Seminar on Free Probability
and Random Matrices

Winter-Spring 2021

Organizer: J. Mingo


This term will be a learning seminar on Brown measure delivered via Zoom. Send me an email if you wish to join us. We will be following the notes of Flemming Larsen and Chapter 11 in the book of Mingo-Speicher and the 2000 JFA paper of Haagerup and Larsen. Notes for lectures 1 -5, lectures 9 - 11; lecture 12; lecture 13.

Friday, July 16, 10:00 - 11:00, via Zoom
Mihai Popa (San Antonio)
The lecture aims to give a different take on the $S$-transform. We will show that its multiplicative inverse, the so-called $T$-transform, has easier to determine coefficients and allows an intuitive justification of the multiplication property.

Friday, July 9, 10:00 - 11:00, via Zoom
Pei-Lun Tseng (Queen's)
I will conclude the proof of the theorem Haagerup-Larsen [2000] which shows how the $S$-transform can be used to give the Brown measure of a $R$-diagonal operator.
Friday, July 2, 10:00 - 11:00, via Zoom
Pei-Lun Tseng (Queen's)
I will continue the proof of the theorem Haagerup-Larsen [2000] which shows how the $S$-transform can be used to give the Brown measure of a $R$-diagonal operator.
Friday, June 25, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
I will start the proof of the theorem Haagerup-Larsen [2000] which shows how the $S$-transform can be used to give the Brown measure of a $R$-diagonal operator.
Friday, June 18, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
I will review the basic construction of the $R$ and $S$ transforms.
Friday, June 11, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
A crucial part of the calculation of the Brown measure of $R$-diagonal operators is the representation of every $R$-diagonal operator as the product of a freely independent Bernoulli random variable and an even operator.

Friday, June 4, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
In this lecture I will free independence and $R$-diagonal operators, which will be the focus for the rest of the lectures.

Friday, May 28, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
In this lecture I will review what is meant by the circular operator.

Friday, May 21, 10:00 - 11:00, via Zoom
Ian Charlesworth (Berkeley)
In this lecture I continue to describe the basic properties of the Brown measure.

Friday, May 14, 10:00 - 11:00, via Zoom
Ian Charlesworth (Berkeley)
In this lecture I continue to describe the basic properties of the Brown measure.

Friday, May 7, 10:00 - 11:00, via Zoom
Ian Charlesworth (Berkeley)
In this lecture I describe the basic properties of the Brown measure.

Friday, April 30, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
In this lecture I will complete the proof that $\lambda \mapsto L(a - \lambda 1)$ is subharmonic.

Friday, April 23, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
In this lecture I will discuss some basic facts about subharmonic functions. Our goal will be to show that $\lambda \mapsto L(a - \lambda 1)$ is subharmonic.

Friday, April 16, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
In this lecture I will prove the additivity, $L(ab) = L(a) + L(b)$, of the Fuglede-Kadison logarithm in a finite von-Neumann algebra,

Thursday, April 1, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
In this lecture I will present the Fuglede-Kadison logarithm, $L(a) = \tau(\log(|a|))$, of a non-normal operator in $(M, \tau)$, a finite von-Neumann algebra, and determine its basic properties.

Thursday, March 25, 10:00 - 11:00, via Zoom
James Mingo (Queen's)
In this initial lecture I will present a broad outline of Brown measure and show that the eigenvalue distribution (normalized to be a probability measure) of a matrix $A$ is the Brown measure of $A$.

Previous Schedules

Fall 2017 Fall 2018 Fall 2019
Winter 2018 Winter 2019 Winter 2020
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