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 National Science Foundation Project Grant of $250,000 supports research into low-dimensional topology through July 2025. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), the award to Duke University will advance understanding of fundamental questions in knot theory and 4-manifold topology. Specifically, the principal investigator will investigate knot concordance problems tied to the unique properties of 4-dimensional manifolds compared to higher dimensions....
This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $452,656 to California State University Fresno Foundation to support research in low-dimensional topology from September 1, 2022 to August 31, 2025. The funding will advance understanding of link homology theories and other quantum invariants through construction and study of new Khovanov-type homology theories for classical and singular knots. It will also investigate...
This $299,996 Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental mathematical research by a team at Utah State University. The project aims to develop new algebraic and geometric tools to formalize and advance the mathematical theory underlying quantum physics, particularly in low-dimensional topology and the theory of quantum invariants. The key products and...
This $300,000 federal Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) supports research on the symmetries of Floer theoretic invariants and their applications to low-dimensional topology. The primary objectives are to study certain algebraic structures on the set of three-dimensional spaces, address topological questions related to mathematical knots, and further develop versions of Floer theory...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports a research and training program at the University of California, Irvine (UC Irvine). The $998,809 award will fund a series of improvements and new additions to UC Irvine's undergraduate, graduate, and postdoctoral training programs in geometry and topology, which have applications in mathematical physics, data science, and video game design. The projects aim to...
This Project Grant award of $317,407 from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support research at the University of Nebraska on the topology of 3- and 4-dimensional manifolds. The project aims to uncover deep connections between manifold theory in these dimensions, with potential applications in fields such as biology, chemistry, physics, and quantum computing. Specific objectives include proving additional cases of the Smooth...
This federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in differential equations and the geometry of manifolds. The award, totaling $223,343, will fund the principal investigator's work in three main areas: classification of gravitational instantons in 4 dimensions, understanding Gromov-Hausdorff limits of Einstein metrics in the collapsing case, and the study of higher-dimensional...
This is a $100,000 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The grant will support research by Virginia Commonwealth University (VCU) to investigate conformal field theories and their applications to the geometry of higher-dimensional algebraic varieties, as well as advancements in the theory of homological blocks for knots and 3-manifolds. The project aims to...
This $400,000 federal Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049) will support research by President and Fellows of Harvard College (Harvard University) to develop tools for studying the geometry of intersecting surfaces using novel techniques from mathematics and gauge theory. Specifically, the research will focus on advancing instanton homology, a mathematical construct...