Program

A 4H    Introduction: motivation and some reminder
1. Analyticity and resonances in physics     M. Pindor 1h

2. Complex analysis, a reminder (old and new)     B. Candelpergher 2h

3. Theory and practice of Padé table     M. Pindor 1h



B 5H     Rational approximation, harmonic analysis and probability:
Selected pieces of mathematics
4. Fourier transform and complex analysis     J.R. Partington 2h

5. Analytic and rational approximation     E.B. Saff 2h

6. Statistics and probability, around the central limit theorem     P. Collet 1h



C 11H30     Applications, with or without aleas:
Mathematics for the user
7. Dynamical systems and celestial mechanics
   1. A reminder on hamiltonian dynamic. Three bodies problem     L. Biasco 1h

   2. Series in celestial mechanics; analyticity domains     A. Celletti 2h

   3. Resonances in hyperbolic and hamiltonian systems     V. Baladi 1h

8. Control and signal processing

   1. Historical and a reminder     M. Deistler 2h

   2. Spectral theory and control theory     N. Nikolski 1h

   3. Recent approaches     L. Baratchart 1h30

9. Rational approximation with noise
   1. In real or parameters space     M. Pindor 1h

   2. In Fourier space     B. Dujardin 1h

   3. Spectral decomposition of stationnary gaussian processes     A. Gombani 1h




D 4h30    Perspectives and opening
10. Interferometric gravitational waves detection     J.-Y. Vinet, F. Bondu, E. Cuoco 1h

11. Turbulence and information     P. Borgnat 1h

12. Round-table course: disguises of a concept in various fields     E.B. Saff, animateur 2 x45m



E 3H     Evening courses: synthesis and panoramas
13. The Fourier transform in mathematics history     J.-P. Kahane 1h

14. Singularities and approximation in several complex variables     N. Sibony 1h

15. Good bases     J.R. Partington 1h




F 3H     Workshops and seminars of young participants
16. ASome tapas of approximation theory     F. Seyfert animator, M.Smith and B.Beckermann 1h

17. Software demonstrations     J. Grimm, animator 1h

18. Talks and discussion about young participants works     M. Olivi, animator 1h