Veranstaltungskalender

More than 50 years ago, the Cambridge undergraduate Bryan Birch showed that “3N points in a plane”' can be split into N triples that span triangles with a non-empty intersection. He also conjectured a sharp, higher-dimensional version of this, which was proved by Helge Tverberg in 1964 (freezing, in a hotel room in Manchester).

In a 1988 Computational Geometry paper, Bárány, Füredi & Lovász noted that they needed a “colored version of Tverberg's theorem”. Bárány & Larman proved such a theorem for 3N colored points in a plane, and conjectured a version for d dimensions. A remarkable 1992 paper by Živaljević & Vrećica obtained this, though not with a tight bound on the number of points. The proof was based on equivariant topology and the beautiful combinatorics of “chessboard complexes”.

We propose a new “colored Tverberg theorem”, which is tight, and which generalizes Tverberg's original theorem. The proof uses a (by now) standard set-up of a “configuration space/test map” scheme, the combinatorics of special chessboard complexes that are pseudomanifolds, and finishes it off using (your choice) either equivariant obstruction theory, or a degree argument. (Joint work with Pavle V. Blagojević and Benjamin Matschke: http://arxiv.org/abs/0910.4987, http://arxiv.org/abs/0911.2692)

Eingeladen von Prof. Dr. Christine Bessenrodt

Prof. Dr. Günter M. Ziegler/TU Berlin

Fakultät für Mathematik und Physik

Dienstag, 22. Juni 2010, 17:15 Uhr

Hauptgebäude (Gebäude 1101, Kleiner Physikhörsaal, F342)
Welfengarten 1, 30167 Hannover

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