## Colloquium - Florent Baudier

**Date:** January 16, 2019

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Florent Baudier, Texas A&M University

**Description:**

**Title:** Faithful embeddability of metric spaces and graphs into Banach spaces.

**Abstract:** Faithful embeddability of metric spaces into Banach spaces is pivotal to research areas as diverse as: -the design of approximation algorithms in theoretical computer science (sparsest cut problem, multi-commodity flows, approximate nearest neighbor search, sketching...), -topology (Novikov conjecture), -noncommutative geometry (coarse Baum-Connes conjecture), -geometric group theory (Von Neumann's amenability, Gromov's program). This non-exhaustive list can be stretched at will since metric spaces, with a wide variety of features, arise in nearly all areas of mathematics. In this talk, I will focus on bi-Lipschitz and coarse embeddings of graphs (finite and infinite) into Banach spaces with some desirable geometric properties. I will discuss fundamental geometric problems of either local or asymptotic nature, in particular purely metric characterizations of "linear" properties of Banach spaces in the spirit of the Ribe program. One of the main goal of the talk is to present some fundamental ideas and techniques, as well as to convey the geometric intuition behind them.