An operator algebras seminar at SIMIS: Expander graphs and ideal structure of uniform Roe algebras

Speaker: Qin Wang (East China Normal University)

Host: Huaxin Lin

Abstract: The uniform Roe algebra of a discrete metric space is a C*-algebra which analytically encodes the coarse geometry of the underlying space. It is known that counter-examples to the coarse Baum-Connes conjecture can be constructed by using expander graphs, the crucial point of which lies in the fact that the uniform Roe algebra of expander graphs contains a noncompact projection P, called the ghost projection, which is locally invisible at infinity. In terms of ideal structure, accordingly, the finite propagation operators in the principal ideal generated by P are not dense in the ideal. In this talk, we will first focus on the class of ideals of a uniform Roe algebra in which finite propagation operators are dense, and show that these ideals can be described geometrically in terms of coarse structure and invariant open subsets of the unit space of the Skandalis-Tu-Yu groupoid. We show that if the metric space has Yu’s property A, then all ideals are geometric. We will then introduce a notion of ghostly ideal and partial property A to investigate the ideal structure of the uniform Roe algebra beyond the scope of Yu’s property A. This talk is based on joint works with Xiaoman Chen and with Jiawen Zhang.

Time: 2:30-3:30pm, Thursday, October 17th, 2024

Location: Room 1510, Block A, No. 657 Songhu Road, Yangpu District, Shanghai


About the speaker: Qin Wang is a Professor of Mathematics in the Research Center for Operator Algebras, School of Mathematical Sciences, East China Normal University. Professor Qin Wang was a winner of the New Century Excellent Talents Support Program from the Ministry of Education. He was also selected as Shanghai Pujiang Scholar and Shuguang Scholar. His research interest involves operator algebras, coarse geometry, and noncommutative geometry, especially around the coarse Baum-Connes conjecture in higher index theory.

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