Title: Dynamics of Schwarz reflections: mating polynomials with groups
Speaker: Sabya Mukherjee
Speaker Info: Stony Brook University
A domain in the complex plane is called a quadrature domain if it admits a global Schwarz reflection map. Topology of quadrature domains has impor- tant applications to physics, and is intimately related to iteration of Schwarz reflection maps.Date: Thursday, May 03, 2018
We will look at a specific one-parameter family of Schwarz reflection maps, and show that every post-critically finite map in this family arises as the mating of a post-critically finite quadratic anti-holomorphic polynomial and the ideal triangle group. Time permitting, we will also describe a combinatorial model for the “connectedness locus” of this family.
Joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov.