Convexity Spaces and Extremal Set Theory

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• Boris Bukh (University of Cambridge)
• Thursday 24 February 2011, 15:00-16:00
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

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 point. 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 that it does. We show that the conjecture is false. In addition, we show that the conjecture is almost true, and explain how this problem relates to interesting questions in extremal set theory.

This talk is part of the Combinatorics Seminar series.

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