Wednesday afternoon

There are two official options for the free afternoon (or of course you may explore Glasgow independently!)

Operator algebra Seminar (4 PM Wednesday 24 May, Room 110) 

Adrian Ioana (UC San Diego) "Wreath like product groups and rigidity of their von Neumann algebras"

Abstract: Wreath-like products are a new class of groups, which are close relatives of the classical wreath products. Examples of wreath-like product groups arise from every non-elementary hyperbolic groups by taking suitable quotients. As a consequence, unlike classical wreath products, many wreath-like products have Kazhdan's property (T).

In this talk, I will present several rigidity results for von Neumann algebras of wreath-like product groups. We show that any group G in a natural family of wreath-like products with property (T) is W*-superrigid: the group von Neumann algebra L(G) remembers the isomorphism class of G. This provides the first examples of W*-superrigid groups with property (T). For a wider class wreath-like products with property (T), we show that any isomorphism of their group von Neumann algebras arises from an isomorphism of the groups.  As an application, we prove that any countable group can be realized as the outer automorphism group of L(G), for an icc property (T) group G. This can be viewed as a converse to Connes’ 1980 rigidity theorem asserting that the outer automorphism of L(G) is countable, for any icc property (T) group G. These results were obtained in joint works with Ionut Chifan, Denis Osin and Bin Sun.  

I will also mention an additional application of wreath-like products obtained in joint work with Ionut Chifan and Daniel Drimbe, and showing that any separable II_1 factor is contained in one with property (T). This provides an operator algebraic counterpart of the group theoretic fact that every countable group is contained in one with property (T).

Boat trip Loch Lomond

Take the train to Balloch from Partick station (at 14:50 or 15:20). A return ticket is £6.20.  The walk from the Mathematics building is about 15 minutes, see Google Maps link.

Balloch is the final stop on the route. Exit the station and turn right towards the bridge. The ferry landing is about 150m from the station.  

Please make sure your arrive at the terminal by 16:15. The boat departs at 16:30, and the trip takes 1 hour.

Exploring the area

Below is a map of the area local to the university, with some shopping information.