The Summer School will consist of three mini-courses on relevant aspects of C*-dynamics, set theory, and their interactions.
The school will take place at the Institut Henri Poincaré https://www.ihp.fr/fr
There is a social dinner on Wednesday at 20.00 at Chez Gladines Les Halles. If you haven’t signed up and wish to come, please speak to one of the organisers!
Marzieh Forough (Czech Technical University). This lecture series will begin with an introduction to group actions on C*-algbras and to their crossed products. Then I will focus on the main ideas leading to the classification of crossed products by discrete amenable groups. Finally, inspired by the classification results for crossed products by (minimal) homeomorphisms, I will discuss the structure of C*-algebras associated to homeomorphisms twisted by vector bundles.
David Kerr (Münster). In this minicourse I will first explain the connection between -stability for C*-algebras and tiling and comparison properties for group actions on compact spaces, and then show how the latter dynamical phenomena can be verified for many classes of examples, leading to classification results for C*-crossed products.
Anush Tserunyan (McGill). Descriptive set theory offers methods of studying global properties of sets and functions on a space via local combinatorics on the level of points of the space. We will illustrate this mantra by showing how to reduce pointwise ergodic theorems to finitary tiling problems. We will discuss such theorems for probability measure preserving (pmp) actions of amenable and nonamenable groups, as well as a more recent backward ergodic theorem for one pmp transformation. Finally, we will discuss graphs on probability spaces and a general pointwise ergodic theorem for them.