Symmetries and Integrability

of Difference Equations

June 9-21, 2008

Département de Mathématiques

Université de Montréal

The field of symmetries and integrability of difference equations is a very dynamical one in which great progress has been made over the last 15 years or so. The key methods that have been developed in this area are based either on the inverse spectral approach or on the application of geometric and group theoretical techniques. Specifically the topics to be covered are the following : (1) Discrete integrable and isomonodromic systems ; (2) Discrete Painlevé equations ; (3) Singularity confinement, algebraic entropy and Nevanlinna theory ; (4) Discrete differential geometry ; (5) Special functions as solutions of difference or q-difference equations ; (6) Integrability, symmetry and numerical methods ; (7) Lie symmetries of difference systems ; (8) Integrable chains. The most relevant applications of this field of scientific activity are to coding theory, image reconstruction and processing and visual tracking, starting from discrete and usually sparse data.

Titles and Speakers

- Isomonodromy Transformations of Linear Difference Equations and Painlevé Hierarchy, Alexei Borodin (Caltech)

- Symmetry Preserving Discretization of Ordinary and Partial Differential Equations, Vladimir A. Dorodnitsyn (Keldysh Institute)

- Discrete Painlevé Equations, Basile Grammaticos (Paris VII)

- Definitions and Predictions of Integrability for Difference Equations, Jarmo Hietarinta (Turku)

- Orthogonal Polynomials and Integrable Systems, Mourad Ismail (University of Central Florida)

- Discrete Painlevé Equations and Random Matrices, Alexander Its (Indianapolis)

- Generalized Lie Symmetries of Difference Equations, Decio Levi (Rome TRE)

- Complete Integrability of Discrete Nonlinear Systems, Sergey P. Novikov (Moscow U/U of Maryland)

- Moving Frames in Applications, Peter Olver (Minnesota)

- Lie Group Transforms in the Interpolation of Digital Data, Jiri Patera (CRM, Montreal)

- Discrete Differential Geometry, Yuri Suris (TU Munich)

- Lie Point Symmetries of Difference Equations, Pavel Winternitz (CRM, Montreal)