EPFL Topology Seminar Fall 2026

Location: Room CM 1 517 (And sometimes Zoom)

Programme

Abstracts

Steve Oudot
Estimating the persistent homotopy type of filtered topological spaces from point samples

Given a sufficiently regular topological space X, Latschev’s theorem says that, for a dense enough sample P on X, and for suitable values of delta>0, one can recover the homotopy type of X from the Rips complex of parameter delta built on P. Our question here is: can this result be extended to recovering the persistent homotopy type of the filtration of X by the sublevel sets of a sufficiently regular function f: X->R^n? We answer the question in the affirmative, stating a persistent version  of Latschev’s theorem in which the Rips complex is filtered by the values of f at its vertices. For the sake of the exposition, I will first focus on estimating the persistent homology of the filtration from a pair of filtered Rips complexes, using techniques in topological data analysis; then, I will move on to estimating the persistent homotopy type of the filtration from a single filtered Rips complex,  using ingredients coming from homotopy theory.

The main result of this talk is joint work with Lukas Waas; the intermediate result on persistent homology estimation is joint work with Ethan André, Jingyi Li and David Loiseaux.