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)