Omega 99 - Short Course

Short Course

From June 14 to 18 and June 28 to July 2 (weeks before and after the Conference) the following shortcourse will be offered at the Mathematics Department of IST:

Algebraically Integrable Systems

Michèle Audin (Strasbourg)

Schedule:

Mondays: 16h00-17h00

Tuesdays: 15h00-16h00

Wednesdays: 10h00-11h00 and 15h00-16h00

Thursdays: 10h00-11h00

Discussion Sessions:

Wednesdays and Thursdays: 11h00-12h00
Tuesdays and Wednesdays: 17h00-18h00
In the first week all sessions meet in Room PA1, and in the second week all sessions meet in Room PA2, both in the Math Department Building, Floor 01.

Conference participants who wish to stay for this short course, should contact the organizers at omega99@math.ist.utl.pt.

The following is a sketch of the course:

The basics of the theory of integrable systems;
Algebro-geometric concepts which have become useful in this theory, namely algebraic curves, (moduli) spaces of algebraic curves and jacobians;
Description of the ingredients of a symplectic geometry (Poisson structures, Lagrangian foliations) on these algebraic-geometric objects;
How to solve actual (mechanical) integrable systems using this approach.

The whole course will rely on classical constructions and results of Adams-Harnad-Previato-Hurtubise, Beauville, Griffiths, Moser, Reyman-Semenov-Tyan-Shanski, and others. The following books and surveys contain a large part of the material and most of the references:

[1] Audin, M., Spinning Tops, A Course on Integrable Systems, Cambridge Studies in Advanced Mathematics, 51, Cambridge University Press, Cambridge, 1996.

[2] Donagi, R., Markman, E., Spectral covers, algebraically completely integrable Hamiltonian systems, and moduli of bundles, in "Integrable systems and quantum groups" (Montecatini Terme, 1993), Lecture Notes in Math., 1620, pp. 1-119, Springer, Berlin, 1996.

[3] Dubrovin, B., Krichever I., Novikov S.P., Integrable Systems I, in "Dynamical systems IV. Symplectic geometry and its applications.", vol. 4 of the Encyclopaedia of Mathematical Sciences, ed. by V. I. Arnol'd and S. P. Novikov, Springer-Verlag, Berlin-New York, 1990.

[4] Reyman, A. G., Semenov-Tyan-Shanski, M., Group Theoretical methods in the Theory of Finite-Dimensional Integrable Systems, in "Dynamical systems VII. Integrable systems, nonholonomic dynamical systems.", vol. 16 of the Encyclopaedia of Mathematical Sciences, ed. by V. I. Arnol'd and S. P. Novikov, Springer-Verlag, Berlin-New York, 1994.

This annoucement is also available in postscript format (ps) and pdf format (pdf).

omega99@math.ist.utl.pt June 10, 1999