Title: Conformal Dynamics: Julia sets, Kleinian
groups, and Schwarz reflections.
Abstract: We will discuss the interplay between
three branches of Conformal Dynamics:
iteration of (anti-)rational maps,
actions of Kleinian groups,
and dynamics generated by Schwarz
reflections in quadrature domains.
We will present examples of matings
between anti-quadratic maps and the
triangle modular group, and of the
Julia reasization for the
classical Apollonian gasket. We will
also describe the group of
quasisymmetries for some classes of
Julia sets, including the Apollonian
one, certain Sierpinski carperts, and
the Basilica. The Thompson group will
naturally emerge in the latter case.