Project Grant 2213295

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 conjectures. Specifically, the research will construct "invariant-to-knot" generative adversarial networks to generate knots with prescribed properties, learn new latent representations of knots with respect to topological metrics, and generalize existing reinforcement learning approaches to problems like slice genus and braid band rank. The results will provide clearer understanding of knot distributions and targeted knot generation. Additionally, the award establishes an undergraduate research training program pairing students with academic and industry mentors to solve data science problems and increase participation from underrepresented groups. The research runs from September 1, 2022 to August 31, 2024.