This term will be a learning
seminar on Brown measure and the circular law 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, September 10, 10:00 - 11:00, via Zoom
Kamil Szpojankowski (Politechnika Warszawska)
I will continue the ideas from last week behind the proof of so called circular law, which says that the empirical spectral distribution of a matrix with iid entries (expectation 0 and variance 1) converges as the dimension tends to infinity to the uniform distribution on the disk. The talk is based on the survey paper.
Friday, September 3, 10:00 - 11:00, via Zoom
Kamil Szpojankowski (Politechnika Warszawska)
I will continue the ideas from last week behind the proof of so called circular law, which says that the empirical spectral distribution of a matrix with iid entries (expectation 0 and variance 1) converges as the dimension tends to infinity to the uniform distribution on the disk. The talk is based on the survey paper.
Friday, August 27, 10:00 - 11:00, via Zoom
Kamil Szpojankowski (Politechnika Warszawska)
I will continue the ideas from last week behind the proof of so called circular law, which says that the empirical spectral distribution of a matrix with iid entries (expectation 0 and variance 1) converges as the dimension tends to infinity to the uniform distribution on the disk. The talk is based on the survey paper.
Thursday, August 5, 10:00 - 11:00, via Zoom
Kamil Szpojankowski (Politechnika Warszawska)
I will present the ideas behind the proof of so called circular law, which says that the empirical spectral distribution of a matrix with iid entries (expectation 0 and variance 1) converges as the dimension tends to infinity to the uniform distribution on the disk. I will discuss the key technical lemmas and show how one can deduce the circular law from these lemmas.
The talk is based on the survey paper.
Friday, July 23, 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 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
Hotel Belvedere