Dynamics of Schwarz reflections: mating polynomials with groups

by Prof. Sabyasachi Mukherjee (Stony Brook University, USA)

Thursday 7 Jun 2018, 16:00 → 17:00 Asia/Kolkata

AG-69 (TIFR, Mumbai)

Abstract: A domain in the complex plane is called a quadrature domain if it admits a global Schwarz reflection map. Topology of quadrature domains has important applications to physics, and is intimately related to iteration of Schwarz reflection maps. 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.