# Beyond the Borsuk-Ulam/Dold theorem (in Combinatorial Geometry)

Wednesday, October 16, 2013 - 1:30pm - 2:30pm

Lind 305

Pavle Blagojević (Freie Universität Berlin)

In this talk we present an evolution of equivariant topology methods in Combinatorial Geometry.

We start with

(a) the Topological Radon's theorem, an application of the Borsuk-Ulam theorem,

and proceed, via non-planarity of K_{3,3}, to

(b) the Topological Tverberg and the Weak Colored Tverberg theorem for primes,

which are applications of Dold's theorem, to continue with

(c) the Topological Tverberg for prime powers, an application beyond Dold's theorem based on

the connectivity and localization theorem for elementary abelian groups,

to finally ask:

What needs to be done in the case of Barany-Larman conjecture and Nandakumar & Ramana-Rao

problem when all the previously known methods fail?

We start with

(a) the Topological Radon's theorem, an application of the Borsuk-Ulam theorem,

and proceed, via non-planarity of K_{3,3}, to

(b) the Topological Tverberg and the Weak Colored Tverberg theorem for primes,

which are applications of Dold's theorem, to continue with

(c) the Topological Tverberg for prime powers, an application beyond Dold's theorem based on

the connectivity and localization theorem for elementary abelian groups,

to finally ask:

What needs to be done in the case of Barany-Larman conjecture and Nandakumar & Ramana-Rao

problem when all the previously known methods fail?