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SUMMARY:Forbidden vector-valued intersections - Eoin Long (University of O
 xford)
DTSTART:20170126T143000Z
DTEND:20170126T153000Z
UID:TALK70306@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Given vectors V = (v_i: i \\in [n]) in R^D\, we define the V-i
 ntersection of A\,B \\subset [n] to be the vector sum_{i \\in A \\cap B} v
 _i. In this talk I will discuss a new\, essentially optimal\, supersaturat
 ion theorem for\nV-intersections\, which can be roughly stated as saying t
 hat any large family of sets contains many pairs (A\,B) with V-intersectio
 n w\, for a wide range of V and w. A famous theorem of Frankl and Rödl co
 rresponds to the\ncase D=1 and all v_i=1 of our theorem. The case D=2 and 
 v_i=(1\,i) solves a conjecture of Kalai.\n\nJoint work with Peter Keevash.
 \n
LOCATION:MR12
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