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for events the day of Wednesday, May 13, 2020.

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Wednesday, May 13, 2020

3:30 pm in https://illinois.zoom.us/j/806582029 (email Anush Tserunyan for password),Wednesday, May 13, 2020

Introduction to 𝓁2-Betti numbers for groups, part 3: 𝓁2-homology

Ruiyuan (Ronnie) Chen (UIUC Math)

Abstract: We will first finish our discussion of ordinary group homology by giving an alternative definition via equivariant chain complexes, completely bypassing topology. We will then discuss $\ell^2$-homology, defined by replacing (chain) homotopy quotients by $\ell^2$-completion to Hilbert $\Gamma$-modules. The $\ell^2$-Betti numbers are the von Neumann dimensions of the resulting homology Hilbert $\Gamma$-modules.