The algebraic stability for persistent Laplacians

Abstract

The stability for topological persistence is one of the fundamental issues in topological data analysis. Many methods have been proposed to deal with the stability for persistent modules or persistence diagrams. The persistent Laplacians, as a relatively new topological persistence, have gained more attention and applications in different fields. In this talk, we start to consider the stability for persistent Laplacians. We introduce the concept of the Laplacian tree to describe the collection of persistent Laplacians that persist from a given parameter. We construct the category of Laplacian trees and prove an algebraic stability theorem for persistence Laplacian trees. Specifically, our stability theorem is applied to the real-valued functions on simplicial complexes and digraphs.