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JOINT INSTITUTE FOR NUCLEAR RESEARCH			INSTITUTE OF THEORETICAL AND EXPERIMENTAL PHYSICS

BOGOLIUBOV LABORATORY OF THEORETICAL PHYSICS

International School

SYMMETRIES AND INTEGRABLE SYSTEMS

Dubna, Russia, June 8 - 11, 1999

Sponsored by Russian Foundation of Basic Research and the UNESCO

ORGANIZING COMMITTEE

A.N.Sissakian (Chairman, Dubna) S.Z.Pakuliak (Scientific secretary, Dubna) A.S.Losev (Moscow) A.D.Mironov (Moscow) G.S.Pogosyan (Dubna)

Scientific Program

The following subjects will be covered during lectures presented at the school:

1.

Separation of variables in classical and quantum integrable systems; dynamical symmetries and superintegrability.

2.

Geometrical methods in the integrable systems theory; the relations between finite and infinite-dimensional systems.

3.

Modern aspects of the integrability: quantum algebras and their quasi-Hopf deformations, quadratic algebras, W-algebras, supersymmetry in application to the modern string theories.

4.

Integrability of the string theories and quantum field theory.

5.

Group-theoretical methods in the integrable models.

List of the lectures

1.

E.Akhmedov. "Introduction to AdS/CFT correspondence" (2 hours).

2.

D.Fursaev. "Thermodynamics and statistical mechanics of black holes" (2 hours).

3.

D.Lebedev. "Separation of variables in quantum periodic Toda lattice" (2 hours).

4.

V.B. Priezzhev. "Analytical results in the abelian sandpile model" (1 hour).

5.

P.Pyatov. "Hecke algebra: construction of Young projectors and representation theory" (2 hours).

6.

K.Sarajkin. "Conformal blocks in WZW theories" (1 hour).

7.

V.Spiridonov. "Solitons and Coulomb gas, semilarity reductions and special functions" (2 hours).

8.

V.Ter-Antonyan. "Dyon-Oscillator duality of Schrödinger equation" (2 hours).

9.

V.Tolstoy. "Combinatorial structure of root systems of Lie algebras and superalgebras" (1 hour).

10.

K.Zarembo. "Solitons on branes" (1 hour).

The organizing committee of the school is planning the student seminar, where the students will be invited to give the review talks on the subjects of the modern mathematical physics.