Research

My research investigates the structure of low-dimensional manifolds and explores the "shape" of complex datasets through Manifold Learning and Diffusion Geometry.

In my theoretical work, I utilize Heegaard Floer homology to study 3- and 4-dimensional manifolds.

Simultaneously, I am building computational models using fiber bundles and diffusion maps to identify intrinsic community structures in high-dimensional datasets, an approach I am currently applying to the study of computational redistricting.

For an overview of some of my current projects, please see my Research Statement and 2026 Joint Math Meetings Presentation Slides below.