In this first lecture, we will describe a general recipe for constructing (anti-)holomorphic correspondences on the Riemann sphere from univalent restrictions of rational maps and study their basic dynamical properties. This will lead to simple criteria for unmating such a correspondence into a(n) (anti-)rational map and a group. The exposition will be accompanied by explicit examples.

Based on joint works with Seung-Yeop Lee, Mikhail Lyubich, Nikolai Makarov, and Jacob Mazor.