The lectures on free probability are back!
I have now started to put scans of my handwritten lecture notes online; they correspond more or less to what I write on the blackboard. As we are now, in the context of random matrix calculations, having a lot of indices hanging around it might in some cases be easier to decipher those from my notes than from the blackboard. Maybe sometimes in the future I will even tex them, but don’t count on this … In any case, most of the material I am presenting in this class is either from my book with Andu or from my book with Jamie, so that there exist already nicely written notes on this.
There is of course much more to say about random matrices. One issue is that in this class I cover only convergence and asymptotic freeness results in the averaged sense. Of course, almost sure versions of those results usually also exist. For more on those and other aspects of random matrices I refer to the random matrix literature (part of which you can find on the homepage of my class “Random Matrices” from last term). There exists also a nice tex-ed version of the lectures notes from my class on random matrices.
2019 will again be a year with quite a few meetings around free probability.
The main event will be a month-long program on New Developments in Free Probability and Applications at CRM in Montreal in March 2019. There will be two workshops: one, at the beginning of March, on the theory and its extensions and the second, at the end of March, on the applied perspective. In the two weeks in between there will also be quite some activity, in particular, we are aiming at bringing graduate students and postdoctoral fellows quickly to the frontiers of the subject. Furthermore, Alice Guionnet will give the Aisenstadt Chair lecture series between both workshops.
This program is part of the year long celebration of the CRM’s 50th anniversary. It seems very appropriate to have such a meeting on the blossoming of free probability theory, and its promise for the future at the place where the seed was sown. In the spring of 1991 Dan Voiculescu was the holder of the Andre Aisenstadt chair at the CRM in Montreal during the ’91 operator algebra program. At this time, free probability was still in its infancy and only known to a small group of enthusiasts. This was going to change. Voiculescu gave the Aisenstadt Lectures on free probability in Montreal, organizing the material and bringing it with the help of his students Ken Dykema and Alexandru Nica into a publishable form. The resulting book was the first volume in the CRM Monograph Series and was instrumental for making the theory more generally accessible and attracting many, in particular young, researchers to the subject. It is still the most cited literature on free probability. Andu, Dan, and Ken (as well as a couple of other experts) will stay as Simons Scholars-in-Residence for the whole program at CRM
Another month-long program with a substantial free probability component will be the Focus Program on Applications of Noncommutative Functions at the Fields Institute in Toronto, June 10 – July 5, 2019. In particular, one of the workshops of the program, June 17-21, deals with applications of noncommutative functions to random matrices and free probability.
The focus program at the Fields Institute will also include a celebratory banquet on June 14, in honour of the 70th birthday of Dan Voiculescu.
This is a blog on topics around Free Probability Theory. Originally, I created this to provide a forum around my lecture on free probability theory. But now I plan (at least hope) to extend it to general blog on free probability theory.
So I hope to post here also all kind of information which is relevant in the context of free probability theory, like: meetings, new results, discussions of open problems or general directions in the subject.
I hope that others will also make some contributions; if you are interested in writing your own posts in this context, please contact me!
We have now the Christmas break for our term. This means there will be no classes for two weeks. We will continue on January 7, 2019; there will be about ten more lectures. We will then cover two more main themes:
i) the random matrix connections of free probability (in particular, show the asymptotic freeness of many random matrix models)
ii) applications of free probability to von Neumann algebras (in particular, treat results about compressions of free group factors)
This is a blog on my videotaped lectures on “Free Probability Theory” from the winter term 2018/2019 at Saarland University.
Here is the link to the recordings of the lectures.
For now, the main purpose of this blog is to give viewers the oportunity to comment on the lectures or ask questions about the content.