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FIELD
Math:Topology
DATE
Dec 16 (Tue), 2025
TIME
11:00 ~ 12:30
PLACE
1423
SPEAKER
Lim, Sunhyuk
HOST
Kim, Sang-hyun
INSTITUTE
SungKyunKwan University
TITLE
Gromov-Hausdorff Distance and Quantified Borsuk-Ulam Theorems via Vietoris-Rips Complexes
ABSTRACT
The Gromov-Hausdorff distance is a fundamental metric defined on the space of isometry classes of compact metric spaces. In this presentation, we discuss recent developments in the computation of the Gromov-Hausdorff distance. In particular, we will focus on: (1) The connection between Gromov-Hausdorff distance and quantitative versions of the Borsuk-Ulam Theorem; and (2) How the Vietoris-Rips complex—a geometric simplicial complex—can strengthen the quantitative Borsuk-Ulam Theorem, ultimately achieving better lower bounds for the Gromov-Hausdorff distance. Time permitting, we will discuss how the topology of Vietoris-Rips complexes contributes to the theoretical understanding of persistent homology, or by comparing the Gromov-Hausdorff distance with the Gromov-Wasserstein distance (which incorporates measure-theoretic "weights").
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