The National Science Foundation (NSF) awarded a $405,500 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Duke University to support a research program in A1-homotopy theory and its applications to enumerative geometry and number theory. The award will fund research to develop enriched counting methods that can detect differences in the number of solutions to equations requiring real or imaginary numbers, with potential applications in number theory and...
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 award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $165,000 to Syracuse University to conduct research on homological approaches to differential forms, differential operators, and transfer of algebra structures. The award will support the principal investigator's research on measures of singularity in algebraic geometry, focusing on differential forms, differential operators, cotangent complexes, and DG-algebra and...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill (UNC) a $185,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports a three-year research project to develop Hodge theoretic techniques for studying Knizhnik-Zamolodchikov differential equations, which link representation theory, algebraic geometry, and mathematical physics. Key research activities include developing a...
This $185,987 National Science Foundation Division of Mathematical Sciences Project Grant supports continued collaborative research in enumerative algebraic geometry at the University of North Carolina at Chapel Hill from August 1, 2022 through July 31, 2025. Specifically, the investigators and their graduate students will further their work resolving outstanding questions in enumerative algebraic geometry through techniques including intersection theory, equivariant localization, symmetric...
This $280,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research in birational geometry at New York University from April 2022 through March 2025. Specifically, the principal investigator will use methods from Galois cohomology of function fields, properties of algebraic cycles over non-algebraically closed fields, K-theory, and degeneration techniques to advance understanding of rationality and stable...
The University of North Carolina at Chapel Hill received a $740,299 Project Grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The funding will support research into complex Lagrangian geometry as a tool to study geometric questions and quantization arising at the intersection of geometry and topology. Specifically, the award will allow researchers to construct concrete models...
This Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences, under the NSF's Mathematical and Physical Sciences program (CFDA 47.049), provides $200,000 in funding to the University of California, Davis (UC Davis) from August 15, 2023 to July 31, 2026. The funding supports research aimed at uncovering patterns and symmetries in Khovanov-Rozansky link homology, a generalization of the famous HOMFLY polynomial in knot theory. The project will build upon...
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...
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...