Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, June 01, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Uli Wagner

A combinatorial/geometric proof of the Colored Tverberg Theorem

Several basic theorems in discrete geometry, such as Radon's Theorem and Tverberg's Theorem, concern partions of finite sets in d-space into a prescribed number r of parts in such a way that the convex hulls of the parts have a common point of intersection. One of the most advanced theorems of this type is the so-called Colored Tverberg theorem, whose precise statement we will review in the course of the talk.

This result (originally conjectured by Bárány, Füredi, and Lovász) was first established by Živaljević and Vrećica, with suboptimal bounds or the size of the point set required to achieve a partition into r parts. Recently, Blagojević, Matsche, and Ziegler gave a new proof, which yields sharp bounds for prime r. Shortly afterwards, this was further simplified by Vrećica and Živaljević. All known proofs are topological.

Here, we present a "de-topologized" version of the recent BMZ-VZ proof, in the hope to make it more accessible to a wider audience.

Joint work with J. Matoušek and M. Tancer

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