Category Archives: online seminar

Announcement of two talks on free probability at the Technion … and of some more talks

I will give a colloquium talk at the Math Department of the Technion, Israel on next Monday, January 25 – online, of course. They have the nice option of a pre-colloquium talk, which provides students with some background for the material appearing in the colloquium talk. Tobias agreed to give such a preparation for my talk. So he will give tomorrow (on Thursday, January 21) an introduction to free probability and its relation with random matrices. Surely a great opportunity for everyone to learn (more) about the subject.

My talk will, of course, have such material in the background, but I tried to prepare it in such a way that even without knowing about free probability one should be able to get the main ideas. So, it might help to know what free semi-circulars are, but it is not necessary (and not assumed) for my talk.

Below are the titles and abstracts of our talks; and here is a link to the Technion page with access information:


update: actually, next week seems to be a busy week for talks around free probability; don’t forget that the UC Berkeley Probabilistic Operator Algebra Seminar will be starting again, on Monday, January 25, with a talk of Friedrich Goetze; and then there will also be a talk by Serban Belinschi on “The Christoffel-Darboux kernel in noncommutative probability” at the Probability Seminar at  Warsaw University of Technology, on Tuesday, January 26.

Tobias Mai: What actually is free probability theory? (Thursday, January 21, 2021)

In my talk, I want to answer this question by giving an introduction to the underlying ideas, basic concepts, and fundamental results of free probability theory. In particular, I will highlight the deep connections of this field with random matrix theory.

Roland Speicher: Singularity of matrices in non-commuting variables and free probability (Monday, January 25, 2021)

The Edmonds’ problem asks to decide about the singularity of a given matrix with linear polynomials in commuting variables as entries, or more general to compute the rank of such a matrix over the field of rational functions. This problem has no known deterministic polynomial time algorithm and it relates to fundamental questions in complexity theory.

Recently, there has been much interest in analyzing a non-commutative variant of the Edmonds’ problem, where the entries are linear polynomials in non-commuting variables and the rank is over the field of non-commutative rational functions (aka free skew field). Garg, Gurvits, Oliveira, and Wigderson showed that for this non-commutative Edmonds’ problem there exists a deterministic polynomial time algorithm. This problem has a remarkable number of diverse origins and motivations and I will present in my talk another such manifestation of the problem, arising from the relation with free probability and random matrix theory. In particular, this approach results also in another, quite analytic, algorithm for calculating the non-commutative rank.

This talk is based on joint work with Johannes Hoffmann, Tobias Mai, and Sheng Yin.

Another online seminar: Wales MPPM Zoom Seminar

At the moment there are many online activities going on …. and here is another one: the Wales Mathematical Physics Zoom Seminar, organized by Edwin BeggsDavid EvansGwion Evans,Rolf GohmTim Porter.

Why do I mention in particular this one; there are at least two reasons. Today there is a talk by Mikael Rordam around the Connes embedding problem, and next week I will give a talk, on my joint work with Tobias Mai and Sheng Yin of the last years around rational functions of random matrices and operators.

If you are interested in any of this, here is the website of the seminar, where you can find more information.

Update: The talks are usually recorded and posted on a youtube channel. There you can find my talk on “Random Matrices and Their Limits”.

Berkeley’s Probabilistic Operator Algebra Seminar (Hosted by Voiculescu) is Now Online

Due to the current conditions, Voiculescu’s seminar on free probability and operator algebras is now being held online via the platform Zoom. Members of the community worldwide are welcome to join.
Announcements and the Zoom link for each talk will be shared via a mailing list. If you would like to be added to this list, please send an email to:

In this webpage you can find the titles, abstracts and dates for past and future talks:

Jorge Garza Vargas