Geometric Analysis and Topology Seminar

A New Vertical-Versus-Horizontal Isoperimetric Inequality on the Heisenberg Group, with Applications to Metric Geometry and Approximation Algorithms

Speaker: Assaf Naor, Princeton

Location: Warren Weaver Hall 1314

Date: Thursday, November 10, 2016, 10 a.m.


In this talk we will show that for every measurable subset of the Heisenberg group of dimension at least 5, an appropriately defined notion of its "vertical perimeter" is at most a constant multiple of its horizontal (Heisenberg) perimeter. We will explain how this new isoperimetric-type inequality solves open questions in analysis (an endpoint estimate for a certain singular integral on \(W^{1,1}\)), metric geometry (sharp nonembeddability into \(L_1\)) and approximation algorithms (asymptotic evaluation of the performance of the Goemans-Linial algorithm for the Sparsest Cut problem). Joint work with Robert Young.