and Random Matrices

Winter 2017

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Schedule for Current Term
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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

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

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

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