Koichi Oyakawa (Vanderbilt University)
Title: Geometry and dynamics of the extension graph of graph product of groups
Abstract: In this talk, I will introduce the extension graph of graph product of groups and explain its geometry. This notion enables us to study the properties of graph product by exploiting the large-scale geometry of its defining graph. In particular, I show that the asymptotic dimension of the extension graph exhibits the same behavior as in the case of quasi-trees of metric spaces studied by Bestvina-Bromberg-Fujiwara. In addition, I present applications of the extension graph to the study of convergence actions, graph wreath products, and group von Neumann algebras when the defining graph is hyperbolic.
We will gather for teatime in the lounge after the talk. After teatime, we will go for dinner with Koichi.
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