Quasi-locality and asymptotic expanders

Jiawen Zhang ¼  (University of Southampton)

14:00-15:00, Dec 17, 2019   Science Building A510


Roe algebras are C*-algebras associated to metric spaces, which encode their large scale structure. These algebras play a key role in higher index theory, bridging geometry, topology and analysis together. Recently we provide a new quasi-local perspective on Roe algebras, provided the underlying spaces have Yus Property A. In the special case of a sequence of finite graphs, we study the quasi-locality of the averaging projection and introduce the notion of asymptotic expanders. Furthermore, we provide a structure theorem showing that asymptotic expanders can be exhausted by classic expanders. Consequently, we show that asymptotic expanders cannot be coarsely embedded into any Hilbert space, and being asymptotic expanders can be detected via the Roe algebras. This is a joint project with Ana Khukhro, Kang Li, Piotr Nowak, Jan Spakula and Federico Vigolo.

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