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SUMMARY:Shadows and intersections: stability and new proofs - Peter Keevas
 h (Queen Mary London)
DTSTART:20090514T133000Z
DTEND:20090514T143000Z
UID:TALK17103@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:We give a short new proof of a version of the Kruskal-Katona t
 heorem due to Lov\\'asz. Our method can be extended to a stability result\
 , describing the approximate structure of configurations that are close to
  being extremal\, which answers a question of Mubayi.  This in turn leads 
 to another combinatorial proof of a stability theorem for intersecting fam
 ilies\, which was originally obtained by Friedgut using spectral\ntechniqu
 es and then sharpened by Keevash and Mubayi by means of a purely combinato
 rial result of Frankl.  We also give an algebraic perspective on these pro
 blems\, giving yet another proof of intersection stability that\nrelies on
  expansion of a certain Cayley graph of the symmetric group\, and an algeb
 raic generalisation of Lov\\'asz's theorem that answers a question of Fran
 kl and Tokushige.\n
LOCATION:MR12
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