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SUMMARY:Emergence of regularity in large graphs - Benny Sudakov (ETH Züri
 ch)
DTSTART:20240410T080000Z
DTEND:20240410T090000Z
UID:TALK213961@talks.cam.ac.uk
DESCRIPTION:"Every large system\, chaotic as it may be\, contains a well-o
 rganized subsystem".This phenomenon is truly ubiquitous and manifests itse
 lf in different mathematicalareas. One of the central problems in extremal
  combinatorics\, which was extensively studied in thelast hundred years\, 
 is to estimate how large a graph/hypergraph needs to be to guarantee theem
 ergence of such well-organized substructures.\nIn the first part of this t
 alk we will give an introduction to this topic\, mentioning some classical
  resultsas well as a few applications to other areas of mathematics. Then 
 we discuss the recent solution(with Oliver Janzer) of the following fundam
 ental problem\, posed by Erdos and Sauer about 50 years ago:"How many edge
 s on n vertices force the existence of an r-regular subgraph (r>2)?"Our pr
 oof uses algebraic and probabilistic tools\, building on earlier works byA
 lon\, Friedland\, Kalai\, Pyber\, R&ouml\;dl and Szemer&eacute\;di.
LOCATION:Seminar Room 1\, Newton Institute
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