Groups and Operator Algebras Seminar

Speaker: Sorin Popa (UCLA)

Title: Some remarks on the free group factors

Abstract: The structure and classification of the so-called free group II_1 factors, arising as vN-algebras of the free groups F_n with n generators, n between 2 and infinity, 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 II_1 factors remained open: (1) L(F_n) = L(F_m) iff n=m; (2) Fundamental group of F_n is {1} when n<infinity; (3) infinite generation of F_\infty; (4) existence of non freely complemented maximal amenable MASAs in L(F_n); (5) do L(F_n) embed in any non-amenable II_1 factor?
I will comment on the progress made on these problems and possible approaches to solve them.

GOA website: