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UID:fcd80300bce5dd9806d1de7afd8ec08e
CATEGORIES:Special Colloquium
CREATED:20220103T131034
SUMMARY:Regularity lemma: discrete and continuous perspectives
LOCATION:Zoom
DESCRIPTION:<p>Abstract: Szemerédi's regularity lemma is a game-changer in extremal com
 binatorics and provides a global perspective to study large combinatorial o
 bjects. It has connections to number theory, discrete geometry, and theoret
 ical computer science. One of its classical applications, the removal lemma
 , is the essence for many property testing problems, an active field in the
 oretical computer science. Unfortunately, the bound on the sample size from
  the regularity method typically is either not explicit or is enormous. For
  testing natural permutation properties, we show one can avoid the regulari
 ty proof and yield a tester with polynomial sample size. For graphs, we pro
 ve a stronger, "L_infty'' version of the graph removal lemma, where we conj
 ecture that the essence of this new removal lemma for cliques is indeed the
  regularity-type proof. The analytic interpretation of the regularity lemma
  also plays an important role in graph limits, a recently developed powerfu
 l theory in studying graphs from a continuous perspective. Based on graph l
 imits, we developed a method combining with both analytic and spectral meth
 ods, to answer and make advances towards some famous conjectures on a commo
 n theme in extremal combinatorics: when does randomness give nearly optimal
  bounds? These works are based on joint works with Jacob Fox, Dan Kral',&nb
 sp; Jonathan Noel, Sergey Norin, and Jan Volec.</p>
CONTACT:Fan Wei - Princeton University
X-EXTRAINFO:This talk is for the local Rutgers Math Community only, Zoom links will be 
 sent by the Department Chair via email
DTSTAMP:20260828T093750
DTSTART;TZID=America/New_York:20220105T113000
DTEND;TZID=America/New_York:20220105T123000
SEQUENCE:0
TRANSP:OPAQUE
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