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Seminar by Ami Viselter

Thursday, August 17, 2017 - 16:30 to 17:30
Seminar Room, School of Mathematical Sciences
Ami Viselter
University of Haifa, Israel
Around Property (T) for Quantum Groups
Kazhdan's property (T) is a notion of fundamental importance, with numerous applications in various fields of mathematics such as abstract harmonic analysis, ergodic theory and operator algebras. By using property (T), Connes was the first to exhibit a rigidity phenomenon of von Neumann algebras. Since then, the various forms of property (T) have played a central role in operator algebras, and in particular in Popa's deformation/rigidity theory. This talk is devoted to some recent progress in the notion of property (T) for locally compact quantum groups. In a suitable class of quantum groups, property (T) is shown to be equivalent to property (T)$^{1,1}$ of Bekka and Valette. As applications, several known results about groups are extended, including theorems on "typical" representations (due to Kerr and Pichot) and on connections of property (T) with spectral gaps (due to Li and Ng) and with strong ergodicity of weakly mixing actions on a particular von Neumann algebra (due to Connes and Weiss). Based on joint work with Matthew Daws and Adam Skalski, and on a very recent work of Michael Brannan and David Kerr.

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