## Operator Algebra Seminar Winter 2004

Schedule for Fall 2004 Friday,March 19, 20049:30 - 10:20, Jeffery 118 Speaker: Brian Forrest, University of Waterloo Bounded Approximate Identities in Ideals of the Fourier Algebra. In this talk we will use ideas from the theory of operator spaces to completely characterize the ideals of the Fourier algebra of an amenable locally compact group with bounded approximate identities. We will also try to show how operator spaces play a fundamental role in studying the Fourier algebra of a noncommutative group. Monday,February 23, 2004, 9:30 - 11:20, Jeffery 319 Speaker: Roland Speicher, Queen's University Title: Almost Sure Convergence of the Largest Eigenvalue (III) Abstract: I will continue with the proof of Haagerup and Thorbjornsen on the largest eigenvalue of a polynomial in independent Gaussian random matrices. I will present the general strategy of the proof and some details about (operator-valued) resolvents or Cauchy transforms. All relevant concepts and notations are recalled, so that the talk should be mostly self-contained. Monday,February 9 2004, 9:30 - 11:20, Jeffery 319 Speaker: Jamie Mingo, Queen's University Title: Almost Sure Convergence of the Largest Eigenvalue (II) Abstract: I will start the proof of Haagerup and Thorbjornsen on the largest eigenvalue of a product of independent Gaussian random matrices. The main tool will be the genus expansion for the moments and some basic facts from probability theory. Monday,January 26, 9:30 - 11:20, Jeffery 319 Speaker: Roland Speicher, Queen's University Title: Fluctuations of random matrices and cyclic Fock spaces Abstract: I will report on a recent joint work with J. Mingo about the description of global fluctuations of Gaussian and Wishart random matrices. In particular, I will present an operator-algebraic description in terms of cyclic Fock spaces which allows to diagonalize these fluctuations.Monday,

January 19, 9:30 - 10:20, Jeffery 319 Speaker: Jamie Mingo, Queen's University Title: An Operator Norm version of Voiculescu's Limit Law (after Haagerup and Thorbjornsen) This term we will have a series of lectures exploring a recent preprint of U. Haagerup and S. Thorbjornsen. The main result of the paper is a striking generalization of the theorem of Geman and Silverstein on the largest eigenvalue of a (suitably normalized) self-adjoint Gaussian random matrix -- namely that it converges to 2. Haagerup and Thorbjornsen show that a similar result holds for a polynomial in r independent random matrices. This is a strong version of Voiculescu's limit law theorem, which is the central limit theorem in free probability. Haagerup and Thorbjornsen's result is the most exciting result in random matrix theory for some time. The proof uses quite an array of mathematical techniques from special functions and combinatorics to classical operator theory with some complex analysis and applications to K-homology in between. So there will be something to interest everybody. In this first lecture I will explain the statement of the theorem and present an outline of the method of attack. Roland Speicher and I plan to offer NSERC summer research projects on problems related to his work.Schedule for Fall 2003