Winter 2013
Schedule for Current Term
Tuesday, April 16, 3:00 - 4:30, Jeff 222
Shock waves and critical phenomena in dynamic random matrix
models
Maciej Nowak, (Smoluchowski Institute of Physics,
Jagellonian University, Cracow)
We obtain several classes of non-linear partial differential
equations for various random matrix ensembles undergoing
Brownian type of random walk. These equations for spectral
flow of eigenvalues as a function of dynamical parameter
(”time”) are exact for any finite size N of the random
matrix ensemble and resemble viscid Burgers-like equations
known in the theory of turbulence. In the limit of infinite
size of the matrix, these equations reduce to complex
inviscid Burgers equations, proposed originally by
Voiculescu in the context of free processes. We identify
spectral shock waves for these equations in the limit of the
infinite size of the matrix, and then we solve exact viscid
nonlinear equations in the vicinity of the shocks, obtaining
in this way universal, microscopic scalings equivalent to
Airy, Bessel and cuspoid kernels. We link observed spectral
universalities to several critical phenomena in theoretical
physics.
Tuesday, April 9, 4:00 - 5:30, Jeff 222
Integration on the Orthogonal Group and the Weingarten
Function, part V
Jamie Mingo (Queen's)
This week I will conclude the discussion of the relation
between the Weingarten function and the Jucys-Murphy
operator. This is based on a recent paper of Paul
Zinn-Justin.
Tuesday, April 2, 3:30 - 5:00, Jeff 222
Integration on the Orthogonal Group and the Weingarten
Function, part IV
Jamie Mingo (Queen's)
This week I will continue the discussion of the relation
between the Weingarten function and the Jucys-Murphy
operator. This is based on a recent paper of Paul
Zinn-Justin.
Tuesday, March 26, 3:30 - 5:00, Jeff 222
Integration on the Orthogonal Group and the Weingarten
Function, part III
Jamie Mingo (Queen's)
This week I will continue the discussion of the relation
between the Weingarten function and the Jucys-Murphy
operator. This is based on a recent paper of Paul
Zinn-Justin.
Tuesday, March 19, 3:30 - 5:00, Jeff 222
Integration on the Orthogonal Group and the Weingarten
Function, part II
Jamie Mingo (Queen's)
This week I explain the relation between the Weingarten
function and the Jucys-Murphy operator. This is based on a
recent paper of Paul Zinn-Justin.
Tuesday, March 12, 3:30 - 5:00, Jeff 222
Integration on the Orthogonal Group and the Weingarten
Function
Jamie Mingo (Queen's)
A recurring problem in many areas has been to find an
effective way of integrating over Haar measure on orthogonal
and unitary groups. A method using Schur-Weyl duality was
found thirty years ago by Dan Weingarten that reduces the
calculation to one over the symmetric group for which there
is a combinatorial analysis. This method is very useful in
random matrix theory. I will begin by discussing the
construction of the Weingarten function and its basic
properties. No previous knowledge of random matrix theory or
free probability will be assumed. Those with an interest in
representation theory are particularly welcome.
Tuesday, March 5, 1:30 - 3:00, Jeff 222
Jerry Gu (Queen's)
Orthogonally Invariant Random Matrices and Matricial
Cumulants, part IV
I will continue from last week.
Tuesday, February 26, 1:30 - 3:00, Jeff 222
Jerry Gu (Queen's)
Orthogonally Invariant Random Matrices and Matricial
Cumulants, part III
I will continue from last week.
Tuesday, February 12, 1:30 - 3:00, Jeff 222
Jerry Gu (Queen's)
Orthogonally Invariant Random Matrices and Matricial
Cumulants, part II
I will continue from last week.
Tuesday, February 5, 1:30 - 3:00, Jeff 222
Jerry Gu (Queen's)
Orthogonally Invariant Random Matrices and Matricial
Cumulants.
I will follow the paper of Capitaine and Casalis 'Cumulants
for Random Matrices as Convolutions on the Symmetric Group,
II' (2007)
Previous Schedules