Project Grant 2532488
- 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...
- The National Science Foundation (NSF) awarded a $219,165 Project Grant under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) to the University of South Alabama. The grant, titled "LEAPS-MPS: Categorification in Algebra and Topology," aims to use categorification techniques to study knot theory, which has applications in biology, medicine, chemistry, and physics. The research is expected to create new tools to address challenging open problems in knot theory...
- This Project Grant from the National Science Foundation's $47.049 Mathematical and Physical Sciences program provides $294,584 to Virginia Commonwealth University from August 1, 2022 to July 31, 2025. The award supports research exploring knot theory and its applications to low-dimensional topology, as well as disseminating related knowledge. Specifically, the university will conduct fundamental investigations into knot invariants, crossing changes, tangle decompositions and unknotting...
- 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 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 $150,000 Project Grant award was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The funding supports collaborative research combining ideas and techniques from several exciting areas of contemporary mathematical thought, including homotopy theory, algebraic K-theory, smooth manifolds, polyhedra, and knots. The project aims to develop new connections between these fields, with plans to classify important...
- This $200,000 four-year project grant was awarded by the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) to North Carolina State University to conduct research in geometric topology, including the study of knots, three- and four-dimensional shapes, and the development of tools to measure the complexity of these objects. The project aims to produce new exotic smooth four-manifolds, study surfaces in four-manifolds, and apply instanton gauge theory to address...
- The National Science Foundation (NSF) awarded a $150,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the Georgia Tech Research Corporation. The grant, awarded on September 15, 2025, will support a research project investigating important problems in quantum topology and its connections with classical topology and hyperbolic geometry. The project aims to advance the understanding of three- and four-dimensional topology and knot theory, which...
- 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...
- The National Science Foundation (NSF) awarded a $149,999 Project Grant under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) to the Research Foundation for the State University of New York (RF SUNY) to conduct collaborative research on the intersection of homotopy theory, algebraic K-theory, smooth manifolds, polyhedra, and knots. The research aims to develop powerful connections between these mathematical fields, including classifying important geometric objects,...
The National Science Foundation (NSF) awarded a $249,941 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to Duquesne University of the Holy Spirit, doing business as Duquesne University, for the project "LEAPS-MPS: EXAMINATION OF KNOT INVARIANTS VIA COMPUTATIONAL METHODS." The project investigates knot theory, a field of mathematics focused on understanding how loops can be embedded and manipulated in three-dimensional space, with applications in molecular biology, physics, and computer science. The research will utilize machine learning and predictive modeling to uncover new patterns and propose novel tools for identifying certain families of knots, advancing the computational accessibility of topology. In addition, the project will involve undergraduate students in active research, create computational packages for further exploration, and engage with K-12 communities through outreach programs. The award has an initial period of performance from September 1, 2025 to August 31, 2027.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $249.9k | 7/18/25 |