Painleve equations and monodromy problems: an introduction

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Workshop theme

Partially supported by the European Community through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-2004-5652)

This workshop will give an introduction to Painlevé equations and monodromy problems suitable for postgraduate students and postdoctoral researchers. Topics to be covered include: History of the Painlevé Equations; Application of the Painlevé equations to Mathematical Physics; Differential Galois theory and the Painlevé equations; Discrete Painlevé equations; Asymptotics expansions for the Painlevé equations; Connection formulae and Riemann-Hilbert problems for Painlevé equations; Algebraic and rational solutions of the Painlevé equations; Random matrix and the Painlevé equations.

Timetable

Monday 11th September 2006
08:30 to 09:45	Registration	No Room Required
09:45 to 10:00	Opening	Room 1
10:00 to 11:00	Kazuo Okamoto University of Tokyo Introduction to the Painlev\'e equations	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Hiroshi Umemura Nagoya University Differential Galois theory and the Painlev\'e equations	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Kazuo Okamoto University of Tokyo Introduction to the Painlev\'e equations II	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Nalini Joshi University of Sydney Asymptotics of Painlev\'e equations	Room 1
16:30 to 17:30	Frank Nijhoff University of Leeds Integrable lattics and discrete Painlev\'e equations	Room 1
17:30 to 18:15	Wine and Beer Reception and Poster Session	No Room Required
18:30 to 19:30	Dinner at Selwyn College (Residents only)	No Room Required

Tuesday 12th September 2006
09:00 to 10:00	Kazuo Okamoto University of Tokyo Introduction to the Painlev\'e equations III	Room 1
10:00 to 11:00	Hiroshi Umemura Nagoya University Differential Galois theory and the Painlev\'e equations II	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:00	Stijn Lievens Symmetry groups underlying Bailey's transfomations for $^{10}\phi^9$ series	Room 1
12:00 to 12:30	Vassilios Papageorgiou University of Patras Yang-Baxter maps and integrable difference equations	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Kazuo Okamoto University of Tokyo Introduction to the Painlev\'e equations IV	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Nalini Joshi University of Sydney Asymptotics of Painlev\'e equations II	Room 1
16:30 to 17:30	Frank Nijhoff University of Leeds Discrete Painlev\'e equations II	Room 1
18:30 to 19:30	Dinner at Selwyn College (Residents only)	No Room Required

Wednesday 13th September 2006
09:00 to 10:00	Jon Keating University of Bristol Random matrices and Painlev\'e equations	Room 1
10:00 to 11:00	Hiroshi Umemura Nagoya University Differential Galois theory and the Painlev\'e equations III	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:00	Tropical representation of Weyl groups associated with certain rational varieties	Room 1
12:00 to 12:30	Anastasios Tongas University of Patras Symmetries and group invariant reductions of integrable equations on quad-graphs to discrete Painlev\'e equations	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Special solutions of the Painleve equations: P1 to P5	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 17:30	Informal discussions	Room 1
18:30 to 19:30	Dinner at Selwyn College (Residents only)	No Room Required

Thursday 14th September 2006
09:00 to 10:00	Athanssios Fokas University of Cambridge Riemann-Hilbert problems	Room 1
10:00 to 11:00	Hiroshi Umemura Nagoya University Differential Galois theory and the Painlev\'e equations IV	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:00	Local irreducibility of the first Painlev\'e equation	Room 1
12:00 to 12:30	Maurice Duits KU Leuven Painlev\'e I asymptotics for orthogonal polynomials with respect to a varying quartic weight	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Jon Keating University of Bristol Random matrices and Painlev\'e equations II	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Marta Mazzocco University of Manchester Hamiltonian structure of the Painlev\'e equations	Room 1
16:30 to 17:30	Philip Boalch CNRS - Ecole Normale Superieure Paris Algebraic solutions of the Painlevé equations	Room 1
19:30 to 18:00	Conference Dinner in the Hall at Magdalene College	No Room Required

Friday 15th September 2006
09:00 to 10:00	Athanssios Fokas University of Cambridge Riemann-Hilbert problems II	Room 1
10:00 to 11:00	Classical solutions on the Painlev\'e equations: from PII to PV II	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:00	Tom Claeys KU Leuven A real pole-free solution of the 4th order analogue of the Painlev\'e I equation and critical edge points in random matrix ensembles	Room 1
12:00 to 12:30	Galina Filipuk On the middle convolution for Fuschian systems	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Marta Mazzocco University of Manchester Hamiltonian structure of the Painlev\'e equations II	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Philip Boalch CNRS - Ecole Normale Superieure Paris Algebraic solutions of the Painlevé equations II	Room 1
16:30 to 16:45	Closing	Room 1
18:30 to 19:30	Dinner at Selwyn College (Residents only)	No Room Required

Speakers

Philip Boalch CNRS - Ecole Normale Superieure Paris
Tom Claeys KU Leuven
Maurice Duits KU Leuven
Galina Filipuk
Athanssios Fokas Imperial College London
Nalini Joshi University of Adelaide
Jon Keating University of Bristol
Stijn Lievens
Marta Mazzocco Chennai Mathematical Institute
Frank Nijhoff Aalborg Universitet
Kazuo Okamoto University of Tokyo
Vassilios Papageorgiou
Anastasios Tongas University of Patras
Hiroshi Umemura Nagoya University

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Painleve equations and monodromy problems: an introduction

Workshop theme

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