Objectives

The goal of our ANR project is to bring together European mathematicians who work in areas related to von Neumann algebras, measurable group theory, topology and dynamics in order to further progress in these subjects which have known dramatic development in the last ten years. This progress was only made possible by interactions between different mathematical subjects; for instance, much of the recent progress in operator algebras and orbit equivalence theory was the result of a successful cross-pollinization between the two subjects, together with an additionnal interplay with other fields like geometry, geometric group theory, topology, representation theory, random graphs, and descriptive set theory. We also hope, via Post-Doc positions, conferences, and advanced courses, to disseminate the knowledge acquired, and to stimulate young mathematicians to work in this area, at the intersection of several domain of mathematics, where there are so many attractive and interdisciplinary open problems.

We hope to dig out and better understand the relationship between two important classes of mathematical objects: on the one hand, geometrical type objects as measurable group actions and foliations and, on the other hand, their algebraic conterpart von Neumann algebras. The interaction between these fields was extremely fruitful and led to unexpected spectacular advances in particular during the last decade.

 

We will organize regularly working seminars and workgroups on different sites. These short meetings aim at exchanging ideas and stimulating collaboration among the people involved in our project. Each working seminar will be structured around one main subject: von Neumann algebras, measurable group theory, L^2 invariants, percolation...

 

We are in the process of organizing an international conference. We plan to bring together the best researchers working in France and abroad to present their last results. This conference will be the occasion for the people of our team to exchange ideas and collaborate with the other researchers working outside France. We will present our project and offer to national and european researchers an overview of the subject and all its connexions with various other fields in order to attract young people to work in the domain.