The Painlevé equations and monodromy problems
PEM
4 September 2006 to 29 September 2006
Programme theme
The study of the Painlevé equations has progressed explosively in the last thirty years. At first, the Painlevé equations were studied mainly by the inverse scattering method. Isomonodromic deformations are one of the origins of the Painlevé equations, and the isomonodromy technique is a powerful method to investigate the Painlevé transcendents. Conversely, Painlevé analysis is useful for studying monodromy problems, especially the Riemann–Hilbert problem.
More recently, various new methods have been used to study the Painlevé equations, such as WKB methods, twistor theory, algebraic geometry of initial value spaces, affine Weyl groups, differential Galois groups, symplectic geometry of the moduli space of connections and so on. Equally, the Painlevé equations have many applications, for instance to soliton equations, random matrices, quantum field theory (especially topological field theory), differential geometry of self-dual metrics, etc. Moreover, the Painlevé equations themselves have been generalised to Schlesinger systems, discrete systems and q-difference systems.
H. Poincaré said of Painlevé, "Les mathématiqués constituent un continent solidment agencé, dont tous les pays sont bien reliés les uns aux autres; l'œuvre de Paul Painlevé est une île originale et splendide dans l'océan voisin," but Painlevé's work is now part of the continent and is related to other countries. In this programme, we expect that an understanding of different approaches will bring forth new developments in many fields of pure and applied mathematics. We will gather together experts with various backgrounds, and will share common knowledge.
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Preprints
| Title | Year | Programme | Publication Date |
|---|---|---|---|
Painleve analysis and similarity reductions for the magma equationAuthors: Peter Clarkson, SE Harris |
2006 | PEM | 21 October 2016 |
Electro-magneto-encephalography for the three-Shell model: Numerical implementation for distributed current in spherical geometryAuthors: AS Fokas, V Michel |
2006 | PEM | 21 October 2016 |
Workshops
Painleve equations and monodromy problems: an introduction
11 September 2006 to 15 September 2006
Painleve equations and monodromy problems: recent developments
18 September 2006 to 22 September 2006
Seminars
| Monday 25th September 2006 | |||
|---|---|---|---|
| 16:00 to 17:00 | Room 1 | ||
| Wednesday 27th September 2006 | |||
|---|---|---|---|
| 11:30 to 12:30 | Room 1 | ||
| 16:00 to 17:00 | Room 1 | ||
Organisers
- Philip Boalch CNRS - Ecole Normale Superieure Paris
- Peter Clarkson University of Kent
- Lionel Mason University of Oxford
- Yousuke Ohyama Osaka University
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