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General and Set-Theoretic Topology

General/ST Session #5 #1

Subevent of General/ST Session #5

Central Time (US & Canada)

Starts at: 2025-08-14 08:30AM

Ends at: 2025-08-14 08:50AM

Holey Vietoris--Rips complex, Batman!

Chris Wells ⟨coc0014@auburn.edu⟩

Abstract:

Given a metric space and a positive number d, the Vietoris–Rips (VR) complex of scale d is the simplicial complex whose faces are all sets of diameter at most d. Recently, there’s been a push to understand the VR

  • How many holes (non-trivial homologies) are there?
  • How big is the largest facet?
  • How small is the smallest facet?
  • How many differently-sized facets are there?

Based on joint work with Joe Briggs and Ziqin Feng.

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