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UID:315@math.technion.ac.il

DTSTART;TZID=Asia/Jerusalem:20241113T143000

DTEND;TZID=Asia/Jerusalem:20241113T152000

DTSTAMP:20250109T093819Z

URL:https://math.technion.ac.il/events/raphael-yuster/

SUMMARY:Raphael Yuster (Haifa) -- An entropy inequality and almost k-union 
 closed set systems
DESCRIPTION:Lecturer:Raphael Yuster\n Location:814 Amado\n We consider the 
 following inequality relating the entropy h(p) of a Bernoulli r.v. of a si
 ngle positive outcome with the entropy h(p^k) of the corresponding r.v. of
  k positive outcomes:\nphi^{k-1} h(p^k) &gt\;= p^{k-1} h(p) where phi is t
 he positive root of x^k+x-1.\n\nThe case k=2 of this inequality was recent
 ly proved by Alweiss\, Huang\, and Sellke and by Boppana\, and served\, to
 gether with a breakthrough idea of Gilmer\, an important ingredient in the
  proof of the stability version of Frankl's union-closed conjecture by Cha
 se and Lovett. Other applications of this inequality were recently conside
 red by Wakhare.\n\nWe prove this inequality for all 3 &lt\;= k &lt\;= 20 a
 nd prove a variant for all k where phi^{k-1} is replaced with a slightly l
 arger constant. In fact\, we show that the inequality reduces to a conject
 ure about the number of real roots of an explicit polynomial. We use this 
 result to prove the k-dimensional analogue of the Chase-Lovett theorem.\n\
 nParts of this work is joint with Geva Yashfe.\n 
CATEGORIES:Combinatorics Seminar,Seminars
LOCATION:814 Amado

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