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SUMMARY:Convexity Spaces and Extremal Set Theory - Boris Bukh (University 
 of Cambridge)
DTSTART:20110224T150000Z
DTEND:20110224T160000Z
UID:TALK29753@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Tverberg's theorem asserts that every (r-1)(d+1)+1 points in R
 ^d can be partitioned into r parts whose convex hulls meet at a single poi
 nt. Radon's lemma is the special case r=2 of Tverberg's theorem. Can it be
  that Radon's lemma implies Tverberg's theorem? Eckhoff's conjecture is th
 at it does. We show that the conjecture is false. In addition\, we show th
 at the conjecture is almost true\, and explain how this problem relates to
  interesting questions in extremal set theory.
LOCATION:MR12
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