Topological Data Analysis

Our group works on the mathematical foundations of Topological Data Analysis and its application to interdisciplinary projects. Current topics include homological and algebraic methods for studying persistence modules, including multiparameter persistence. The aim is to produce stable and computable invariants that can be used in statistics and machine learning, and applications to biological networks and materials science.

The StableBear package for Python and C++ was originally developed by, and is maintained within, our group. StableBear serves as a statistics engine for TDA, providing core functionality such as computation of topological invariants and bootstrapping. It operates on entire collections of datasets at once, with highly parallelized and reproducible computations on both CPU and GPU.

We co-host the Applied CATS seminar , which covers TDA as well as applied algebraic geometry, combinatorics and statistics.