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Division of Communications and Marketing
Kansas State University
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### March 26, 2019

#### ADVANCE Distinguished Lecture Series presents Dylan Thurston

Submitted by Tawny Ochs

The ADVANCE Distinguished Lecture Series and Tatiana Firsova, assistant professor of math, will host Dylan Thurston, professor at Indiana University, Bloomington. Thurston will present "Rational maps, graphs, and self-similar groups" from 2:30-3:30 p.m. Tuesday, April 2, in 122 Cardwell Hall.

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, 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 self-similar groups, for instance, a concise description of the Grigorchuk group, the first-constructed group of intermediate growth.