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Penn Mathematics Colloquium

Wednesday, March 17, 2021 - 3:30pm

Tianyi Zheng



University of Pennsylvania


 The space of marked groups, equipped with the Cayley topology, was first used by Grigorchuk to show the existence of an uncountable family of groups with pairwise inequivalent growth functions. Most known constructions of continuous families of non-quasi-isometric groups can be viewed as finding subsets in this space with certain properties. In this talk we will survey examples of such constructions with interesting algebraic and geometric properties; and explain the aspects that random walks interact well with the topology of the space.