Topology Seminar (Introductory Talk): The evasion path problem and zig-zag persistent homology

Seminar | March 13 | 2:10-3 p.m. | 740 Evans Hall

 Benjamin Filippenko, UC Berkeley

 Department of Mathematics

The evasion path problem asks: Given a finite collection of sensors continuously moving in a bounded domain in \(\mathbb R^n\) for a finite length of time, such that each sensor can detect the presence of objects in a ball of fixed radius around itself, when can an intruder in the domain avoid being detected for the full length of time? The continuous path that such an intruder takes is called an evasion path, and the question asks about existence of an evasion path. We describe prior results on this problem by da Silva-Ghrist, Adams-Carlsson, and Ghrist-Krishnan, focusing in particular on the necessary condition for existence of an evasion path provided by Adams-Carlsson and based on zig-zag persistent homology of the time-varying Cech complex. We will first review persistent homology and zig-zag persistence.