The Functoriality of Persistent Homology

Abstract: The pipeline that takes a filtration to its persistence diagram is functorial: it takes morphisms of filtrations to morphisms of persistence diagrams. We will analyze this structure, focusing on the one-parameter setting. We will start with an overview of the categories of filtrations and persistence diagrams followed by some examples of morphisms between filtrations arising in practice and what the induced morphisms between persistence diagrams can tell us.

algebraic topologydifferential geometrygeneral mathematicsgeneral topologygeometric topologymetric geometry

Audience: researchers in the topic

Topology, Geometry, & Data Analysis (TGDA) Seminar