Title: Exotic group $$C^*$$-algebras from representation theory.
Speaker: Martin Finn-Sell (Vienna)
Abstract: I will summarise the results of a paper of Brown-Guentner, which defines new $$C^*$$-completions of discrete groups beyond the regular and maximal ones. I will also explain the relationship between analytic properties of discrete groups, such as property (T) and the Haagerup property, and certain $$C^*$$-completions - these results are reminiscent of the Hulanicki-Reiter characterisation of amenability in terms of $$C^*$$-completions.