Topology Seminar: Optimal bounds for the colored Tverberg problem

  • Date: 01/27/2010
Benjamin Matschke

University of British Columbia


The "colored Tverberg problem" asks for a smallest size of the color
classes in a (d+1)-colored point set C in R^d that forces
the existence of an intersecting family of r "rainbow" simplices with
disjoint, multicolored vertex sets from C. Using equivariant topology
applied to a modified problem, we prove the optimal lower bound
conjectured by Barany and Larman (1992) for the case of partition into
r parts, if r+1 is a prime.
The modified problem has a "unifying" Tverberg-Vrecica type
generalization, which implies Tverberg's theorem as well as the ham
sandwich theorem.
This is joint work with Pavle V. Blagojevic and Gunter M. Ziegler.


3:00pm - 4:00pm, WMAX 110