CRM Short Program on
Random Matrices, Random Processes and Integrable Systems
20 June - 8 July 2005
Schedule
Lectures will be held in room 6214 (6th floor, André-Aisenstadt
building)
Registration: Room 5345
Coffee and tea breaks: Room 6245
Week 1: 20 - 24 June 2005
Monday June 20 / lundi le 20 juin
| Speaker/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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/Conferencier | Title/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 | |