Speaker: Dr. Alan Edelman, Professor of Applied Mathematics, MIT

 

Abstract: In orthogonal polynomial theory one quickly learns about the special place occupied by Hermite, Laguerre, and Jacobi polynomials. I have often wondered why they are so special. I have heard dozens of correct answers. I am still not satisified that I really know why they are special. Somehow in probability, Hermite, Laguerre, and Jacobi takes the form of Gaussian, Chi, and Beta Random variables.

In computation, the triad takes the form of the symmetric eigenvalue problem, the singular value decomposition, and the lesser known, but very useful, generalized singular value decomposition. In Random Matrix theory we have the Gaussian ensembles, the Wishart Matrices, and the Manova Matrices. This talk will illustrate these ideas from a random matrix theory viewpoint. Discuss multivariate orthogonal polynomials, and the random matrix method of "Ghosts and Shadows"