SMS scnews item created by Stephan Tillmann at Thu 9 Oct 2014 1020
Type: Seminar
Distribution: World
Expiry: 8 Jan 2015
Calendar1: 29 Oct 2014 1100-1200
CalLoc1: Carslaw 535A
Auth: tillmann@p710.pc (assumed)

# Ergodic theorems for amenable groups

### Sasha Fish (Sydney)

GTA Seminar - Wednesday, 29 October, 11:00-12:00 in Carlaw 535A

## Ergodic theorems for amenable groups

We will talk on the validity of the mean ergodic theorem along left Følner sequences in a countable amenable group G. Although the weak ergodic theorem always holds along any left Følner sequence in G, we will provide examples where the mean ergodic theorem fails in quite dramatic ways. On the other hand, if G does not admit any ICC quotients, e.g. if G is virtually nilpotent, then we will prove that the mean ergodic theorem does indeed hold along any left Følner sequence. Based on the joint work with M. Bjorklund (Chalmers).