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.