### Non-singular ergodic theorems for countable group actions

Ergodic Theory and Dynamical Systems Seminar

12th October 2017, 3:00 pm – 4:00 pm

Howard House, 4th Floor Seminar Room

Birkhoff’s pointwise ergodic theorem has been extended to measure preserving actions of many countable groups, in particular Lindenstrauss proved that it holds for all amenable group actions. However its non-singular analogue, the Hurewicz ergodic theorem, is far less well understood. In this talk I will give some background on extensions of Hurewicz’s theorem, indicate how one uses the geometry of the group to counter the non-singularity of the action and present results from my work with Tony Dooley which generalise the theorem to further group actions.

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