NATO ASI - European Summer School - 2001 in Russia

“Asymptotic combinatorics with applications to mathematical physics”

PROGRAM

July 8 – 20

July 8, Sunday (Euler International Mathematical Institute, Pesochnaya nab., 10)

15.00 – 20.00 REGISTRATION

1st day, July 9, Monday (Steklov Mathematical Institute, Fontanka, 27)

08.30 – 09.45 REGISTRATION

10.00 – 10.30 Opening Session

10.30 – 11.30 Brezin E. An introduction to matrix models – 1

11.30 – 12.00 Coffee break

12.00 – 13.00 Vershik A. Introduction to asymptotic theory of representations – 1

13.00 – 15.00 Lunch

15.00 – 15.50 Korepin V. Quantum spin chains and Riemann Zeta function with odd arguments

16.10 – 17.00 Bozejko M. Positive definite functions on Coxeter groups and second quantization of Yang–Baxter type

17.30 – 18.30 Reception

2nd day, July 10, Tuesday (Euler International Mathematical Institute, Pesochnaya nab., 10)

9.30 – 10.30 Ol'shanski G. Harmonic analysis on big groups, and determinantal point processes - 1

10.40 – 11.40 Brezin E. An introduction to matrix models - 2

11.40 – 12.10 Coffee break

12.10 – 13.10 Malyshev V. Combinatorics and probability for maps on two dimensional surfaces

13.10 – 15.00 Lunch

15.00 – 15.50 Hora A. An algebraic and combinatorial approach to central limit theorems related to discrete Laplacians

16.00 – 16.50 Nazarov M. On the Frobenius rank of a skew Young diagram

16.50 – 17.20 Coffee break

17.20 – 18.10 Kenyon R. Hyperbolic geometry and the low-temperature expansion of the Wulff shape in the 3D Ising model

18.30 – 19.30 Dinner

19.40 Brezin E. Informal discussion on matrix models

3rd day, July 11, Wednesday

9.30 – 10.30 Okounkov A. Combinatorics and moduli spaces of curves - 1

10.40 – 11.40 Brezin E. An introduction to matrix models - 3

11.40 – 12.10 Coffee break

12.10 – 13.10 Biane Ph. Asymptotics of representations of symmetric groups, random matrices and free cumulants

13.10 – 15.00 Lunch

14.00 – 17.00 Excursion over St. Petersburg

17.30 – 18.30 Dinner

19.00 Mariinski Theatre

4th day, July 12, Thursday

9.30 – 10.30 Deift P. Random matrix theory and combinatorics: a Riemann-Hilbert approach - 1

10.40 – 11.40 Okounkov A. Combinatorics and moduli spaces of curves - 2

11.40 – 12.10 Coffee break

12.10 – 13.10 Kazakov V. Matrix quantum mechanics and statistical physics on planar graphs - 1

13.10 – 15.00 Lunch

15.00 – 15.50 Faddeev L. 3-dimensional solitons and knots.

16.00 – 16.30 Coffee break

16.30 – 18.10 Krichever I. τ - functions of conformal maps

18.30 – 19.30 Dinner

19.30 Boat trip

5th day, July 13, Friday

9.30 – 10.30 Deift P. Random matrix theory and combinatorics: a Riemann-Hilbert approach - 2

10.40 – 11.40 Okounkov A. Combinatorics and moduli spaces of curves - 3

11.40 – 12.10 Coffee break

12.10 – 13.10 Ol'shanski G. Harmonic analysis on big groups, and determinantal point processes - 2

13.10 – 15.00 Lunch

15.00 – 15.50 Kazakov V. Matrix quantum mechanics and statistical physics on planar graphs - 2

16.00 – 16.50 Round table on combinatorics of the configurations and limit shapes

16.50 – 17.20 Coffee break

17.20 – 18.10 Liskovets V. Some asymptotic distribution patterns for planar maps

19.00 Banquet

July 14 Excursions, Museums, etc.

July 15 Excursion to Petergof 10:00 (from Euler Institute)

6th day, July 16, Monday

9.30 – 10.30 Deift P. Random matrix theory and combinatorics: a Riemann-Hilbert approach - 3

10.40 – 11.30 Kazakov V. Combinatorics of planar graphs in matrix quantum mechanics - 3

11.40 – 12.10 Coffee break

12.10 – 13.10 Borodin A. Asymptotic representation theory and Riemann-Hilbert problem-1

13.10 – 15.00 Lunch

15.00 – 15.50 Novikov S. On the weakly nonlocal Poisson and Symplectic Structures

16.00 – 16.50 Spiridonov V. Special functions of hypergeometric type associated with elliptic beta integrals

16.50 – 17.20 Coffee break

17.20 – 18.10 Missarov M. Exactly solvable renormalization group model

18.30 – 19.30 Dinner

7th day, July 17, Tuesday

9.30 – 10.30 Deift P. Random matrix theory and combinatorics: a Riemann-Hilbert approach - 4

10.40 – 11.40 Borodin A. Asymptotic representation theory and Riemann-Hilbert problem- 2

11.40 – 12.10 Coffee break

12.10 – 13.10 Okounkov A. Combinatorics and moduli spaces of curves - 4

13.10 – 15.00 Lunch

15.00 – 15.50 Speicher R. Free probability and Random matrices

16.00 – 16.50 Korotkin D. Riemann-Hil’bert problems related to branched coverings of CP¹, τ-function and Liouville action

16.50 – 17.20 Coffee break

17.20 – 18.10 Litvinov G. Representation theory in Idempotent (asymptotic) Mathematics

18.30 – 19.30 Dinner

8th day, July 18, Wednesday

9.30 – 10.30 Smirnov S. Critical percolation is conformally invariant - 1

10.40 – 11.40 Pastur L. Eigenvalue distribution of unitary invariant ensembles of random matrices of large order - 1

11.40 – 12.10 Coffee break

12.10 – 13.10 Pevzner M. On tensor products and Beresin kernels

13.10 – 15.00 Lunch

15.00 – 17.00 Memorial session devoted to Sergei Kerov and Anatoly Izergin

18.30 – 19.30 Dinner

9th day, July 19, Thursday

9.30 – 10.30 Speicher R. Free probability and Random matrices - 2

10.40 – 11.40 Bozejko M. White noise associated to the characters of the infinite symmetric group — Hopf-Kerov deformation

11.40 – 12.10 Coffee break

12.10 – 13.00 Jacobsen J. L. Enumerating coloured tangles

13.05 – 13.35 Sniady P. Random matrices and free probability

13.35 – 15.00 Lunch

15.00 – 15.30 Mlotkowski W. Λ-free probability

15.30 – 16.00 Petrogradskij V. Asymptotical theory of infinite dimensional Lie algebras

16.00 – 16.30 Coffee break

16.30 – 17.00 Kuznetsov V. On explicit formulae for special Macdonald polynomials

17.05 – 17.35 Dubrovskiy S. Moduli space of symmetric connections

17.40 – 18.10 Stukopin V. Representations of Yangians of Lie Superalgebras A(m,n) type

18.30 – 19.30 Dinner

10th day, July 20, Friday

9.30 – 10.30 Pastur L. Eigenvalue distribution of unitary invariant ensembles of random matrices of large order - 2

10.40 – 11.10 Vershik A. Introduction to asymptotic theory of representations - 2

11.15 – 11.45 Yambartsev A. Two-dimensional Lorentzian Models

11.45 – 12.15 Coffee break

12.15 – 13.00 Round table: Problems of the theory of integrable operators and determinant processes

13.00 – 13.30 Closing the school

13.30 – 15.00 Lunch

18.30 – 19.30 Dinner