Amine Marrakchi: Ergodic theory of affine isometric actions on Hilbert spaces
Time: Wed 2020-09-23 13.15 - 15.00
Location: Zoom meeting ID: 657 9019 8929
Lecturer: Amine Marrakchi, ENS Lyon
The Gaussian functor associates to every orthogonal representation of a group G on a Hilbert space, a probability measure preserving action of G called a Gaussian action. This construction is a fundamental tool in ergodic theory and is the source of a large and interesting class of probability measure preserving actions. In this talk, I will present a generalization of the Gaussian functor which associates to every affine isometric action of G on a Hilbert space, a nonsingular Gaussian action which is not measure preserving. This provides a new and large class of nonsingular actions whose properties are related in a very subtle way to the geometry of the original affine isometric action. In some cases, such as affine isometric actions coming from groups acting on trees, a fascinating phase transition phenomenon occurs. This talk is based on a joint work with Yuki Arano and Yusuke Isono, as well as a more recent joint work with Stefaan Vaes.
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