|TITLE:||Freeness, von Neumann algebras and matricial microstates|
|SPEAKER:||Ken Dykema (Texas A&M)|
|DATE:||Jeudi, 8 Novembre 2007|
Freeness is a noncommutative probabilistic notion, introduced over 20 year ago by Voiculescu, that corresponds to the behavior of words in a free group. The study free probability theory has yielded, as one of many applications, a much deeper understanding of the von Neumann algebras of free groups. One of the essential examples of freeness for these applications comes from the asymptotic behavior of random matrices as the matrix size grows without bound. This, in turn motivates the defintion of the free entropy dimension, a quantity introduced by Voiculescu, and which, in one manifestation, is based on matricial microstates (or matrix approximants) of operators. We will finish by describing some results on amalgamated free products of von Neumann algebras.
About the speaker Kenneth J. Dykema has been at Texas A&M University since 1999 and is Professor since 2003. He obtained his Ph.D. from University of California, Berkeley in 1993 under the supervision of Dan Voiculescu. Before being appointed at Texas A&M, Dr Dykema had an appointment at Odense University (Denmark, 96-99), and before he was a Fields and NSF researcher. Over the last years he has held many prestigious visiting positions at institutions including CNRS (IHP Paris, and Luminy), MSRI and Muenster (Alexander-von-Humboldt Foundation).
The research area of Dr Dykema covers a broad spectrum in operator algebra theory. In particular, he is one of the few leading researchers in the very developed area of free probability, a branch of operator algebras invented by Voiculescu and with ramifications in classical probability theory, mathematical physics and combinatorics.