Spectral gaps, higher Kazhdan projections and L^2-Betti numbers

Piotr Nowak

*(University of Warsaw)*

8:00-9:00,August 3,2023 ÎÄ¸½Â¥ (Wenfu Building) 219

__Abstract:__

I will define the notion of a higher Kazdhan projection, which is an idempotent
over the maximal C*-algebra, and discuss how it is relevant in the context of higher index
theory. More precisely, I will show how these projections can be used as a strategy to construct
new counterexamples to the coarse Baum-Connes conjecture, in the spirit of high-dimensional
expanders. This is joint work with Kang Li and Sanaz Pooya.

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