## 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.

conway@berkeley.edu