Title: Lecture II: Persistent Local System
Speaker: Amit Patel (Colorado State University)
Abstract: Given a map $f: X \rightarrow \mathbb{R}$ to the real line, we use the total ordering on $\mathbb{R}$ to filter $X$ by the sublevel sets of $f$. This leads to a persistence module which has a persistence diagram. The main result in persistent homology is that the persistence diagram of $f$ is stable to perturbations of $f$. We are interested in developing a theory of persistent homology for constructible maps $f: X \rightarrow M$ to a manifold $M$. The goal is to define a persistence diagram that is stable to perturbations of the map $f$. Our first paper is available on arxiv. When $M$ is the circle, our invariants look similar to the invariants of Burghelea and Dey. I will discuss the first important step in this program.
- MacPherson, Patel. Persistent Local Systems.
Seminar URL: https://tgda.osu.edu/
