CRM Short Program on

Random Matrices, Random Processes and Integrable Systems

20 June - 8 July 2005

Schedule

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Lectures will be held in room 6214 (6th floor, André-Aisenstadt building)
Registration: Room 5345
Coffee and tea breaks: Room 6245

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Week 1: 20 - 24 June 2005

Monday June 20 / lundi le 20 juin

Speaker/ConferencierTitle/Titre
8:30-9:20 Registration (Room 5345) and Coffee (Room 6245)
9:20-9:30 Welcoming address by Luc Vinet
Rector, Université de Montréal
. Morning session chair: J. Harnad
9:30-10:30 Pierre van Moerbeke Random matrices, permutations and processes from the integrable point of view
1. An introduction to random matrices
10:30-11:00 Coffee Break
11:00-12:00 Mark Adler Random matrices, permutations and processes from the integrable point of view
2. Recursion relations for Unitary integrals
12:00-14:00 Lunch
. Afternoon session chair: J. Hurtubise
14:30-15:30 Dmitri Korotkin Genus one correction to free energy of Hermitian matrix models,
G-function of Hurwitz Frobenius manifolds and isomonodromic tau-function
15:30-16:00 Tea Break
16:00-17:00 Alexey Kokotov Flat metrics with conical singularities on Riemann surfaces
and determinants of Laplacians
17:30-18:30 Wine and Cheese Reception

Tuesday June 21 / mardi le 21 juin

Speaker/ConferencierTitle/Titre
Morning session chair:Marco Bertola
9:30-10:30 Pierre van Moerbeke Random matrices, permutations and processes from the integrable point of view
3. The length of longest increasing sequences in random permutations and words: some basic facts
10:30-11:00 Coffee Break
11:00-12:00 Mark Adler Random matrices, permutations and processes from the integrable point of view
4. Random matrices and solitons
12:00-14:00 Lunch
. Afternoon session chair: Dmitri Korotkin
14:30-15:30 Ofer Zeitouni Fluctuations and deviations for symmetric matrices
15:30-16:00 Tea Break
16:00-17:00 Vladimir Kazakov Integrability and algebraic curve in AdS/CFT

Wednesday June 22 / mercredi le 22 juin

Speaker/ConferencierTitle/Titre
Morning session chair: Alexander Soshnikov
9:30-10:30 Pierre van Moerbeke Random matrices, permutations and processes from the integrable point of view
5. A probability measure on partitions, Toeplitz and Fredholm determinants and the 2d-Toda lattice.
10:30-11:00 Coffee Break
11:00-12:00 Mark Adler Random matrices, permutations and processes from the integrable point of view
6. Coupled Random matrices and the 2d-Toda lattice
12:00-14:00 Lunch
. Afternoon session chair: Vladimir Kazakov
14:00-15:00 Sam Howison The Hele-Shaw problem: 1898-2005
15:00-15:30 Tea Break
15:30-16:30 Anton Zabrodin Large N expansion for normal and complex matrix ensembles
16:30-17:30 Razvan Teodorescu Emergence of Painlevé I equation from the critical Normal Matrix Ensembles

Thursday June 23 / jeudi le 23 juin

Speaker/ConferencierTitle/Titre
Morning session chair: Sam Howison
9:30-10:30 Pierre van Moerbeke Random matrices, permutations and processes from the integrable point of view
7. Length of longest increasing sequences and Painlevé equations
10:30-11:00 Coffee Break
11:00-12:00 Mark Adler Random matrices, permutations and processes from the integrable point of view
8. The Dyson Brownian motion and the Airy process
12:00-14:00 Lunch
. Afternoon session chair: Anton Zabrodin
14:00-15:00 Alexander Its Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 1.
15:00-15:30 Tea Break
. Contributed session
15:30-16:00 Irina Nenciu Matrix models for circular ensembles
16:00-17:00 Nicholas Witte Algebraic theory of the Painlevé Equations and applications to Random Matrices
. .
19:00 Banquet - Restaurant Edouardo, 1014 Laurier W.
(Take 51 bus from Edouard Montpetit /Université de Montréal
bus stop to Laurier; ask driver to let you off at "Van Houtte")

Friday June 24 / vendredi le 24 juin

Speaker/ConferencierTitle/Titre
Morning session chair: Ofer Zeitouni
9:30-10:30 Pierre van Moerbeke Random matrices, permutations and processes from the integrable point of view
9. Distribution of the length of longest increasing subsequences for very large permutations
10:30-11:00 Coffee Break
11:00-12:00 Mark Adler Random matrices, permutations and processes from the integrable point of view
10. The Pearcey distribution
12:00-14:00 Lunch
. Afternoon session chair: Jacques Hurtubise
14:00-15:00 Alexander Its Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 2.
15:00-15:30 Tea Break
15:30-16:30 Alexander Soshnikov Statistics of Extreme Spacings in Determinantal Random Point Processes
. Contributed session
16:30-17:00 Dmitri Vasiliev Complex Geometry of Matrix Models

Week 2: 27 June - 1 July 2005

Monday June 27 / lundi le 27 juin

Speaker/ConferencierTitle/Titre
9:00-9:25 Registration (Room 5345) and Coffee (Room 6245)
Morning session chair: John Harnad
9:30-10:30 Alexander Its Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 3.
10:30-11:00 Coffee Break
11:00-12:00 Pavel Bleher Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 4.
12:00-14:00 Lunch
. Afternoon session chair: Jacques Hurtubise
14:00-15:00 Bertrand Eynard Two matrix models and biorthogonal polynomials 1.
Introduction to two matrix and multimatrix models
15:00-15:30 Tea Break
15:30-16:30 Nina Snaith Random Matrices and L-Functions 1.
16:30-17:30 Brian Conrey Random Matrices and L-Functions 2.

Tuesday June 28 / mardi le 28 juin

Speaker/ConferencierTitle/Titre
Morning session chair: Bertrand Eynard
9:30-10:30 Alexander Its Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 5.
10:30-11:00 Coffee Break
11:00-12:00 Pavel Bleher Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 6.
12:00-14:00 Lunch
. Afternoon session chair: Nina Snaith
14:00-15:00 Marco Bertola Two matrix models and biorthogonal polynomials 2.
Differential equations, finite N spectral curve and duality
15:00-15:30 Tea Break
15:30-16:30 Arno Kuijlaars Universality of the double scaling limit in unitary random matrix ensembles
17:30-18:30 Wine and Cheese Reception

Wednesday June 29 / mercredi le 29 juin

Speaker/ConferencierTitle/Titre
Morning session chair: Bertrand Eynard
9:30-10:30 Ken McLauughlin Asymptotic analysis of Riemann-Hilbert problems and applications 1.
10:30-11:00 Coffee Break
11:00-12:00 Pavel Bleher Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 7.
12:00-14:00 Lunch
. Afternoon session chair: Arno Kuijlaars
14:00-15:00 John Harnad Two matrix models and biorthogonal polynomials 3.
Integral representations of fundamental systems
15:00-15:30 Tea Break
15:30-16:30 Marco Bertola Two matrix models and biorthogonal polynomials 4.
Dual Riemann-Hilbert approach to biorthogonal polynomials
16:30-17:30 Alexander Orlov Schur function expansions of matrix integrals

Thursday June 30 / jeudi le 30 juin

Speaker/ConferencierTitle/Titre
Morning session chair: Jacques Hurtubise
9:30-10:30 Ken McLaughlin Asymptotic analysis of Riemann-Hilbert problems and applications 2.
10:30-11:00 Coffee Break
11:00-12:00 Pavel Bleher Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 8.
12:00-14:00 Lunch
. Afternoon session chair: John Harnad
14:00-15:00 Bertrand Eynard Two matrix models and biorthogonal polynomials 5.
Formal large N expansion for the 2-matrix model
15:00-15:30 Tea Break
. Contributed session chair: John Harnad
15:30-16:30 Alex Gamburd Averages of characterisitc polynomials from classical groups
16:30-17:30 Tamara Grava Partition function large N asymptotics beyond the one cut case
19:00 Banquet - Restaurant Edouardo, 1014 Laurier W.
(Take 51 bus from Edouard Montpetit /Université de Montréal
bus stop to Laurier; ask driver to let you off at "Van Houtte")

Friday July 1 / vendredi le 1 juillet

Speaker/ConferencierTitle/Titre
Morning session chair: Jacques Hurtubise
9:30-10:30 Ken McLaughlin Asymptotic analysis of Riemann-Hilbert problems and applications 3.
10:30-11:00 Coffee Break
11:00-12:00 Pavel Bleher Large N Asymptotics in Random Matrices. The Riemann-Hilbert Approach. 9.
12:00-14:00 Lunch
. Afternoon session chair: Tamara Grava
14:00-15:00 Bertrand Eynard Two matrix models and biorthogonal polynomials 6.
Large N asymptotics of biorthogonal polynomials
15:00-15:30 Tea Break
. Contributed session chair: Tamara Grava
15:30-16:00 Aleix Prats Ferrer Relations between the unitary ensemble and the triangular ensemble:
How to compute general correlators in the unitary ensemble
16:00-16:30 Nicolas Orantin Mixed correlation functions in the 2-matrix model and Bethe ansatz
16:30-17:00 Tom Claeys Universality of the double scaling limit in unitary random matrix ensembles

Week 3: 4 - 8 July 2005

Monday July 4 / lundi le 4 juillet

Speaker/ConferencierTitle/Titre
9:00-9:25 Registration (Room 5345) and Coffee (Room 6245)
Morning session chair: John Harnad
9:30-10:30 Craig Tracy Application of random matrix theory to Multivariate Statistics 1.
10:30-11:00 Coffee Break
11:00-12:00 Harold Widom Integral operators in random matrix theory 1.
12:00-14:00 Lunch
. Afternoon session chair: Ken McLaughlin
14:30-15:30 Jean-Bernard Zuber Lattice Loop Models and Combinatorics
15:30-16:00 Tea Break
16:00-17:00 Philippe Di Francesco Integrability and combinatorics: loop models, alternating sign matrices
and multidegree of algebraic varieties
17:30-18:30 Wine and Cheese Reception

Tuesday July 5 / mardi le 5 juillet

Speaker/ConferencierTitle/Titre
Morning session chair: Jean-Bernard Zuber
9:30-10:30 Craig Tracy Application of random matrix theory to Multivariate Statistics 2.
10:30-11:00 Coffee Break
11:00-12:00 Ken McLaughlin Asymptotic analysis of Riemann-Hilbert problems and applications 4.
12:00-14:00 Lunch
. Afternoon session chair: Philippe Di Francesco
14:30-15:30 Percy Deift Universality for orthogonal and symplectic ensembles
15:30-16:00 Tea Break
16:00-17:00 Paul Zinn-Justin Nilpotent orbits and the Yang-Baxter Equation

Wednesday July 6 / mercredi le 6 juillet

Speaker/ConferencierTitle/Titre
Morning session chair: Percy Deift
9:30-10:30 Craig Tracy Application of random matrix theory to Multivariate Statistics 3.
10:30-11:00 Coffee Break
11:00-12:00 Harold Widom Integral operators in random matrix theory 2.
12:00-14:00 Lunch
. Afternoon session chair: Paul Zinn-Justin
14:00-15:00 Marco Bertola Toeplitz determinants, minimal Toda orbits and isomonodromic tau functions
15:00-15:30 Tea Break
. Contributed session chair: Paul Zinn-Justin
15:30-16:30 Filipo Colomo Square ice, alternating sign matrices and classical orthogonal polynomials
16:30-17:30 Evgeny Strahov Giambelli point processes

Thursday July 7 / jeudi le 7 juillet

Speaker/ConferencierTitle/Titre
Morning session chair: Harold Widom
9:30-10:30 Craig Tracy Application of random matrix theory to Multivariate Statistics 4.
10:30-11:00 Coffee Break
11:00-12:00 Ken McLaughlin Asymptotic analysis of Riemann-Hilbert problems and applications 5.
12:00-14:00 Lunch
. Afternoon session chair: Marco Bertola
14:00-15:00 Andrei Okounkov A nonstationary deformation of the Calogero-Sutherland
quantum many-body problem
15:00-15:30 Tea Break
. Contributed session chair: Marco Bertola
15:30-16:30 Nicholas Witte The Distribution of the first Eigenvalue Spacing at the Hard Edge
of Random Hermitian Matrices
16:30-17:30 Maarten Vanlessen Universality for Laguerre type orthogonal and symplectic
ensembles at the hard edge of the spectrum
19:00 Banquet - Restaurant Chez Lévèque, 1030 Laurier W.
(Take 51 bus from Edouard Montpetit/Université de Montréal
bus stop to Laurier. Ask the driver to let you off at "Van Houtte".
Or: Walk east 1 block along Edouard Montpetit to Vincent d'Indy;
turn left (N), walk one block to Cote Ste Catherine, turn right (E),
walk about 20 mins. (1.5 km) to Laurier; turn left,
walk 5 mins (4 blocks) on S. side.)

Friday July 8 / vendredi le 8 juillet

Speaker/ConferencierTitle/Titre
Morning session chair: Andrei Okounkov
9:30-10:30 Craig Tracy Application of random matrix theory to Multivariate Statistics 5.
10:30-11:00 Coffee Break
11:00-12:00 Harold Widom Integral operators in random matrix theory 3.
12:00-14:00 Lunch
14:00 CRM Short Program on Random Matrices ends

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