16:00
Convergence of unitary representations of discrete groups
Abstract
Let G be an infinite discrete group; e.g. free group, surface groups, or hyperbolic 3-manifold group.
Finite dimensional unitary representations of G of fixed dimension are usually very hard to understand. However, there are interesting notions of convergence of such representations as the dimension tends to infinity. One notion — strong convergence — is of interest both from the point of view of G alone but also through recently realized applications to spectral gaps of locally symmetric spaces. For example, this notion bypasses (unconditionally) the use of Selberg's Eigenvalue Conjecture in obtaining existence of large area hyperbolic surfaces with near-optimal spectral gaps.
The talk is a broadly accessible discussion on these themes, based on joint works with W. Hide, L. Louder, D. Puder, J. Thomas, R. van Handel.
We are all getting the emails asking us to fill in the staff survey. But why should we?
Well, though things are pretty good round here (we could be in another country, naming no names), there is room for better. One of the things about staff surveys in your Bulletin Editor's long experience is not just the aggregating of opinions, but the throwing up of new ideas that no-one had ever considered previously. And with so many smart people around, we should be good at that.