Réductibilité presque partout des flots fibrés quasi-périodiques à valeurs dans des groupes compacts
Relative property (T) and linear groups
Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group admits a special linear representation with non-amenable -Zariski closure if and only if it acts on an Abelian group (of...
Remarks on the tightness of cocycles
We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.
Rigidity results for Bernoulli actions and their von Neumann algebras
Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II factors with prescribed countable fundamental group.