Sastanak Odeljenja za matematiku, 18. jun 2010.


U petak, 18.06.2010. 14 časova, u sali 2 MI SANU, predavanje će održati Benjamin Matschke, Technische Universität - Berlin.

Naziv predavanja: Optimal bounds on the colored Tverberg problem and a transversal Tverberg-Vrećica type generalization

Abstract:  This is joint work with Pavle V. Blagojević and Gunter M. Ziegler.  We present an optimal colorful Tverberg-Vrećica type transversal theorem about transversals meeting convex hulls of rainbow partitions of several colored set in Euklidean space.  This is a "unifying" theorem. It implies among others a new tight colored Tverberg theorem for primes, which in turn implies the Barany-Larman conjecture (1992) for primes plus one, as well as variations of the famous ham sandwich theorem. On the surface these seem to have not much in common. Along the proof we obtain two results of independent interest: We present calculate the cohomological index for some joins of chessboard complexes, and establish a new Borsuk-Ulam type theorem for (Z_p)^m-equivariant bundles that generalizes results of Volovikov (1996) and Živaljević (1999).

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