Seminar on Free Probability
and Random Matrices

Winter 2017

Organizer: J. Mingo


Friday, June 23, 2:30 - 3:30, Jeff 322
Roland Speicher (Saarlands University)
Random Matrices and Their Limits
The free probability perspective on random matrices is that the large size limit of random matrices is given by some (usually interesting) operators on Hilbert spaces and corresponding operator algebras. The prototypical example for this is that independent GUE random matrices converge to free semicircular operators, which generate the free group von Neumann algebra. The usual convergence in distribution has been strengthened in recent years to a strong convergence, also taking operator norms into account. All this is on the level of polynomials. In my talk I will recall this and then go over from polynomials to rational functions (in non-commuting variables). Unbounded operators will also play a role.
Monday, June 19, 2:00 - 3:30, Jeff 222
Mario Diaz (Queen's)
Second-order Cauchy transform and the covariance of the linear statistics of random matrices, Part III
I will continue from Friday's talk.

Friday, June 16, 2:00 - 3:30, Jeff 222
Mario Diaz (Queen's)
Second-order Cauchy transform and the covariance of the linear statistics of random matrices, Part II
I will continue from Monday's talk.
Monday, June 12, 2:00 - 3:30, Jeff 222
Mario Diaz (Queen's)
Second-order Cauchy transform and the covariance of the linear statistics of random matrices
In this talk we will discuss some recent developments in second-order free probability theory. In particular, we will present some results concerning the second-order Cauchy transform and the covariance of the linear statistics of random matrices.
Monday, March 27, 2:30 - 4:00, Jeff 202
Yinzheng Gu (Queen's)
Analytic subordination for bi-free convolution, Part II
We discuss some analytic properties of the additive bi-free convolution, both scalar-valued and operator-valued. We show that using the one-variable subordination functions associated with the additive free convolution, simple formulas for additive bi-free convolutions can be derived. As an application, we prove a result about atoms of the additive bi-free convolution.
Monday, March 20, 2:30 - 4:00, Jeff 202
Yinzheng Gu (Queen's)
Analytic subordination for bi-free convolution
We discuss some analytic properties of the additive bi-free convolution, both scalar-valued and operator-valued. We show that using the one-variable subordination functions associated with the additive free convolution, simple formulas for additive bi-free convolutions can be derived. As an application, we prove a result about atoms of the additive bi-free convolution.
Monday, March 6, 2:30 - 4:00, Jeff 202
Mario Diaz (Queen's)
The linearization technique.
Part III: non-commutative rational functions and their linearizations
This will be a continuation from last week.
Tuesday, February 28, 2:30 - 3:20, Jeff 222
Mario Diaz (Queen's)
The linearization technique.
Part II: non-commutative rational functions and their linearizations
Last time we showed that every complex polynomial in non-commutative variables can be linearized into a linear polynomial with matricial coefficients. In this talk we will show that this is also true for a non-commutative rational function.
Tuesday, February 14, 2:30 - 3:20, Jeff 222
Mario Diaz (Queen's)
The linearization technique.
Part I: motivation and linearization of polynomials
In this talk we will show that every complex polynomial in non-commutative variables can be linearized into a polynomial with matricial coefficients. This linearization technique, also knows as 'descriptor realizations' in the control theory community, has important consequences in the realm of free probability theory.
Tuesday, February 7, 2:30 - 3:20, Jeff 222
Josué Daniel Vázquez Becerra (Queen's)
The effect of asymptotic liberation on the covariance of traces of random matrices, II
I will continue from last week.
Tuesday, January 31, 2:30 - 3:20, Jeff 222
Josué Daniel Vázquez Becerra (Queen's)
The effect of asymptotic liberation on the covariance of traces of random matrices
In this talk, we present some estimations for the asymptotic behaviour of the covariance of (unnormalized) traces of random matrices, when conjugated by asymptotically liberating random unitary matrices.
Tuesday, January 24, 2:30 - 3:20, Jeff 222
Jamie Mingo (Queen's)
Free Probability of Type B, Part II
Since Voiculescu introduced free independence 35 years ago, many variants have appeared: Boolean, monotone, type B, second order, higher order, real, quaternionic, infinitesimal, and bi-free independence (plus combinations of the above) to name a few. Most of the constructions are given combinatorially, but some have an interpretation in terms of analytic functions. I will discuss the 2003 paper of Biane, Goodman, and Nica, which introduced freeness of type B.

This will be the first of two lectures. This lecture will describe free cumulants of type B and type B freeness. The second lecture will explain how the hyperoctahedral group comes into play and hence why this is called type B freeness.

Tuesday, January 17, 2:30 - 3:20, Jeff 222
Jamie Mingo (Queen's)
Free Probability of Type B
Since Voiculescu introduced free independence 35 years ago, many variants have appeared: Boolean, monotone, type B, second order, higher order, real, quaternionic, infinitesimal, and bi-free independence (plus combinations of the above) to name a few. Most of the constructions are given combinatorially, but some have an interpretation in terms of analytic functions. I will discuss the 2003 paper of Biane, Goodman, and Nica, which introduced freeness of type B.

This will be the first of two lectures. This lecture will describe free cumulants of type B and type B freeness. The second lecture will explain how the hyperoctahedral group comes into play and hence why this is called type B freeness.

Previous Schedules

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
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