Bounding Gromov-Hausdorff distances with Borsuk-Ulam theorems and Vietoris-Rips complexes

Abstract: The Gromov-Hausdorff distance between two metric spaces is an important tool in geometry, but it is difficult to compute. For example, the Gromov-Hausdorff distance between unit spheres of different dimensions is unknown in nearly all cases. I will introduce recent work by Lim, Mémoli, and Okutan that lower bounds the Gromov-Hausdorff distance between spheres using Borsuk-Ulam theorems. We improve these lower bounds by connecting this story to Vietoris-Rips complexes, providing new generalizations of Borsuk-Ulam.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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