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UID:20250626T141614EDT-73228IGDgZ@132.216.98.100
DTSTAMP:20250626T181614Z
DESCRIPTION:Title: Recent progress on the Kannan-Lovasz-Simonovits (KLS) co
 njecture and Bourgain's slicing problem I\n\nAbstract: Kannan\, Lovász\, a
 nd Simonovits (KLS) conjectured in 1995 that the Cheeger isoperimetric coe
 fficient of any log-concave density or any convex body is achieved by half
 -spaces up to a universal constant factor. This conjecture now plays a cen
 tral role in the field of convex geometry\, unifying or implying older con
 jectures. In particular\, it implies Bourgain's slicing conjecture (1986) 
 and the thin-shell conjecture (2003). While it is natural to expect convex
  bodies to have good isoperimetry (in other words\, not look like dumbbell
 s)\, the progress on bringing down the Cheeger isoperimetric coefficient i
 n the KLS conjecture has been stagnant in recent years. The previous best 
 bound\, with dimension dependency d^1/4\, was established by Lee and Vempa
 la in 2017 using Eldan's stochastic localization\, and matches the best di
 mension dependency Klartag obtained in 2006 for Bourgain's slicing conject
 ure.\n	After becoming familiar with Eldan's stochastic localization techniq
 ue in the previous lecture\, first we aim to get familiar with the concept
  of 'localization' and to view stochastic localization as an extension. Th
 en we go through the Lee and Vempala (2017) proof to see in action a concr
 ete application of stochastic localization.\n\n \n\nZoom link \n\nhttps://
 us06web.zoom.us/j/82247948277?pwd=RmtjbzRYaml6aHg3c1RTRFpvVXNDUT09\n\nID d
 e réunion : 822 4794 8277\n\nCode secret : 699575\n\n \n\n \n\n \n
DTSTART:20211006T150000Z
DTEND:20211006T160000Z
SUMMARY:Yuansi Chen (Duke University) CRM Nirenberg Lectures in Geometric A
 nalysis
URL:/mathstat/channels/event/yuansi-chen-duke-universi
 ty-crm-nirenberg-lectures-geometric-analysis-333728
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