BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:The Junta Method for Hypergraphs - Noam Lifschitz (Bar-Ilan Univer
 sity)
DTSTART:20180531T133000Z
DTEND:20180531T143000Z
UID:TALK104356@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Numerous problems in extremal hypergraph theory ask to determi
 ne the maximal size of a k-uniform hypergraph on n vertices that does not 
 contain an 'enlarged' copy H^+^ of a fixed hypergraph H. These include wel
 l-known problems such as the Erdős 'forbidding one intersection' problem 
 and the Frankl-Füredi 'special simplex' problem.\n\nIn this talk we prese
 nt a general approach to such problems\, using a 'junta approximation meth
 od' that originates from analysis of Boolean functions. We prove that any 
 (H^+^)-free hypergraph is essentially contained\nin a 'junta' -- a hypergr
 aph determined by a small number of vertices -- that is also (H^+^)-free\,
  which effectively reduces the extremal problem to an easier problem on ju
 ntas. Using this approach\, 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\, whi
 ch includes  the aforementioned problems\, and solves them for a\nlarge ne
 w set of parameters.\n\nBased on joint works with David Ellis and Nathan K
 eller
LOCATION:MR13
END:VEVENT
END:VCALENDAR