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4:00 pm Thursday, February 22, 2018 Colloquium: Rational maps, graphs, and self-similar groupsby Dylan Thurston (Indiana University Bloomington) in HBH 227- 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 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.
Submitted by ml28@rice.edu |