Isomorphic reverse isoperimetry and Lipschitz extension

In the Lipschitz extension problem we are given a pair of metric spaces X,Y and ask for the smallest K such that for any subset A of X every L-Lipschitz mapping from A to Y can be extended to a KL-Lipschitz mapping from X to Y. Most of this talk will be devoted to an introductory overview of part of the large amount of knowledge that has accumulated on this question over the past century, and its multifaceted connections to various mathematical areas. We will also explain longstanding mysteries that remain open despite major efforts, and describe recent progress that relates the Lipschitz extension problem to the question of reversing the classical isoperimetric inequality.

Speaker Biography

Prior to starting his current position in 2014 as Professor of Mathematics at Princeton University, Assaf Naor received his doctorate from the Hebrew University (advised by Joram Lindenstrauss), was a researcher at Microsoft Research, and a Professor at the Courant Institute. His work is devoted to analysis and metric geometry, as well as its interactions with other areas such as probability, combinatorics and computer science. Naor is the winner of the Salem, Nemmers and Ostrowski prizes amongst other awards.