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 National Science Foundation (NSF) Division of Mathematical Sciences Project Grant for $281,433 awarded to Claremont McKenna College supports research in pure and applied knot theory. The project aims to connect quantum topology with hyperbolic geometry and apply knot theory techniques to the study of knotted biopolymers. Key research focus areas include: Investigating how quantum invariants of knots relate to the geometric properties of knots and 3-dimensional spaces, with potential...
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 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 three-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $215,864, will fund research into low-dimensional topology through August 2025. Specifically, the principal investigator at the University of Notre Dame will employ combinatorial tools to study problems involving knots, surfaces embedded in four-dimensional manifolds, and the detection of exotic smooth structures in dimension four. This includes investigating the meridional...
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 $200,000 National Science Foundation project grant supports mathematical and physical sciences research at Michigan State University from September 2022 through August 2025. The award falls under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and address national problems through basic research and education in these fields. Specifically, the principal investigator and their team will investigate Floer and Khovanov theories...
This $249,783 National Science Foundation Project Grant under the Mathematical and Physical Sciences program will support Brigham Young University's research applying machine learning techniques to knot theory. The Principal Investigator will adapt generative adversarial networks, variational autoencoders, and reinforcement learning algorithms to study topological properties of knots, learn latent distributions of knots and their invariants, and guide searches for counterexamples to open...
This Project Grant from the National Science Foundation Directorate for Mathematical and Physical Sciences, under the Mathematical and Physical Sciences federal grant program (CFDA 47.049), provides $122,662 to investigate several research questions in topology at Brooklyn College of the City University of New York from July 1, 2022 to June 30, 2024. Specifically, the award supports three projects exploring how properties of three-dimensional knots and manifolds can be represented by...
The National Science Foundation (NSF) awarded a $185,923 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to the Rector & Visitors of the University of Virginia (UVA) to conduct research in stable homotopy theory and its applications in algebra, topology, and geometry. The project aims to explore further applications of stable homotopy theory, including studying the stable stems and their connections to geometric topology, number theory, and algebraic...