4:00 pm Thursday, February 22, 2018

Dylan Thruston

Abstract: In the theory of rational maps (holomorphic functions from
$\mathbb{CP}^1$ to itself), a natural question is how to describe the
maps. This is most tractable in the case when the map is
\emph{post-critically finite}. In this case, this honest 2-dimensional
dynamical system in terms of a correspondence on graphs.
On the one hand, this correspondence on graphs allows us to
characterize which topological maps from the sphere to itself can be
made into a geometric rational map. On the other hand, these graph
correspondences can be generalized to give short descriptions of
self-similar groups, for instance a concise description of the
Grigorchuk group, the first-constructed group of intermediate growth.