KK-duality and quantum hyperbolicity

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• Sergey Neshveyev (University of Oslo)
• Monday 02 December 2024, 11:50-12:30
• Seminar Room 1, Newton Institute.

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

KK-duality is a noncommutative analogue of the Spanier-Whitehead duality which relates the homology of a finite complex with the cohomology of some dual finite complex. As was shown by Kaminker, Putnam and Whittaker, hyperbolic dynamical systems is a rich source of KK-dual algebras. In my talk I will discuss what can be thought of as a quantum analogue of their construction, a class of algebras that are quantum relatives of the crossed products of free groups acting on their boundaries. Both the construction of the dual classes and the proof of duality rely in a crucial way on quantum symmetries of the algebras. (Joint work with Francesca Arici and Dimitris Gerontogiannis.)

This talk is part of the Isaac Newton Institute Seminar Series series.

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