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UID:www.tcs.tifr.res.in/event/982
DTSTAMP:20230914T125945Z
SUMMARY:Polynomial to Exponential Transition in Ramsey Theory
DESCRIPTION:Speaker: Dhruv Mubayi (University of Illinois at Chicago\nChica
 go\, Illinois\, U.S.)\n\nAbstract: \nAbstract:  After a brief introductio
 n to classical hypergraph Ramsey numbers\, I will focus on the following p
 roblem. What is the minimum t such that there exist arbitrarily large k-un
 iform hypergraphs whose independence number is at most polylogarithmic in 
 the number of vertices and every s vertices span at most t edges? Erdos an
 d Hajnal conjectured (1972) that this minimum can be calculated precisely 
 using a recursive formula and Erdos offered a $500 prize for a proof. For 
 k = 3\, this has been settled for many values of s\, but it was not known 
 for larger k.\nHere we settle the conjecture for all k at least 4. Our met
 hod also answers a question of Bhat and Rodl about the maximum upper densi
 ty of quasirandom hypergraphs.\nThis is joint work with Alexander Razborov
 .\n
URL:https://www.tcs.tifr.res.in/web/events/982
DTSTART;TZID=Asia/Kolkata:20190806T113000
DTEND;TZID=Asia/Kolkata:20190806T123000
LOCATION:A-201 (STCS Seminar Room)
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