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.
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