Fwd: Random matrices seminars

[Emanuele Tuillier Illingworth]

Working seminar on random matrices
http://www.sissa.it/mp/courses/w.php?q=2011_random_matrices.php

The seminars will take place in room 136.

(1) Hermitian Random Matrices. Orthogonal Polynomials. Hankel Determinant
and  Toda Lattice. 1/N expansion and graph enumeration.
Boris Dubrovin, Monday February 7, Monday February 14, Monday February
21, 2.30pm

(2) Unitary Random Matrices. Toeplitz determinant and Ablowitz Laddik
equation.
Stefano Romano Wednesday March 2 and March 9, 2.30pm.
References
Adler, M.; Van Moerbeke P. Integrals over classical Groups, Random
permutations, Toda and Toeplitz lattices. arXiv:math/9912143.
Masato Hisakado, Unitary Matrix Models and Painlev III. arXiv:hep-th/9609214.

(3) Moments of the Riemann zeta function and unitary random matrices.
Antonio Moro, Wednesday March 23 and March 30, 2.30pm.
References:
Keating, J. P.; Snaith, N. C. Random matrix theory andζ (1/2 + it).
Comm. Math.  Phys. 214 (2000), no. 1, 57 - 89.

(4) Kontsevich Integral and KdV equation.
Andrea Raimondo, Wednesday April 6, April 13 and April 20, 2.30pm.
References
Itzykson, C.; Zuber, J.-B. Combinatorics of the modular group. II. The
Kontsevich  integrals. Internat. J. Modern Phys. A 7 (1992), no. 23, 5661-
5705.
Kontsevich, M. Intersection theory on the moduli space of curves and the
matrix  Airy function. Comm. Math. Phys. 147 (1992), no. 1, 1-23.

(5) Distribution of the spectrum of eigenvalues of random Hermitian
matrices: gap probability distribution, sine kernel, Airy kernel, and
Tracy-Widom distribution.
Tamara Grava , Wednesday May 4, 2.30pm.
References
Tracy, C.A.; Widom, H. Distribution functions for largest eigenvalues and
their  applications. Proceedings of the International Congress of
Mathematicians, Vol. I
(Beijing, 2002), 587- 596, Higher Ed. Press, Beijing, 2002,
Tracy, C. A.; Widom, H. Level-spacing distributions and the Airy kernel.
Comm.  Math. Phys. 159 (1994), no. 1, 151 - 174.

(6) Combinatorial probability, random matrices and integrable systems.
Tamara Grava, Wednesday May 11 and May 18, 2.30pm.
References
Baik, J.; Deift, P.; Johansson, K. On the distribution of the length of
the longest  increasing subsequence of random permutations. J. Amer. Math.
Soc. 12 (1999), no. 4, 1119 - 1178.






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