Title: Quasidiagonality vs amenability of discrete groups
Abstract: An operator in a Hilbert space is (informally) said to be quasidiagonal if its' behaviour can be approximated by some of its' corners' behaviour. This notion was introduced by Halmos in the seventies, and has since been used extensively in various areas of mathematics. In this talk we will introduce it and study its' relation to amenability of discrete groups. In particular, we shall prove that if the left regular representation of a group is quasidiagonal then the group itself is amenable. We also show the converse in the case of the integers (using Berg's technique) and, more generally, in the case of residually finite amenable groups. The construction for the general case remains open.