Persistent homology, hypergraphs and geometric cycle matching

Topological data analysis has been demonstrated to be a powerful tool to describe topological signatures in real-life data, and to extract complex patterns arising in natural systems. An important challenge in topological data analysis is to find robust ways of computing and analysing persistent generators, and to match significant topological signals across distinct systems. In this talk, I will present some recent work dealing with these problems. Our method is based on an interpretation of persistent homology summaries with network theoretical tools, combined with statistical and optimal transport techniques.