Persistent homology, hypergraphs and geometric cycle matching

Abstract: 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.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html