This was part of Randomness in Topology and its Applications

Persistence Diagrams, Euler Characteristics, and Mobius Inversion

Primoz Skraba, Queen Mary University of London and Jozef Stefan Institute, Slovenia
Tuesday, March 21, 2023



Slides
Abstract:

There are many ways of defining persistence diagrams. In this talk I will discuss the definition based on the Mobius inversion function which was introduced by Amit Patel under the name Generalized Persistence Diagrams. I will cover how this approach has appeared implicitly and explicitly in various results on persistence as well as various implications of this approach and (very) new developments. In particular, I will cover a surprising connection between Euler characteristics and persistence diagrams.  This is joint work with Amit Patel.