Classification of group von Neumann algebras

January 29 to February 2, 2018

at the

American Institute of Mathematics, San Jose, California

organized by

Ionut Chifan, Adrian Ioana, Thomas Sinclair, and Stefaan Vaes

Original Announcement

This workshop will be devoted to developing new ideas and approaches to the classification of group and group-action von Neumann algebras. The workshop will bring together researchers with deep expertise in von Neumann algebras, geometric group theory, and Lie groups, as well as young researchers, to cooperate intensively on some of the outstanding open problems in the field, such as Connes' rigidity conjecture, while also exploring new avenues of research and interactions among these disciplines.

At a March 2009 workshop at UCLA, Sorin Popa proposed an ambitious list of open problems in group and group-action von Neumann algebras which has since steered the direction of the field. This initial list of problems was attacked with a flurry of definitive results, leading Popa to revisit the list in 2013. The workshop will allow an opportunity to reassess the state of the field in the wake of a string of even more recent successes, to catalyze new directions in research and to provide an updated vision for the field.

The topics of the workshop are the following three outstanding problems appearing on Popa's lists:

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Maximal rigid subalgebras of deformations and $L^2$-cohomology
by  Rolando de Santiago, Ben Hayes, Daniel J. Hoff, Thomas Sinclair