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Rothschild Lecture: Classification of von Neumann algebras

Presented by: 
Stefaan Vaes KU Leuven
Date: 
Monday 12th June 2017 - 16:00 to 17:00
Venue: 
INI Seminar Room 1
Abstract: 

The theme of this talk is the dichotomy between amenability and non-amenability. Because the group of motions of the three-dimensional Euclidean space is non-amenable (as a group with the discrete topology), we have the Banach-Tarski paradox. In dimension two, the group of motions is amenable and there is therefore no paradoxical decomposition of the disk. This dichotomy is most apparent in the theory of von Neumann algebras: the amenable ones are completely classified by the work of Connes and Haagerup, while the non-amenable ones give rise to amazing rigidity theorems, especially within Sorin Popa's deformation/rigidity theory. I will illustrate the gap between amenability and non-amenability for von Neumann algebras associated with countable groups, with locally compact groups, and with group actions on probability spaces.
 

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons