We propose a natural version of Connes' Rigidity Conjecture (1982) that involves property (T) groups with infinite centre. Using methods at the rich intersection between von Neumann algebras and geometric group theory, we identify several instances where this conjecture holds. This is joint work with Ionut Chifan, Denis Osin, and Hui Tan.

Several PhD students from the department will give short 5 minute talks on their research. This is also targeted at undergraduates interested in doing PhDs .

We will be joined by Dr Brigitte Stenhouse from the Open University to discuss harassment, particularly in academic settings. 

This is a joint event by the Mathematrix and Mirzakhani Societies for all women and non-binary people in the Maths department. Join us in the South Mezzanine for some hot drinks and sweet treats. 

Come along for free Pizza and to hear about the Mathematrix events this term. 

Rota’s Alternierende Verfahren theorem in classical probability theory, which examines the convergence of iterates of measure preserving Markov operators, relies on a dilation technique. In the noncommutative setting of von Neumann algebras, this idea leads to the notion of absolute dilation.  

In this talk, we explore when a Fourier multiplier on a group von Neumann algebra is absolutely dilatable. We discuss conditions that guarantee absolute dilatability and present an explicit counterexample—a Fourier multiplier that does not satisfy this property. This talk is based on a joint work with Christian Le Merdy.

A countable group G is said to be W*-superrigid if G can be entirely recovered from its ambient group von Neumann algebra L(G). I will present a series of joint works with Milan Donvil in which we establish new degrees of W*-superrigidity: isomorphisms may be replaced by virtual isomorphisms expressed by finite index bimodules, the group von Neumann algebra may be twisted by a 2-cocycle, the group G might have infinite center, or we may enlarge the category of discrete groups to the broader class of discrete quantum groups.