School of Mathematics Colloquium

Dynamics of Schwarz reflections: mating polynomials with groups

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

Thursday, June 7, 2018 from to (Asia/Kolkata)
at TIFR, Mumbai ( AG-69 )
Description
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.