Topology Seminar (Main Talk): Connected components of the space of evasion paths

Seminar | March 13 | 4:10-5 p.m. | 3 Evans Hall

 Benjamin Filippenko, UC Berkeley

 Department of Mathematics

In the introductory talk, we discussed results on the evasion path problem for sensors wandering in a bounded domain in \(\mathbb R^n\). In the case of planar domains (\(n = 2\)), Adams and Carlsson provide a computable algorithm that determines the existence of an evasion path based on the time-varying alpha complex and the time-varying cyclic ordering on the set of sensors in the plane neighboring any given sensor. We provide a generalization of their result to \(\mathbb R^n\). Moreover, we show that their algorithm (and its generalization to \(\mathbb R^n\)) actually computes the number of connected components of the space of evasion paths and provides a representative path in each component.