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Progress on the KLS Conjecture

Geometric functional analysis and applications November 13, 2017 - November 17, 2017

November 16, 2017 (01:30 PM PST - 02:30 PM PST)
Speaker(s): Santosh Vempala (Georgia Institute of Technology)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • KLS

  • Cheeger

  • logconcave

  • localization

  • logSobolev

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

We show that the Cheeger constant of any logconcave density is at least Tr(A^2)^{-1/4} where A is its covariance matrix, i.e., n^{-1/4} for isotropic logconcave densities. This improves on known bounds for the KLS, thin-shell, concentration and Poincare constants, and gives an alternative proof of the current best bound for the slicing constant. We then show how our proof can be used to derive a nearly tight bound for the log-Sobolev constant of isotropic logconcave distributions.

The talk is joint work with Yin Tat Lee (UW and MSR).

Supplements
30101?type=thumb Vempala Notes 2.44 MB application/pdf Download
Video/Audio Files

14-Vempala

H.264 Video 14-Vempala.mp4 137 MB video/mp4 rtsp://videos.msri.org/data/000/030/023/original/14-Vempala.mp4 Download
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