Around Property (T) for quantum groups

Seminar
Speaker
Dr. Ami Viselter, Haifa University
Date
22/05/2017 - 15:10 - 14:00Add to Calendar 2017-05-22 14:00:00 2017-05-22 15:10:00 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. Most of our results are concerned with second countable discrete  unimodular quantum groups with low duals. In this class of quantum groups, Property (T) is  shown to be equivalent to Property (T)$^{1,1}$ of Bekka and Valette. As applications, we  extend to this class several known results about countable groups, 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). Joint work with Matthew Daws and Adam Skalski. The talk will be self-contained: no prior knowledge of quantum groups or Property (T) for groups is required. 2nd floor Colloquium Room, Building 216 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
2nd floor Colloquium Room, Building 216
Abstract

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. Most of our results are concerned with second countable discrete 
unimodular quantum groups with low duals. In this class of quantum groups, Property (T) is 
shown to be equivalent to Property (T)$^{1,1}$ of Bekka and Valette. As applications, we 
extend to this class several known results about countable groups, 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).
Joint work with Matthew Daws and Adam Skalski.
The talk will be self-contained: no prior knowledge of quantum groups or Property (T) for groups is required.

Last Updated Date : 15/05/2017