Seminar on Free Probability
and Random Matrices

Fall 2021

Organizer: J. Mingo


Friday, October 220, 10:00 - 11:00, Jeff 222 and via Zoom
Michael Brannan (Waterloo)
On the von Neumann algebras of quantum automorphism groups of finite dimensional C*-algebras.
I will report on some ongoing work with Floris Elzinga (Oslo), Samuel Harris (TAMU), and Makoto Yamashita (Oslo), where we study the II_1-factors that arise as the quantum automorphism groups of finite-dimensional C*-algebras. Among other things, we show that many of these von Neumann algebras are strongly 1-bounded (in particular, they are not isomorphic to free group factors), and that they are always Connes embeddable.

Friday, October 15, 10:00 - 11:00, via Zoom
Serban Belinschi (Toulouse)
Brown measure of polynomials in star-free variables, Part II
This talk will outline a method of finding/studying the Brown measure of an arbitrary polynomial in free, possibly non-selfadjoint random variables belonging to a tracial W^*-noncommutative probability space. After a brief reminder of the hermitization procedure and of what the Brown measure is, we shall look at how the linearization procedure applies to non-selfadjoint variables and how the Brown measure is found from the linearization matrix. We conclude by examining the (simplest) case, namely that of the sum of two free random variables. The talk is mostly based on the 2018 paper Serban T. Belinschi, Piotr Śniady, and Roland Speicher, Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method..

Friday, October 8, 10:00 - 11:00, via Zoom
Serban Belinschi (Toulouse)
Brown measure of polynomials in star-free variables, Part I
This talk will outline a method of finding/studying the Brown measure of an arbitrary \ polynomial in free, possibly non-selfadjoint random variables belonging to a tracial W^*-\ noncommutative probability space. After a brief reminder of the hermitization procedure a\ nd of what the Brown measure is, we shall look at how the linearization procedure applies\ to non-selfadjoint variables and how the Brown measure is found from the linearization m\ atrix. We conclude by examining the (simplest) case, namely that of the sum of two free r\ andom variables. The talk is mostly based on the 2018 paper Serban T. Belinschi, Piotr Śn\ iady, and Roland Speicher, Eigenvalues of non-Hermitian random matrices and Brown measure\ of non-normal operators: Hermitian reduction and linearization method..


Previous Schedules

Fall 2017 Fall 2018 Fall 2019
Winter 2018 Winter 2019 Winter 2020 Winter 2021
Fall 2010 Fall 2011 Fall 2012 Fall 2013 Fall 2014 Fall 2015 Fall 2016
Winter 2011 Winter 2012 Winter 2013 Winter 2014 Winter 2015 Winter 2016 Winter 2017
Fall 2003 Fall 2004 Fall 2005 Fall 2006 Fall 2007 Fall 2008 Fall 2009
Winter 2004 Winter 2005 Winter 2006 Winter 2007 Winter 2008 Winter 2009 Winter 2010

Getting to Jeffery Hall from the Hotel Belvedere