Mating Quadratic Maps with the Modular Group

Explore the fascinating world of holomorphic correspondences in this mathematics seminar. Delve into the dynamics of multi-valued self-maps on the Riemann sphere, focusing on a specific 1-parameter family of (2:2) correspondences introduced by Bullett and Penrose. Discover how these correspondences mate the modular group with rational maps, and examine the development of a complete dynamical theory paralleling Douady-Hubbard's work on quadratic polynomials. Learn about the connectedness locus and its role in this intricate mathematical landscape. Gain insights from speaker Luna Lomonaco's joint work with S. Bullett, bridging concepts from complex dynamics, algebra, and geometry.