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Applied Topology

Matthew Zaremsky

Subevent of Applied Topology - Fri. AM

Forbes 1022

Eastern Time (US & Canada)

Starts at: 2025-03-07 10:40AM

Ends at: 2025-03-07 11:00AM

Bestvina-Brady discrete Morse theory and Vietoris-Rips complexes

Matthew Zaremsky ⟨mzaremsky@albany.edu⟩

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.

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