Prof. Günter M. Ziegler (TU Berlin): A Sharp Colored Tverberg Theorem |
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| Startdatum/-zeit: | 05.05.2010 17:15 |
| Enddatum/-zeit: | 05.05.2010 |
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| Adresse: | Fachbereich Mathematik/ Informatik, Institut für Mathematik Prof. Dr. Winfried Bruns Albrechtstr. 28a 49076 Osnabrück |
| Telefon: | 0541 - 969 - 2485 |
| Telefax: | 0541 - 969 - 2770 |
| E-Mail: | wbruns@uos.de |
| Homepage: | http://www.mathematik.uni-osnabrueck.de/kolloquium.html |
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| Adresse: | Institut für Mathematik Institut für Mathematik, Geb. 69/ Raum 125 Albrechtstr. 28a, 49076 Osnabrück |
| Karte: | Bei Google Maps anzeigen |
| Beschreibung: | 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". Soon Bárány & Larman proved such a theorem for 3N colored points in a plane. A d-dimensional version was obtained in a remarkable 1992 paper by Zivaljevic & Vrecica obtained this, though not with a tight bound on the number of points. We propose a new "colored Tverberg theorem", which is tight, and which generalizes Tverberg's original theorem. The proof uses a "configuration space/test map" scheme, the combinatorics of special chessboard complexes, and finishes using (your choice) either equivariant obstruction theory, or a degree argument. (Joint work with Pavle V. M. Blagojevic und Benjamin Matschke). |
| Kategorie: | Mathematisches Kolloquium |
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