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Discrete Integrable Systems
DISCRETE INTEGRABLE SYSTEMS
July 18-22, 2011
Description and aim
The workshop targeted the following five themes:
1. Multi-dimensional Consistency, Lagrangian Forms: Can we extend the classification with respect to multi-dimensional consistency, to include non-scalar cases? What is the significance of the new variational principle connected to Lagrangian forms, e.g. in physics applications?
2. Symmetries, Integrals, Conservation laws, and Symplectic structures: What are the relations between (the number of) symmetries, integrals and conservation laws? Can one decide on symplectivity without deriving a symplectic structure? How to systematically construct symplectic structures?
3. Reductions and Solutions: How to construct (explicit) solutions for periodic reductions, Painlevé reductions, or solutions of other type, i.e. finite gap, rational solutions.
4. Detection and testing of Discrete Integrable Systems: What are currently the most effective methods? Can we identify relations between different notions of integrability, e.g. growth versus consistency?
5. Geometric approaches to Discrete Integrable Systems: Algebraic geometry has been successfully applied to the Painlevé equations, and to the QRT maps. Can this be extended to higher dimensional mappings, and to lattices?
The workshop also aimed to initiate new research and research collaborations.
Each of the 5 days of the conference was devoted to one of the 5 themes above, with talks in the morning and a moderated discussion in the afternoon.
ˇ Notable progress has already been made on points 1 and 2 above (e.g. Lagrangians for the MBSQ system), and several new research collaborations have been started.
ˇ The moderated discussions worked very well.
ˇ The workshop attracted a significant number of starting/early career researchers. It has been very gratifying to observe the synergy, interaction, and enthusiasm of this group.
ˇ The organizers are grateful to the KNAW, to NDNS+, to the Australian Centre for Mathematics and Statistics of Complex Systems (MASCOS), and to the Lorentz Center for much appreciated financial support.
ˇ The restricted web site for the organizers could contain more information, eg regarding the budget.
ˇ Last but not least, restaurant Allemansgeest was a perfect venue for the conference dinner.