectic geometry to prove structural results about...