Rigidity for Roe algebras and measured asymptotic expanders

Jiawen Zhang 章嘉雯  (University of Southampton)

10:00-11:00, March 2, 2021   Tecent Meeting ID：264 598 425

Abstract:

Roe algebras are C*-algebras which encode coarse geometric information of underlying spaces. Rigidity problem concerns the following: whether two metric spaces are coarsely equivalent if their Roe algebras are isomorphic. This has been largely studied over the last decade by Spakula-Willett, Braga-Farah-Vignati, and Braga-Chung-Li. In this talk, I will introduce our recent work on rigidity joint with Li and Spakula. More precisely, we introduced a notion of measured asymptotic expanders and showed that the rigidity holds provided the underlying space does not weakly contain any ghostly measured asymptotic expanders. Our graphic approach to rigidity can be applied to several new examples, e.g., those cannot be coarsely embedded into Hilbert space yet does not coarsely contain any expanders by Arzhantseva-Tessera.

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