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Property (T) and approximate conjugacy of actions

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NPC - Non-positive curvature group actions and cohomology

I will define a notion of approximate conjugacy for probability measure preserving actions and compare it to the a priori stronger classical notion of conjugacy for such actions. In particular, I will spend most of the talk explaining the proof of a theorem stating that two ergodic actions of a fixed group with Kazhdan's property (T) are approximately conjugate if and only if they are actually conjugate. Towards this end, I will discuss some constructions from the theory of von Neumann algebras, including the basic construction of Vaughan Jones and a version of the Feldman-Moore construction. I will also provide some evidence that this theorem may yield a characterization of groups with Kazhdan's property (T).   (Joint work with Sorin Popa)



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