Stefaan Vaes 教授是比利时鲁汶天主教大学数学系教授。作为国际上著名的算子代数方向的专家，他在von Neumann 代数，动力系统和遍历理论，拓扑群以及测度群理论等方面的研究为算子代数学科发展做出了非常大的贡献。Vaes教授在Annals of Mathematics, Inventiones Mathematicae , Acta Mathematica以及Jounal of AMS等国际顶尖数学杂志上发表了多篇文章。
The theme of this talk is the dichotomy between amenability and non-amenability. Because the group of motions of the three-dimensional Euclidean space is non-amenable (as a group with the discrete topology), we have the Banach-Tarski paradox. In dimension two, the group of motions is amenable and there is therefore no paradoxical decomposition of the disk. This dichotomy is most apparent in the theory of von Neumann algebras: the amenable ones are completely classified by the work of Connes and Haagerup, while the non-amenable ones give rise to amazing rigidity theorems, especially within Sorin Popa's deformation/rigidity theory. I will illustrate the gap between amenability and non-amenability for von Neumann algebras associated with countable groups, with locally compact groups, and with group actions on probability spaces.