# 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

**Abstract**

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.

**Zoom Notes:** The Meeting ID and Passcode will be recurring and should work every Wednesday. The password has been sent out on the department mailing lists. Please email
Wushi Goldring
if you are not on these mailing lists and are interested in attending.