Abstract
A central unsolved problem in the area of topological combinatorics is the famous topological Tverberg conjecture, which claims that for any continuous map f from a (d+1)(r-1)-dimensional simplex \Delta to the d-dimensional Euclidean space, there exist r pairwise disjoint faces such that there images under f contain a common point, where r >= 2 and d >= 1 are any integers. Originally proven for r a prime power, recent developments show that counterexamples exist in other cases for sufficiently large d with respect to r.
In this talk, a concise introduction to the background of Tverberg-type problems is given, as well as a brief review of some recent progress about the topological Tverberg conjecture, so that one may appreciate the fruitful interaction between different branches of mathematics contained in the arguments.