Topics in ergodic theory and von Neumann algebras (Fall 2007)

Lectures are on Thursdays, 10h40, Room 128, at the University of Tokyo.
No lecture on January 24th. Last lecture 01/31.

Contents:

  • Lecture 1: Measurable dynamical systems and equivalence relations.

  • Lecture 2: Group-measure-space construction, Krieger's construction, Feldman-Moore.

  • Lecture 3: Dye and Connes-Feldman-Weiss theorems.

  • Lecture 4: End of the proof of CFW. Connes' Folner theorem.

  • Lecture 5: Injective implies AFD (type II_1 case after Popa).

  • Lecture 6: Gaboriau's cost theorem.

  • Lecture 7: HT factors and fundamental groups.

  • Lecture 8: Theorem of Gaboriau-Popa. L2 cohomology.

  • Lecture 9: Theorem of Ozawa-Popa.