UK Nonlinear News, August 2002


Workshop on Integrable Systems

Isaac Newton Institute, Cambridge (23 July to 19 December 2001)

Organisers: J.C. Eilbeck, A.V. Mikhailov, PM Santini, and V.E. Zakharo

By Chris Eilbeck

Almost 60 long stay participants and over 70 short stay participants gathered in various permutations over the 5 month period at the INI to discuss Integrable Systems in all their manifestations. The programme kicked off with a bang by hosting the XVth Meeting of Nonlinear Evolution Equations and Dynamical Systems (NEEDS). This meeting was run by M. Bruschi, F. Calogero, A.V. Mikhailov and P.M. Santini. In the tradition of the NEEDS meetings, there were an eclectic mix of 78 half-hour talks plus a poster session in a very crowded but enjoyable schedule. The meeting covered a range of theory for integrable and near-integrable systems, with examples drawn from fluid mechanics, plasma, physics, nonlinear optics, general relativity, and Böse-Einstein condensation. Techniques considered included spectral methods; direct methods (dbar dressing, finite gap method, bilinear methods); integrability criteria and tests; bi-Hamiltonian systems and separation of variables; integrable quantizations, and integrable functional equations.

A few weeks later we had the Euro Summer School "What is integrability?", organised by A. Degasperis, A. Hone, A.V. Mikhailov and A. Shabat, with the main theme on how to test for integrability in ordinary and partial differential equations. Selected lecture courses will be published in the book ``Integrability'' by Princeton University Press, edited by Mikhailov. After a week to recover, another EuroWorkshop: "Discrete systems and integrability", organised by F.W. Nijhoff, J. Hietarinta and P.M. Santini, with over 30 1hr talks on various themes in this fast-expanding area. After a short break, another Workshop: "Geometrical aspects of integrability", run by N. Manton, L. Mason and R. Ward, with the emphasis on equations coming from particle physics.

Then followed a longer break giving time to recover and do some new work before the next spate of workshops: "Computer algebra in applications to the problems of integrability", organised by T. Wolf, and "Algebraic aspects of integrability", at Loughborough, organised by Yu Berest and A.P. Veselov, the latter preceded by a special week at the INI devoted to Algebraic Aspects of Integrable Systems. Another satellite meeting followed at Heriot-Watt in December: "Classical and Quantum Integrable Systems", organised by R. Weston, E. Corrigan, J.C. Eilbeck and T. Miwa, with a final workshop back in Cambridge at the end of December: "Boundary valued problems", run by T. Fokas, B. Pelloni and A.V. Mikhailov.

In between all these events were a regular series of twice-weekly seminars and even more frequent personal discussions which the INI is well designed to encourage. We were all grateful for the hard work and dedication of the INI staff in making sure everything ran smoothly. I found it a refreshing and invigorating break from my normal routine. The only problem is that so many new ideas are generated that one has trouble following them all up...


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