What is integrability?

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Workshop theme

Aims: The School is intended for young researchers (both postgraduates and postdocs) working in the field of Integrable Systems and related areas. World experts will provide a thorough introduction to the different definitions of Integrability, through lectures supplemented with discussions, tutorials and example classes. The aim is to emphasize the links between the various approaches and points of view, resulting in a synthesis of the many answers to the question What is Integrability?.

Topics: Symmetries and conservation laws. Painlevé approach. Integrable quantum systems. Hirota's method. Geometric integrability. Approximate integrability & normal forms. Testing for integrability.

Timetable

Monday 13th August 2001
08:30 to 09:00	Registration	No Room Required
09:00 to 10:00	Introduction: What is Integrability?	Room 1
10:00 to 11:00	Discrete integrable systems and discrete symmetries	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Martin Kruskal The Painlev\'e property and the poly-Painlev\'e test	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	No Room Required
14:00 to 15:00	Antonio Degasperis Multiscale expansion and integrability of dispersive wave equations	Room 1
15:00 to 15:30	Tea	No Room Required
16:00 to 17:00	Mark Ablowitz University of Colorado On some integrable and non-integrable equations	Room 1
17:15 to 18:15	Welcome Wine Reception	No Room Required
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Tuesday 14th August 2001
09:00 to 10:00	Alexey Shabat L.D.Landau Institute for Theoretical Physics, Moscow Classical heirarchies of integrable equations	Room 1
10:00 to 11:00	Antonio Degasperis Multiscale expansion and integrability of dispersive wave equations	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Tutorial on multiscale expansion	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	No Room Required
14:00 to 15:00	Integrability of finite dimensional dynamical systems	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Lionel Mason University of Oxford Anti-seld-duality and integrability	Room 1
16:30 to 17:30	Martin Kruskal The Painlev\'e property and the poly-Painlev\'e test	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Wednesday 15th August 2001
09:00 to 10:00	Discrete integrable systems and discrete symmetries	Room 1
10:00 to 11:00	Alexey Shabat L.D.Landau Institute for Theoretical Physics, Moscow Dressing chains and darboux transformations	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Lionel Mason University of Oxford Twistor theory and integrability	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	No Room Required
14:00 to 15:00	Symmetries and conservation laws - Formal recursion operators	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Tutorial on the Painlev\'e property	Room 1
16:30 to 17:30	Antonio Degasperis Multiscale expansion and integrability of dispersive wave equations	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Thursday 16th August 2001
09:00 to 10:00	Necessary conditions for integrability	Room 1
10:00 to 11:00	Discrete integrable systems and discrete symmetries	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Tutorial on formal recursion operators and canonical conservation laws	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	Centre for Mathematical Sciences
14:00 to 15:00	Martin Kruskal The Painlev\'e property and the poly-Painlev\'e test	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Discussion/problem solving	Room 1
16:30 to 17:30	Jan Sanders Vrije Universiteit Amsterdam Number theory and the symmetry classification of integrable systems	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Friday 17th August 2001
09:00 to 10:00	Jarmo Hietarinta University of Turku Hirota's bilinear method and its connection with integrability	Room 1
10:00 to 11:00	Vladimir Zakharov Aalborg Universitet Multidimensional perturbation theory	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Tutorial on discrete integrable systems and symmetries	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	No Room Required
14:00 to 15:00	Yuji Kodama Ohio State University Normal forms and solitons	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Discussion/problem solving	Room 1
16:30 to 17:30	Jan Sanders Vrije Universiteit Amsterdam Number theory and the symmetry classification of integrable systems	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Monday 20th August 2001
09:00 to 10:00	Classification problem - main results	Room 1
10:00 to 11:00	Yuji Kodama Ohio State University Normal forms and solitons	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Tutorial - Transformations of PDE's	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	No Room Required
14:00 to 15:00	Jarmo Hietarinta University of Turku Hirota's bilinear method and its connection with integrability	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Tutorial on Hirota's bilinear method	Room 1
16:30 to 17:30	Jan Sanders Vrije Universiteit Amsterdam Number theory and the symmetry classifiction of integrable systems	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Tuesday 21st August 2001
09:00 to 10:00	Yuji Kodama Ohio State University Normal forms and solitons	Room 1
10:00 to 11:00	Jarmo Hietarinta University of Turku Hirota's bilinear method and its connection with integrability	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Tutorial on normal forms and solitons	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	No Room Required
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Tetsuji Miwa Kyoto University Quantum integrable systems	Room 1
16:30 to 17:30	Vladimir Zakharov Aalborg Universitet Multidimensional perturbation theory	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Wednesday 22nd August 2001
09:00 to 10:00	Symmetry, the Chazy equation and Chazy hierarchies	Room 1
10:00 to 11:00	Alexey Shabat L.D.Landau Institute for Theoretical Physics, Moscow Integrable Lagrangian equations	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Tutorial on quantum integrable systems	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	Centre for Mathematical Sciences
14:00 to 15:00	Hermann Flaschka Representation theory and integrability	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	The inverse scattering transform	Room 1
16:30 to 17:30	Multi-Hamiltonian structures and integrability	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Thursday 23rd August 2001
09:00 to 10:00	Vladimir Zakharov Aalborg Universitet Multidimensional perturbation theory	Room 1
10:00 to 11:00	Symmetry, the Chazy equation and Chazy hierarchies	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Tutorial on symmetry and integrability	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Sciences	No Room Required
14:00 to 15:00	Pavel Winternitz Université de Montréal Superintegrability, multiseparability and exact solvability in quantum mechanics I	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Discussion/problem solving	Room 1
16:30 to 17:30	Tetsuji Miwa Kyoto University Quantum integrable systems	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Friday 24th August 2001
09:00 to 10:00	Pavel Winternitz Université de Montréal Superintegrability, multiseparability and exact solvability in quantum mechanics II	Room 1
10:00 to 11:00	Multi-Hamiltonian structures and integrability	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Tutorial on links	Room 1
12:30 to 13:30	Lunch at the Centre for Mathematical Scienes	No Room Required
14:00 to 15:00	Tetsuji Miwa Kyoto University Quantum integrable systems	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Hermann Flaschka Representation theory and integrability	Room 1
16:30 to 17:30	Final discussion - What is integrability?	Room 1
19:00 to 00:00	Dinner at Wolfson Court (Residents only)	No Room Required

Speakers

Mark Ablowitz University of Colorado
Antonio Degasperis
Hermann Flaschka
Jarmo Hietarinta University of Turku
Yuji Kodama Ohio State University
Martin Kruskal
Lionel Mason University of Oxford
Tetsuji Miwa Kyoto University
Jan Sanders Vrije Universiteit Amsterdam
Alexey Shabat L.D.Landau Institute for Theoretical Physics, Moscow
Pavel Winternitz Université de Montréal
Vladimir Zakharov

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