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SUMMARY:Rajko Nenadov (Google)
DTSTART:20211115T140000Z
DTEND:20211115T150000Z
DTSTAMP:20260423T021030Z
UID:EPC/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/77/">A n
 ew proof of the KŁR conjecture</a>\nby Rajko Nenadov (Google) as part of 
 Extremal and probabilistic combinatorics webinar\n\n\nAbstract\nWe give a 
 new\, short and intuitive proof of the celebrated KŁR conjecture.  Slight
 ly rephrased\, the conjecture states that if we condition on uniform edge 
 distribution\, the archetypal property of random graphs\, the probability 
 that the Erdős–Rényi random graph G(n\,m) does not contain a copy of a
  fixed graph H becomes superexponentially small in m\, for sufficiently la
 rge m > m(n\, H). As its most prominent application\, this conjecture impl
 ies that with high probability all subgraphs of the binomial random graph 
 with appropriate parameters satisfy an embedding lemma which complements t
 he sparse regularity lemma. The proof proceeds by induction and\, in some 
 way\, can be considered a `deterministic' analogue of the multiple-exposur
 e technique from random graph theory.\n
LOCATION:https://researchseminars.org/talk/EPC/77/
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