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CATEGORIES:Combinatorics Seminar
SUMMARY:The Junta Method for Hypergraphs - Noam Lifschitz
(Bar-Ilan University)
DTSTART;TZID=Europe/London:20180531T143000
DTEND;TZID=Europe/London:20180531T153000
UID:TALK104356AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/104356
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. These i
nclude well-known problems such as the Erdős 'forb
idding one intersection' problem and the Frankl-Fü
redi 'special simplex' problem.\n\nIn this talk we
present a general approach to such problems\, usi
ng a 'junta approximation method' that originates
from analysis of Boolean functions. We prove that
any (H^+^)-free hypergraph is essentially containe
d\nin a 'junta' -- a hypergraph determined by a sm
all number of vertices -- that is also (H^+^)-free
\, which effectively reduces the extremal problem
to an easier problem on juntas. Using this approac
h\, we obtain\, for all k in the range C to n/C\,
a complete solution of the extremal problem for a
large class of H's\, which includes the aforement
ioned problems\, and solves them for a\nlarge new
set of parameters.\n\nBased on joint works with Da
vid Ellis and Nathan Keller
LOCATION:MR13
CONTACT:Andrew Thomason
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