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Von Neumann algebras and discrete groups.

Von Neumann algebras, and more specifically II_1 factors, arise naturally in the study of countable groups and their actions on measure spaces. A central, but extremely hard problem is the classification of these von Neumann algebras in terms of their group/action data. In 2001 Sorin Popa initiated his breakthrough deformation/rigidity theory leading to the solution of many long standing open problems. Since then overwhelming progress has been made in the understanding of group measure space II_1 factors associated with measure preserving group actions. The aim of this project is to obtain structural results of similar strength about group von Neumann algebras L(G). This includes the construction of a wide class of group von Neumann algebras L(G) that entirely remember the group G. We will also continue the study of group measure space II_1 factors and make a systematic study of (non-)uniqueness of Cartan subalgebras.
Date:1 Jan 2011  →  31 Dec 2014
Keywords:Discrete groups, Von Neumann algebras