TGDA Mini-Course - Amit Patel - Lecture II

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Amit Patel
February 6, 2019
1:50PM - 2:50PM
Location
Cockins Hall 240

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Add to Calendar 2019-02-06 13:50:00 2019-02-06 14:50:00 TGDA Mini-Course - Amit Patel - Lecture II 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/ Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public
Description

Title: Lecture II: Persistent Local System

SpeakerAmit 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.

  1. MacPherson, Patel. Persistent Local Systems

Seminar URLhttps://tgda.osu.edu/

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