News on the colored Tverberg problem

Benjamin Matschke

Abstract

In 2009, we found a new version of the colorful Tverberg theorem in convex geometry, which in turn implied the Barany-Larman conjecture from 1992 in the prime-minus-one case and asymptotically in general. In this talk we will present a natural generalization of this theorem to manifolds. The proof uses equivariant topology, and therefore works only if the symmetry giving parameter is a prime. The non-prime case remains a challenging open problem. This is joint work with Pavle Blagojević and Günter Ziegler.