Symmetries and integrability of difference equations (SIDE VI) - Foreword

Abstract

This special issue of the Journal of Nonlinear Mathematical Physics is de-voted to the sixth SIDE (Symmetries and Integrability of Difference Equa-tions) meeting, held 19–24 June 2004 at the Kallvik Conference Centre inHelsinki, Finland. The papers gathered here are refereed contributions fromresearchers in the field of discrete integrable equations on topics related tothe main themes of the SIDE VI meeting. This collection serves as morethan just a proceedings for SIDE VI as many papers were submitted inresponse to a call for papers sent out soon after the meeting.The first meeting of the SIDE series took place at Esterel, Canada, in1994. Since then meetings have been held every two years: at Canter-bury, UK (1996), Sabaudia, Italy (1998), Tokyo, Japan (2000), and Giens,France (2002). Proceedings have been published for each meeting. Thesecond supplement to volume 10 of the Journal of Nonlinear MathematicalPhysics was devoted to the SIDE V meeting in Giens. SIDE V and SIDEVI were both EuroConferences organised and supported by EURESCO. Thetwo meetings were planned at the outset to emphasize different aspects ofthis expanding field of research. The SIDE V meeting emphasized DiscretePainleve equations and the solvability of difference equations while the SIDEVI meeting emphasized Analytic difference equations, special functions andquantum models on the lattice. Specific themes of SIDE VI included thefollowing.• Analytic difference equations and spectral theory• Difference bispectral problems• Difference Galois theory• Q-hypergeometric and elliptic modular functions• Representation theory and orthogonal polynomials• Algebraic curves and addition formulae of Abelian functions1 -------------------------------------------------------------------------------- Page 2 • Discrete and quantum geometry• Quantum models on the lattice• Quantum mappingsWe gratefully acknowledge the support of the European Commissionthrough its Human Potential Programme, High-Level Scientific Conferences(Contract No: HPCF-CT-2001-00013), the European Science Foundationthrough its EURESCO conferences programme and the Academy of Finland.Finally we would like to thank Norbert Euler for publishing special issues ofthe Journal of Nonlinear Mathematical Physics devoted to this pair of SIDEmeetings.Conference organisersChair: Jarmo Hietarinta, University of Turku, FinlandVice-chair: Frank Nijhoff, University of Leeds, UKGuest editors for this issueJan Felipe van Diejen, Universidad de Talca, ChileRod Halburd, Loughborough University, UK2