Elias Zimmermann (Leipzig)

Titel

Pointwise ergodic theory beyond amenable groups

Abstract

Given a measure preserving and ergodic dynamical system Birkhoff's pointwise ergodic theorem garantuees convergence of the time averages of some integrable function to its integral along almost every orbit of the system. Starting from the 70s there have been a lot of efforts to extend classical ergodic theory to actions of so called amenable groups, which eventually led to the celebrated pointwise ergodic theorem of Lindenstrauss along tempered Følner sequences. However, beyond the setting of amenable groups the situation becomes much more intricate. Nevertheless, for many non-amenable groups versions of the pointwise ergodic theorem could be established. In this talk I want to present one method to prove such an ergodic theorem for actions of free groups based on an orbit theoretic generalization of ergodic theory, which allows for the use of arguments from the amenable setting in the context of non-amenable groups.