Classical and Neo-classical operator spaces

Speaker: 

Professor Bernie Russo

Institution: 

UCI

Time: 

Tuesday, October 19, 2004 - 3:00pm

Location: 

MSTB 254

The operator spaces $H_n^k$ $1\le k\le n$, generalizing the row and column Hilbert spaces, and arising in the authors' previous study of contractively complemented subspaces of $C^*$-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. As an application, the completely bounded Banach-Mazur distance from $H_n^k$ to row or column space is explicitly calculated. This is joint work with Matt Neal.
An overview of "operator space theory" will be given.

Universality in Random Matrix Theory for Universality in Random Matrix Theory for Orthogonal and

Speaker: 

Dmitry Gioev

Institution: 

University of Pennsylvania

Time: 

Thursday, May 13, 2004 - 2:00pm

Location: 

MSTB 254

This is a joint work with P.Deift.
We give a rigorous proof of the Universality Conjecture
in Random Matrix Theory for orthogonal (beta=1) and
symplectic (beta=4) ensembles in the scaling limit
for a class of polynomial potentials
whose equilibrium measure is supported on
a single interval.
Our starting point is Widom's representation
of the correlation kernels for the beta=1,4 cases
in terms of the unitary (beta=2) correlation kernel
plus a correction.
In the asymptotic analysis of the correction terms
we use amongst other things differential equations for the derivatives
of orthogonal polynomials (OP's) due to Tracy-Widom,
and uniform Plancherel-Rotach type asymptotics for OP's
due to Deift-Kriecherbauer-McLaughlin-Venakides-Zhou.
The problem reduces to a small norm problem
for a certain matrix of a fixed size
that is equal to the degree of the polynomial potential.

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