Abstract:
Calculation of fundamental group of type $\rm II_1$ factor is, in general, an extremely hard and central problem in the field of von Neumann algebras. In this direction, a conjecture due to A. Connes states that the fundamental group of the group von Neumann algebra associated to any icc property (T) group is trivial. Up to now there was no single example of property (T) group factor satisfying the conjecture. In this talk, I shall provide the first examples of property (T) group factors with trivial fundamental group. This talk is based on a joint work with Ionut Chifan, Sayan Das and Cyril Houdayer.