Combinatorics Seminar

16:00-18:00

Speaker: Pablo Soberon

Title: Tverberg's theorem beyond prime powers

Abstract: Tverberg-type theory aims to establish sufficient conditions for a simplicial complex $\Sigma$ such that every continuous map $f:\Sigma \to \mathbb{R}^d$ maps $q$ points from pairwise disjoint faces to the same point in $\mathbb{R}^d$.  Such results are plentiful for $q$ a prime power.  However, for $q$ with at least two distinct prime divisors, results that guarantee the existence of $q$-fold points of coincidence are non-existent— aside from immediate corollaries of the prime power case.  Here we present a general method that yields such results beyond the case of prime powers.  Joint work with Florian Frick.