The University of Southern California was awarded a $353,255 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will support research into higher algebraic structures in symplectic geometry and their applications from July 2021 through June 2024. As part of the Mathematical and Physical Sciences program's goal of strengthening the nation's scientific enterprise through advancing...
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 $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 from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $144,726 to support collaborative research in the area of symplectic geometry between Cornell University and other institutions. Specifically, the funding will advance knowledge and understanding of the relationship between the geometry of Hamiltonian systems and the combinatorics of momentum maps through investigations into the...
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 $271,119 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on complex Lagrangians, integrable systems, and quantization in relation to mirror symmetry. The University of California, Davis will lead a research group investigating mirror symmetry as it relates to symplectic geometry and complex algebraic geometry. The group will establish complex Lagrangian geometry as a tool to study geometric...
This federal Project Grant award, issued by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), will provide $300,000 to the University of California, Irvine (UCI) from July 1, 2025 to June 30, 2028. The primary objectives of this research project are to: 1) develop new approaches to understand higher continuous symmetries that emerged in theoretical physics in the early 1990s, and 2) explore discrete symmetries arising in algebraic equations...
The National Science Foundation (NSF) awarded a $180,000 Project Grant to the University of Southern California (USC) Department of Contracts and Grants Division under the Mathematical and Physical Sciences (CFDA 47.049) program. The 3-year grant will support research on "Combinatorial Representation Theory of Quantum Groups and Coinvariant Algebras." The project aims to further develop combinatorial diagrams called "web bases" that encode the representation category of...
This Project Grant award of $300,000.00 from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program supports research on higher-dimensional contact topology and its relationship to quantum physics and topology. The principal investigator will study the mathematical connections between Hecke algebras, higher-dimensional Heegaard Floer homology, and topological quantum field theory. The project will...
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 National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) Project Grant award provides $300,000 in funding to the University of Southern California (USC) to advance research in quantitative symplectic geometry and develop new computational frameworks for analyzing Hamiltonian dynamics. The key components of this 3-year project, which runs from June 2025 to May 2028, include:
Exploring novel strategies for studying higher-dimensional symplectic ellipsoid embeddings by linking symplectic field theory to singular algebraic curves and incorporating ideas from mirror symmetry.
Developing a quantitative theory of Fukaya categories and pushing higher symplectic capacities into contact geometry to advance the understanding of real-valued symplectic capacity invariants.
Building a new "digital symplectic geometry" computational framework to analyze Hamiltonian dynamics and nonsqueezing phenomena through numerical simulations and machine learning techniques.
This award aims to uncover deep connections between quantitative symplectic geometry and other mathematical fields such as algebraic curve theory, birational geometry, and mirror symmetry. The project also includes community-building and mentorship activities to engage the wider Southern California geometry and topology research community.