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Complex Analysis, Dynamics and Geometry Seminar

Gasket Julia sets and their symmetries
Tuesday, March 9, 2021
5:00-6:00 PM
Off Campus Location
The circle packing theorem associates a circle packing to each connected simple planar graph in the Riemann sphere. Drawing inspiration from Sullivan's dictionary, there is a dynamically natural way to associate both a Kleinian group and an anti-rational map to each such packing, and there is a dynamical identification of the limit and Julia sets. Using this identification, we compute the topological symmetry and quasisymmetry groups of the Julia set associated to a large class of graphs (that correspond to so-called "gaskets"). The combinatorics of the original graph has further implications for the topology of the Julia set, boundedness of deformation space, and mate-ability, some of which may be investigated in a future talk by Yusheng Luo.

Joint work with Y. Luo, M. Lyubich, S. Merenkov, S. Mukherjee Speaker(s): Russell Lodge (Indiana State)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics, Complex Analysis, Dynamics and Geometry Seminar - Department of Mathematics