Workshop on Sofic and Hyperlinear Groups and the Connes Embedding Conjecture - June 10 to June 21

June 10 - June 21 at UFSC Florianopolis, Brazil

Objectives

The classes of sofic and hyperlinear groups have drawn in the last ten years the attention of an increasing number of mathematicians in different areas of mathematics, including geometric group theory, operator algebras, dynamical systems and graph theory, just to mention some of them. Despite the amount of research on this subject, several fundamental questions remain open, such as: Is there any group which is not sofic or hyperlinear?
The aim of this school is to lead the attendee through the fascinating world of sofic and hyperlinear groups, from the very definitions to the most recent results on this topic. The approach will be eminently interdisciplinary, and will focus on the connections with model theory and operator algebras. In particular, the Connes Embedding Problem, one of the most important and long-standing open problems in operator algebras and original motivation behind the introduction of hyperlinear groups, will occupy a central place in the course.

Scientific Activity

The workshop will consist of a 20-hour course (click here for the program) taught by Valerio Capraro and Martino Lupini, as well as contributed talks from other speakers in areas broadly related to the main topic of the workshop (functional analysis, dynamical systems, operator algebras, etc.). The working languages of the workshop will be English and Portuguese.

Click here for schedule, here for titles and here for lecture notes.

Here are three introductory lectures by Vladimir about ultrafilters and ultralimits, based on his own pedagogical approach (from his 3rd year Analysis course in Ottawa): 1st, 2nd, and 3rd.
All talks will take place at room 202 in the math department building.

Funding

We have secured funds through Capes (project PVE 085/2012) to partially support speakers. If you wish to give a talk, please send an email to one of the organizers.

Suggested Accomodation

• Slaviero Hotel
• Hotel Quinta da Bica D'Agua - 
• Both hotels offer discounts for participants in UFSC.

Additional Information

For more information, please contact either Daniel Gonçalves (daniel.goncalves at ufsc dot br) or Vladimir Pestov (vpest283 at uottawa dot ca).

Supporting Institutions