The topological Tverberg problem beyond prime powers

Abstract: Tverberg-type theory aims to establish sufficient conditions for a simplicial complex $\Sigma$ such that every continuous map $f\colon \Sigma \to \mathbb{R}^d$ maps $q$ points from pairwise disjoint faces to the same point in~$\mathbb{R}^d$. Such results are plentiful for $q$ a power of a prime. 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.

number theory

Audience: researchers in the topic

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Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

Registration for the conference is free. Register at cant2021.eventbrite.com.

The conference website is www.theoryofnumbers.com/cant/ Lectures will be broadcast on Zoom. The Zoom login will be emailed daily to everyone who has registered on eventbrite. To join the meeting, you may need to download the free software from www.zoom.us.

The conference program, list of speakers, and abstracts are posted on the external website.

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