# Topology Seminar

## Thursday, 14 March, 2013

**SPEAKER**: Prof. Jerzy Dydak

**TITLE**: Coarse amenability and expanders

**ABSTRACT**: Coarse amenability is a generalization of amenability from groups to metric spaces. Historically, there are three basic classes of coarsely non-amenable spaces:

a. expander sequences (G.Yu),

b. infinite unions of powers of a given finite group G that is not trivial (P.Nowak),

c. graph sequences with girth approaching infinity (R.Willett).

The most explicit construction of an expander sequence is as finite quotients of a finitely generated group G with Kazhdan's property (T) (example: SL_n(Z) when n > 2).

I will define expander light sequences, prove they are coarsely non-amenable, and show each of the above classes is a subclass of expander light sequences. Not only expander light sequences form a unifying concept for a)-c), the proof of their coarse non-amenability is quite elementary.