On open-up mappings and their applications

In the talk, we consider direct and inverse problems related to finding a rational function, whose inverse performs a univalent open-up map of the complement of a given set of pairwise disjoint Jordan arcs. We show how these problems are related to Hurwitz numbers and Dehn twists. The talk is based on a joint work with V. Lysov, B. Nagy, and O. Séte.