Ephemeral persistence modules and distance comparison

Speaker: Nicolas Berkouk (Ecole Polytechnique Fédérale de Lausanne)

Occasion: Topological Data Analysis

Date: April 26, 2021

Abstract: 

In this talk, I will provide a definition of ephemeral multi-persistent modules and prove that the quotient of persistent modules by the ephemeral ones is equivalent to the category of γ-sheaves. In the case of one-dimensional persistence, our definition agrees with the usual one showing that the observable category and the category of γ-sheaves are equivalent. I will also establish isometry theorems between the category of persistent modules and γ-sheaves both endowed with their interleaving distance. Finally, we compare the interleaving and convolution distances. Altogether, these results pave a new way to define dimension reduction techniques for multi-parameter persistence modules.

Joint work with François Petit.