Lecturer: Mikaël Pichot (JSPS Postdoctoral Fellow at U. Tokyo)
Title: Topics in ergodic theory, von Neumann algebras, and rigidity
Date/Time: 10:40-12:10, Thursday (starting on October 18, 2007)
Room: 128 Math Science Building

The actual contents of the past lectures are here.

Abstract:
I will explain some of the recent developments in orbit equivalence theory 
and von Neumann algebras, including work of Gaboriau, Popa,...

A tentative schedule is as follows:

* Basic measure-theoretic structures (2 lectures):
Measurable actions of countable groups, Orbit equivalence, crossed product 
von Neumann algebra, Cartan subagebras,...

* Treeability, cost, L2 Betti numbers (3 or 4 lectures):
Sketch of proof of Connes-Feldman-Weiss theorem. Proof of Gaboriau's non 
orbit equivalence of free groups theorem. L2 Betti numbers for 
equivalence relations following Gaboriau and/or Lück's approach.

* Correspondences, Kazhdan's property T, etc. (2 lectures)

* Measure-theoretic Rigidity (the remaining part of the lectures):
Popa's L2 Betti numbers paper Proof of Popa's cocycle superridigity 
theorem Parts of Popa's von Neumann rigidity theorems (i.e. the "malleable" 
papers) Parts of Ozawa-Popa's recent preprint (unicity of Cartan subalgebras)

Precise references will be given during the lectures.