A user's guide to the topological Tverberg conjecture

Understand

The topological Tverberg conjecture was considered a central unsolved problem of topological combinatorics.

• The conjecture asserts that for any integers $r,d>1$ and any continuous map $f:\Delta\to\mathbb R^d$ of the $(d+1)(r-1)$-dimensional simplex there are pairwise disjoint faces $\sigma_1,\ldots,\sigma_r\subset\Delta$ such that $f(\sigma_1)\cap \ldots \cap f(\sigma_r)\ne\emptyset$.
• The conjecture was proved for a prime power $r$.
• Recently counterexamples for other $r$ were found.