Physics and Mathematics of Random Matrix Theory

13 Oct 2010, 08:00 → 15 Oct 2010, 18:00 Europe/Copenhagen

Aud. A (Niels Bohr International Academy)

(Photo courtesy A. D. Jackson) Random Matrix Theory is a mature and yet very active field of research. What is new is the strong link and collaboration between Mathematics and Physics that has appeared in recent years and that we wish to foster here. This meeting aims to cover both theoretical aspects of random matrices, and applications ranging as widely as from Finance to String Theory. On the theoretical side we have seen a huge progress in mathematical universality proofs in the past 1-2 years. They extend know results from invariant to non-invariant classes of random matrices where the matrix elements are random variables subject to a few constraints on their moments. This has deepened our insight in the conditions under which results for eigenvalue correlation functions are independent of the probability distributions used. Progress has also been made in the area of graded symmetry, a technical but insightful tool to generate resolvent operators. It has been understood much better how to treat non-Gaussian ensembles exactly as well as their underlying determinantal or Pfaffian structures. Interestingly, one ingredient here is the free random variable approach for infinite dimensions matrices. Many applications of matrix models rely on the use of the Harish-Chandra integral. in recent year some progress has been made on non-standard Unitary groups and on correlation functions with this measure. Group integrals of this kind will therefore constitute an interesting and challenging part of the program. Turning to the application side - both in Mathematics and Physics we have seen several important developments recently. Topics we wish to cover include Econophysics, Statistical Mechanics, Quantum Chaos, Quantum Chromodynamics, String theory and Number theory. Main speakers:</fi> Y. Fyodorov T. Guhr U. Haagerup J. Keating A. Morozov B. Schlein J. Verbaarschot P. Zinn-Justin Organizing Committee: Gernot Akemann (Brunel University) Poul H. Damgaard (NBIA) Bergfinn Duurhus (Dept. of Mathematics, Copenhagen University) Jan Philip Solovej (Dept. of Mathematics, Copenhagen University) Kim Splittorff (NBI) Conference secretary: Helle Kiilerich (NBIA), e-mail: helle at nbi.dk Sponsored by: the Niels Bohr International Academy and the Danish Science Research Council..

Wednesday 13 October

08:30 → 09:00 Registration, coffee and workshop opening

09:00 → 10:00 Keating: RMT and Elliptic Curve L-functions

10:00 → 11:00 Discussions + Coffee

11:00 → 12:00 Guhr: Doorway states coupled to a background: fidelity and survival probability

12:00 → 14:00 Lunch

14:00 → 14:40 Haagerup: Asymptotic Expansions for the Gaussian Unitary Ensemble

14:40 → 16:00 Discussions + Coffee

Thursday 14 October

09:00 → 10:00 Verbaarschot: Random Matrix Theory and Wilson Fermions

10:00 → 11:00 Discussions + Coffee

11:00 → 12:00 Schlein: Spectral properties of Wigner matrices

12:00 → 14:00 Lunch

14:00 → 15:00 1) Giacomo Livan 2) Pedro Vidal

Giacomo Livan: Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices Pedro Vidal: Preliminary results on the probability to have zero real eigenvalues for the GinOE

15:00 → 16:00 Discussions+Coffee

16:00 → 17:00 Morozov: Challenges of matrix models

17:00 → 18:00 Discussions+Coffee

18:00 → 22:00 Workshop Dinner

Friday 15 October

09:00 → 10:00 Zinn-Justin: Planar algebras and Potts model on random lattices

10:00 → 11:00 Discussions+Coffee

11:00 → 12:00 Fyodorov: Freezing transition in decaying Burgers turbulence and random matrix duality

12:00 → 14:00 Lunch