THEMATIC PROGRAMS

November 20, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

January-June 2014
Thematic Program on Abstract Harmonic Analysis, Banach and Operator Algebras

Coxeter Lecture Series
May 27,28,29, 2014 at 3:30 p.m.
Fields Institute, Room 230


Sorin Popa
University of California, Los Angeles
On $\text{II}_1$ factors arising from free groups acting on spaces

On $\text{II}_1$ factors arising from free groups acting on spaces

A famous problem going back to Murray and von Neumann (1936-1943), asks whether the $\text{II}_1$ factors $L(\Bbb F_n)$, obtained as the centralizers in ${\cal B}(\ell^2 \Gamma)$ of the left regular representation of the free groups on $n$ generators, are non-isomorphic for different $n$. While this is still open, its "group measure space" version, asking whether the crossed product $\text{II}_1$ factors $L^\infty(X)\rtimes \Bbb F_n$, arising from free ergodic probability measure preserving actions $\Bbb F_n\curvearrowright X$, are non-isomoprphic for $n= 2, 3, ...$, independently of the actions, has recently been settled by Stefaan Vaes and myself. I will comment on this result, as well as on some related problems.


Speakers in the Distinguished and Coxeter Lecture Series have made outstanding contributions to their field of mathematics. The Lecture Sereies consists of three one-hour lectures.

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