Anna Schenfisch (Dept. of Mathematics, MSU)

11/14/2022  4:10pm

Abstract: In this talk, we will first see how persistence modules (a primary tool in topological data analysis) have a natural home in the setting of stratified spaces and constructible cosheaves. In particular, we focus on zig-zag modules, which correspond to one-parameter filtrations. We then outline how the algebraic K-theory of zig-zag modules can be computed via an additivity result, aided by an equivalence between the category of zig-zag modules and the combinatorial entrance path category on a stratified \R. Once equipped with the K-theory of zig-zag modules, we discuss how these techniques might be extended to multi-parameter persistence modules.