Résumé : II factors are non-commutative versions of the function algebra ,
the way matrix algebras are analogue to finite spaces. They arise as infinite tensor products and ultra products of matrix algebras, but also from groups and their actions on probability spaces . A key analysis tool to study II factors in terms of their building data is \it deformation-rigidity theory. It fits within the fundamental dichotomy \it structure versus randomness, which appeared in many areas of mathematics in recent years. I will comment on this technique and present several classification results obtained this way, showing for instance that factors arising from Bernoulli actions of property (T) groups ``remember’’ both the group and the action, and that free ergodic actions of the free groups remember the rank .
Lieu : Bât. 425, petit amphi
Département de Mathématiques Bâtiment 425
Faculté des Sciences d'Orsay Université Paris-Sud
F-91405 Orsay Cedex
Tél. : +33 (0) 1-69-15-79-56