Extendability of simplicial maps is undecidable

We explain why the problem of extendability of simplicial maps is interesting to computer scientists. In particular, we illustrate the relation to polygonal lines in the plane, to words in finite alphabets, and to realizability of hypergraphs in higher-dimensional space.We present a short proof of the Čadek-Krčál-Matoušek-Vokřínek-Wagner 2013 result from the title (in the following form due to Filakovský-Wagner-Zhechev, 2020).For any fixed integer l>1 there is no algorithm recognizing the extendability of the identity map of the wedge Y of two l-dimensional spheres to a PL map from X to Y for a given 2l-dimensional simplicial complex X containing a subdivision of Y as a given subcomplex. In this talk topological concepts are exposed in the way interesting and accessible to non-specialists, in particular, to computer science students.