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L^2-Betti numbers of universal quantum groups

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OAS - Operator algebras: subfactors and their applications

I will report on joint works with Julien Bichon, Sven Raum, Matthias Valvekens and Stefaan Vaes, revolving around the computation of L2-Betti numbers for universal quantum groups.  Among our main results is the fact that the first L2-Betti number of the duals of the free unitary quantum groups equals 1, and that all other L^2-Betti numbers vanish.  All objects mentioned in the abstract will be defined, more or less rigorously, during the talk.



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