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SUMMARY:Ronen Eldan (Weizmann Institute)
DTSTART:20210428T170000Z
DTEND:20210428T180000Z
DTSTAMP:20260423T021011Z
UID:TCSPlus/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TCSPlus/26/"
 >Localization\, stochastic localization\, and Chen's recent breakthrough o
 n the Kannan-Lovasz-Simonivits conjecture</a>\nby Ronen Eldan (Weizmann In
 stitute) as part of TCS+\n\n\nAbstract\nThe Kannan-Lovasz and Simonovits (
 KLS) conjecture considers the following isoperimetric problem on high-dime
 nsional convex bodies: Given a convex body $K$\, consider the optimal way 
 to partition it into two pieces of equal volume so as to minimize their in
 terface. Is it true that up to a universal constant\, the minimal partitio
 n is attained via a hyperplane cut? Roughly speaking\, this question can b
 e thought of as asking "to what extent is a convex set a good expander"?\n
 \nIn analogy to expander graphs\, such lower bounds on the capacity would 
 imply bounds on mixing times of Markov chains associated with the convex s
 et\, and so this question has direct implications on the complexity of man
 y computational problems on convex sets. Moreover\, it was shown that a po
 sitive answer would imply Bourgain's slicing conjecture.  \n\nVery recentl
 y\, Yuansi Chen obtained a striking breakthrough\, nearly solving this con
 jecture. In this talk\, we will overview some of the central ideas used in
  the proof. We will start with the classical concept of "localization" (a 
 very useful tool to prove concentration inequalities) and its extension\, 
 stochastic localization - the main technique used in the proof.\n
LOCATION:https://researchseminars.org/talk/TCSPlus/26/
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