Bruce Kleiner (Yale)

BiLipschitz embedding in Banach spaces.

Abstract. Motivated by a conjecture from computer science, I will discuss biLipschitz embeddings $X \to V$ where $X$ is a metric space and $V$ is a Banach space. The focus will be on the case when $X$ is a metric measure space satisfying a Poincare inequality. Of particular interest is the case when the target Banach space is $L^1$,  in which case there is a new link between embedding questions and the structure of sets of finite perimeter in $X$.   By exploiting recent work on geometric measure theory in the Heisenberg group, we show that the Heisenberg group cannot be biLipschitz embedded in $L^1$,   confirming a conjecture of Assaf Naor.

This is joint work with Jeff Cheeger.