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# PIMS Network-Wide Colloquium

**
Thu., Sep. 23, 2021 2:30 p.m.
**

**Speaker:**Assaf Naor (Princeton University)

**Title:**Isomorphic reverse isoperimetry and Lipschitz extension

**Abstract:**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.