projects

I work on problems where geometry and structure matter, from reinforcement learning and generative models to topological data analysis. My background in algebraic topology gives me a unique perspective on ML. Persistent homology, geometric representations, and shape-aware features show up naturally in problems that standard ML and data science methods struggle with. Below is a selection of projects spanning applied ML, TDA, and some of the mathematical foundations underlying both.

tda
project thumbnail

Multi-parameter Persistence

Geometric models for multiparameter persistent homology via generic families of Morse functions.
project thumbnail

TDA applied to fMRI

Using persistent homology on cubical complexes to study task-modulated brain activity.
project thumbnail

Persistence Landscapes of Fractals

Proving that the persistence landscape of a fractal is itself self-similar.

algebraic topology
project thumbnail

Exciton Scattering

Applying algebraic topology to count quasi-particle excitations in molecular systems.
project thumbnail

Stochastic Currents

A higher-dimensional generalization of electrical current, studied via algebraic topology and stochastic processes.