and Random Matrices

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