Award Ceremony for the 2022 Barbara and Jaroslaw Zemanek Prize
Title: An introduction to von Neumann algebras and Marrakchi's work on the structure of type III factors
Von Neumann algebras are weakly closed *-algebras of bounded operators on a Hilbert space. They naturally arise in the context of representation theory, ergodic theory and measurable group theory. Von Neumann algebras come in two very different flavors, distinguished by the key notion of amenability. After a basic introduction to von Neumann algebras, I will give an overview of Alain Connes' classification of amenable factors and then present the groundbreaking work of Amine Marrakchi on the structure of nonamenable factors of type III.
Title: On Connes’ bicentralizer problem.
Connes’ bicentralizer problem is one of the most famous open problems in the theory of type III factors. This conjecture was solved in the amenable case by Haagerup in 1984, hence completing Connes’ work on the classification of amenable factors. But the general non-amenable case is still open to this day, 40 years after Haagerup's celebrated work. In this talk, I will first give an overview of Connes’ bicentralizer problem, its history and motivations, then I will present some recent progress on this conjecture.