Estimating stratified persistent homotopy types

Many invariants of topological data analysis, in particular persistent homology, are constructed in a manner that passes through the world of homotopy theory, before finally producing an algebraic invariant. While this passage through homotopy theory comes with many advantages from a theoretical perspective, it also means that these invariants are often insensitive to features not detected by classical homotopy theory.

For example, classical persistent homology only has limited discriminative power when it comes to distinguishing singular data sets.

In this talk, I will explain how a more refined and recently developed version of homotopy theory – so-called stratified homotopy theory – can be used in TDA to study point clouds approximating singular spaces.