This National Science Foundation Division of Mathematical Sciences Project Grant of $322,321 provides funding from September 15, 2022 through August 31, 2025 to support collaborative research in the area of symplectic geometry between investigators at the University of Illinois. The research focuses on the momentum map and its applications to questions regarding symmetries and invariants in symplectic geometry. Key areas of focus include the equivariant geometry of symplectic four-manifolds,...
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...
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...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental and applied research in symplectic geometry. The principal investigator (PI) at the University of Southern California (USC) will develop new tools and paradigms to study the quantitative aspects of symplectic geometry, including exploring connections with algebraic curve theory, mirror symmetry, and computational approaches through...
Cornell University has been awarded a $360,000 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). Over a three year period from August 2023 through July 2026, Cornell will deliver three subprojects focused on algebraic combinatorics and algebraic geometry. The subprojects will investigate divided difference operators and Schubert polynomials, characterize the scheme of pairs of...
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 Project Grant award for $330,586, provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA No. 47.049), supports research on the geometric and metric properties of two-dimensional surfaces. The principal investigator (PI) at Cornell University will investigate the classification of surfaces under singular flat and hyperbolic metrics, as well as the associated moduli spaces and related mathematical...
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...
The National Science Foundation Division of Mathematical Sciences awarded $173,980 to Florida State University under the Mathematical and Physical Sciences (CFDA 47.049) Project Grant to support research applications of symplectic geometry to frame theory and signal processing from June 1, 2021 to May 31, 2024. This funding will allow Florida State University to advance scientific knowledge and understanding of major problems through collaborative research exploring the use of symplectic...
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,...