Date: Tuesday, September 11, 2018
Title: Rational maps, graphs, and selfsimilar groups
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{postcritically finite}. In this case, we can describe the 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 selfsimilar groups, for instance a concise description of the Grigorchuk group, the firstconstructed group of intermediate growth.
Speaker: Dylan Thurston
Institution: Indiana University
