The theme of this survey talk is the dichotomy between amenability and non-amenability, both in operator algebras and ergodic theory. I will review the fundamental classification results for amenable von Neumann algebras due to Connes and Haagerup. The second part of the talk will focus on rigidity theorems in the non-amenable world, established within Popa's deformation/rigidity theory, especially for Bernoulli actions of discrete groups.

Stefaan Vaes is a full professor and the head of the Analysis section at KU Leuven (Belgium). His research focuses on operator algebras and their connections to group theory and ergodic theory. He was an invited speaker at the International Congress of Mathematicians in 2010 and at the European Congress of Mathematics in 2016. In 2015, he was awarded the Francqui Prize, which is the highest scientific distinction in Belgium. In the spring of 2017, he was a Rothschild Fellow at the Newton Institute in Cambridge. Stefaan Vaes is a member of the Royal Academy of Belgium (KVAB). He is one of the editors-in-chief of Journal of Functional Analysis.

Slide: stefaan-vaes-chern-lecture-1.pdf