Summer 2026

This project investigates how generative AI can automate the discovery of optimal mathematical structures for digital twins, focusing on topology learning and temporal memory in probabilistic graphical models for cardiovascular applications.

This project explores how LLM-based agents can be systematically integrated into research in algebra and number theory, combining computational exploration, informal reasoning, and formal verification into a unified pipeline.

This project uses AI-assisted methods to explore the polygonal Faber-Krahn inequality, which conjectures that among all n-gons of fixed area, the regular n-gon minimizes the first Dirichlet eigenvalue of the Laplacian.