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SS 2024

18.06.2024 um 12:00 Uhr in 69/E23

Prof. Morten Brun (University of Bergen) 

Density Dependent Persistent Homology

Persistent homology is a tool that helps qualitatively describe the shape of the points in a sample taken from a geometric object like Euclidean space. One way to obtain a version of persistent homology of such a sample is via the filtered Rips complex.  The filtered Rips complex and the related filtered Cech complex are both basically ignorant to the concept of density of the points in the sample. The degree-Rips and the degree-Cech bifiltrations are adaptions of the
Rips- and Cech complexes that are filtered both with respect to distance and density. In the talk I will cast these constructions into a more general setting accommodating elementary proofs of some of their stability properties. Specifically, Gromov-Prohorov stability will be explained.