Seminar on Free Probability and Random Matrices
Winter 2012

Organizers: J. Mingo and R. Speicher

Monday February 13, 3:30 - 5:00, Jeff 422 Jamie Mingo, (Queen's) Cumulants from Random Matrices, III This talk will conclude the series.

Monday February 6, 3:30 - 5:00, Jeff 422 [Note Early Start] Jamie Mingo, (Queen's) Cumulants from Random Matrices, II I will continue from last week.

Monday January 30, 4:30-6:00, Jeff 422 Jamie Mingo (Queen's) Cumulants from Random Matrices The classical cumulants of a random variable, X, come from the expansion of log(E(exp(tX))). The free cumulants come from the expansion of the inverse of the Cauchy transform G(t) = E((t - X)^(-1)). There is another path to free cumulants using random matrix theory. In this method one interlaces a random matrix with a deterministic matrix, and whatever comes out on the other side is a free cumulant. I will this demonstrate this method using unitary and Wishart random matrices. This is joint work with Roland Speicher.

Monday January 23, 4:30-6:00, Jeff 422 Mihai Popa (Queen's) Some results concerning the asymptotic behavior of orthogonal random matrices The talk will present several results and open questions concerning the asymptotic behavior of orthogonal random matrices. We will heavily rely on Voiculescu's paper "Limit laws for random matrices and free products" (1991). Tuesday January 17, 2012, 3:30 - 5:00, Jeff 319 Matthew Kennedy, (Carleton) Essential normality of certain commuting families of operators Arveson's work on the theory of commuting families of operators established deep connections with fundamental notions in commutative algebra and algebraic geometry, and attracted the attention of a number of researchers. At the center of much of this work is Arveson's conjecture, made over a decade ago, that many commuting families of linear operators are essentially normal. To date, however, the truth of this conjecture has been established only in certain special cases. In this talk, I will give an introduction to this area of research and explain the interest in essential normality. I will present recent work that provides a new perspective on Arveson’s conjecture, and establishes the conjecture for a new class of examples.

Previous Schedules

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Winter 2011
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