### Mathematics Colloquium

** Henry Adams
**

University of Florida

**Title:** Bridging metric geometry and topology

**Date:** Friday November 3, 2023

**Place and Time:** Love 101, 3:05-3:55 pm

**Abstract.**
The goal of this talk is to show how tools from topology can be used to bound quantities arising in metric geometry. I'll begin by introducing the Gromov-Hausdorff distance, which is a way to measure the "distance" between two metric spaces. Next, I will explain the nerve lemma, which says when a cover of a space faithfully encodes the shape of that space. Then, I'll use the nerve lemma to lower bound the Gromov-Hausdorff distance between a manifold and a finite subset thereof. I'll conclude by advertising a few other problems at the intersection of metric geometry and topology.