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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:The Junta Method for Hypergraphs - Noam Lifshitz (
Bar Ilan University)
DTSTART:20180517T140000Z
DTEND:20180517T150000Z
UID:TALK3186AT
URL:/talk/index/3186
DESCRIPTION:Numerous problems in extremal hypergraph theory as
k to determine the maximal size of a k-uniform hyp
ergraph on n vertices that does not contain an 'en
larged' copy H^\;+ of a fixed hypergraph H. The
se include well-known problems such as the Erdős-
Sós 'forbidding one intersection' problem and the
Frankl-Füredi 'special simplex' problem.\n\nIn thi
s talk we present a general approach to such probl
ems\, using a 'junta approximation method' that or
iginates from analysis of Boolean functions. We pr
ove that any (H^\;+)-free hypergraph is essenti
ally contained in a 'junta' —\; a hypergraph
determined by a small number of vertices —\;
that is also (H^\;+\;)–\;free\, which e
ffectively reduces the extremal problem to an easi
er problem on juntas. Using this approach\, we obt
ain\, for all C <\; k <\; n/C\, a complete s
olution of the extremal problem for a large class
of H's\, which includes the aforementioned proble
ms\, and solves them for a large new set of parame
ters.\n\nBased on joint works with David Ellis and
Nathan Keller.
LOCATION:Watson LTA
CONTACT:Allan Lo
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