Plenary talk of Michael Kerber at the Applied Topology 2025 conference скачать в хорошем качестве

Plenary talk of Michael Kerber at the Applied Topology 2025 conference

Title: Multi-Parameter Persistent Homology is Practical Abstract: Multi-parameter persistent homology (MPH) is an active research branch of topological data analysis. Recent years have witnessed an extending layer of efficient algorithms for various problems in MPH providing tools for its practical usage. We will discuss two recent results in this context: First, we will demonstrate how to extend Delaunay filtrations, also known as alpha filtrations, to the case of point clouds with a real valued function (joint work with Angel Alonso, Tung Lam, and Mike Lesnick). Second, we will introduce graphcodes, a novel way to faithfully represent 2-parameter persistence modules which allows both for employing MPH in machine learning applications and for faster algorithmic approaches in the context of decomposing persistence modules (joint work with Florian Russold).