Léonard Cadilhac

Noncommutative ergodic theorems and tilings of amenable groups

The pointwise theorem of Birkhoff establishes that ergodic averages associated with a measure preserving transformation converge almost everywhere. Over the years, this statement has been refined and generalized in many directions. In this talk, we will be interested in a pointwise theorem valid both for actions of amenable groups (rather than a single transformation) and in the noncommutative setting (actions on a noncommutative measure space). After an introduction of the literature leading up to this result, I will present the two main ingredients involved in its proof: a method of Bourgain linking ergodic and martingale theory and a tiling construction of Ornstein and Weiss. This work is a collaboration with Simeng Wang (Harbin).
Note unusual room.