Ergodic Theory and von Neumann algebras

2The University of Copenhagen October 14-18, 2013

In the last ten years impressive work has been done at the interface between ergodic theory and von Neumann algebras. The purpose of this PhD course is to present – in the two main lecture series by Damien Gaboriau and Cyril Houdayer – the ergodic theory part and the von Neumann algebra side of this newly developed machinery. Steven Deprez will give supplementary lectures on von Neumann algebras.

On the occasion that the Kadison-Singer problem very recently has been solved by Adam Marcus, Daniel Spielman and Nikhil Srivastava, a part of the Masterclass is devoted to a presentation of this problem. Pete Casazza will give a lecture series. In addition, Ilijas Farah will give a lecture on the (other) Kadison-Singer problem, answered in the negative by Akemann and Weaver in 2008 (assuming the continuum hypothesis).

Speakers:

The main lecture series will be delivered by:

• Pete Casazza, University of Missouri.
• Damien Gaboriau, École Normale Supérieure de Lyon.
• Cyril Houdayer, École Normale Supérieure de Lyon.

In addition there will be lectures by

• Steven Deprez, University of Copenhagen
• Ilijas Farah, York University.

Titles and abstracts:

• Pete Casazza: The Kadison-Singer Problem in Mathematics and Engineering
• Steven Deprez: Introduction to the link between von Neumann algebras and ergodic theory
• Ilijas Farah: The other Kadison-Singer Problem
• Damien Gaboriau: Around the orbit equivalence theory of the free groups
• Cyril Houdayer: Von Neumann algebras with unique Cartan decomposition

Click HERE3 for abstracts.

Slides for Pete Casazza's lectures:

• Lecture 1 - Lecture 2 - Lecture 3 - Lecture 4 - Lecture 5 - Lecture 6

Notes for the lectures:

• Damien Gaboriau
• Cyril Houdayer
• Steven Deprez (handwritten lecture notes)
• Ilijas Farah

Organizers: Magdalena Musat, Steven Deprez, Mikael Rørdam, Kristian Olesen, Søren Knudby.