Séminaires : Séminaire d'Algèbres d'Opérateurs

Equipe(s) : ao,
Responsables :Pierre Fima, François Le Maître, Romain Tessera
Email des responsables :
Salle : 1013
Adresse :Sophie Germain

Orateur(s) Sorin Popa - UCLA,
Titre Some remarks on the free group factors
Horaire11:00 à 12:00

The structure and classification of the so-called  free group II1 factors, arising as vN-algebras of the free groups Fn with n generators, 2 ≤ n ≤ ∞, have been the subject of much interest for 80 years by now. But despite many remarkable results and the development of several insightful techniques, some of the most basic questions concerning this fundamental class of II1 factors remained open:

(1) LFn ≃ LFm iff n = m;
(2) F(LFn)=1 when n < ∞;
(3) infinite generation of LF∞;
(4) existence of non freely complemented maximal amenable MASAs in LFn;
(5) do LFn embed in any non-amenable II1 factor. 
I will comment on the progress made on these problems and possible approaches to solve them.