Winter 2011

Schedule for Fall 2011 Thursday,May 12, 1:00 - 2:30, Jeff 422 Jonathan Novak (Waterloo) An introduction to matrix models Matrix models" are integrals over N x N matrices. The name comes from the fact that such integrals tend to admit asymptotic expansions, N → ∞, which coincide with partition functions encountered in 2D quantum gravity. For example, the asymptotic expansion of the Hermitian one-matrix model enumerates tessellations of compact Riemann surfaces by polygons, and the asymptotic expansion of Hermitian multi-matrix models does the same but also allows for coloured polygons. My talk will be fairly informal, and I will try to give an elementary and motivated introduction to this subject.Tuesday,

March 29, 4:30 - 6:00, Jeff 101 Laura Martí Pérez (University of Waterloo) A Fourier algebra for locally compact groupoids If G is a locally compact groupoid, we define a continuous Fourier algebra A(G). If the groupoid is locally trivial and transitive, we use operator space methods to prove that A(G) is isometrically isomorphic to the Haagerup tensor product of spaces of continuous functions on the unit space of G and the Fourier algebra of the isotropy group of G. This allows us to consider an operator space structure on A(G), and we are currently working on proving that A(G) is, in fact, a completely contractive Banach algebra.Tuesday,

March 22, 4:30 - 6:00, Jeff 101 Alex Blomendal (University of Toronto) Continuum limits of spiked random matrices What happens to the spectrum of a large random matrix when you add a fixed low rank matrix? This question arose first in the context of high-dimensional covariance estimation. The largest eigenvalues are known to exhibit a phase transition as a function of the perturbation. I will describe a new way to study this phenomenon, based on the known limiting random Schrödinger operator on the continuum half-line. The approach yields the asymptotic behaviour of the largest eigenvalues near the phase transition, solving an open problem in the real case. One characterization of the limit laws, in terms of a simple linear PDE, also offers a new route to the Painlevé structure in the celebrated Tracy-Widom laws. This is joint work with Bálint Virág (Toronto).Tuesday,

March 15, 4:30 - 6:00, Jeff 101 Tim Harris, (Queen's) The Largest Eigenvalue Distribution of a WignerRandom Matrix I will discuss the paper of Sinai and Soshnikov (1998) on the distribution of the eigenvalues at the edge of the spectrum of a Wigner random matrix.Tuesday,

February 8, 4:30 - 6:00, Jeff 101 Noriyoshi Sakuma (Keio University) A new limit theorem related to free multiplicative convolution Let ⊞, ⊠ and ⊍ be the free additive, free multiplicative, and boolean additive convolutions. For a probability measure µ on R^{+}with second moment, we find a scaling limit of (µ^{⊠N})^{⊞N}as N goes to infinity. The R-transform of the limit distribution can be represented by the Lambert's W function and the distribution is a free compound distribution. We also find similar limit theorem by replacing the free additive convolution by the boolean convolution. This talk is based on joint work with Hiroaki Yoshida of Ochanomizu University.Tuesday,

January 25, 4:30 - 6:00, Jeff 101 Jamie Mingo (Queen's) The Largest Eigenvalue of a Wigner Random Matrix, III A Wigner random matrix is a self-adjoint real random matrix with iid off-diagonal entries and iid diagonal entries (possibly different distribution). The seminar will explore the behaviour of the largest eigenvalue. The method is that of Füredi and Komlós (1981) which uses the combinatorics of graphs. This week I shall finish the proof with the lemma of Füredi and Komlós which gives an upper bound on the number of paths of length k on a graph with t vertices in which each edge is traversed at least twice.Tuesday,

January 18, 4:30 - 6:00, Jeff 101 Jamie Mingo (Queen's) The Largest Eigenvalue of a Wigner Random Matrix, II A Wigner random matrix is a self-adjoint real random matrix with iid off-diagonal entries and iid diagonal entries (possibly different distribution). The seminar will explore the behaviour of the largest eigenvalue. The method is that of Füredi and Komlós (1981) which uses the combinatorics of graphs. Last week I covered the semi-circle law for Wigner matrices. This week I shall start the largest eigenvalue proof.Tuesday,

January 11, 4:30 - 6:00, Jeff 101 Jamie Mingo (Queen's) The Largest Eigenvalue of a Wigner Random Matrix A Wigner random matrix is a self-adjoint real random matrix with iid off-diagonal entries and iid diagonal entries (possibly different distribution). The seminar will explore the behaviour of the largest eigenvalue. The method is that of Füredi and Komlós (1981) which uses the combinatorics of graphs. I will give the first two lectures, following Chapter 2.1 of the recent book of Anderson, Guionnet, and Zeitouni.Previous Schedules Schedule for Fall 2010 Schedule for Winter 2010 Schedule for Fall 2009 Schedule for Winter 2009 Schedule for Fall 2008 Schedule for Winter 2008 Schedule for Winter 2007 Schedule for Fall 2006 Schedule for Winter 2006 Schedule for Fall 2005 Schedule for Winter 2005 Schedule for Fall 2004 Schedule for Winter 2004 Schedule for Fall 2003