Profile: Matthew Zaremsky ⟨mzaremsky@albany.edu⟩
Title: Bestvina-Brady discrete Morse theory and Vietoris-Rips complexes
Abstract:
Bestvina-Brady discrete Morse theory is a topological tool that has historically been most useful in geometric group theory. In this talk I will discuss a version of Bestvina-Brady Morse theory that is particularly conducive to understanding topological properties of Vietoris-Rips complexes of metric spaces, and has applications not only to geometric group theory, but also to applied topology and topological data analysis. In particular I will discuss a recent short proof of a result of Virk, that says the metric space $\mathbb{Z}^n$ with the usual $L^1$ metric has contractible Vietoris-Rips complexes.
Notes:
Status: Accepted
Collection: Applied Topology