CARMA SEMINAR Speaker: Alexander Fish, School of Mathematics and Statistics, The University of Sydney Title: Ergodic theorems for amenable groups Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 23rd Apr 2015 Abstract: 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). [Permanent link]