AMS Seminar: Tom Needham (Florida State University) @ Whitehead 304

Title:  Optimal Transport-Based Distances for Metric Space Matching
Abstract: I will overview some methods for comparing datasets modeled as metric measure spaces (mm-spaces), which are compact metric spaces endowed with probability measures. The main tool is Gromov-Wasserstein (GW) distance, which provides a metric on the collection of all mm-spaces. The definition of GW distance is inspired by ideas from optimal transport and it has fascinating connections to many other areas of mathematics. I will discuss theoretical results on estimating GW distance using distribution-valued invariants of mm-spaces as well as some work on the use of GW distance for practical applications in data science.