This text is devoted to symmetries and integrability of difference equations and q-difference equations and the theory of special functions that occur as solutions of such equations. Techniques that have been traditionally applied to solve linear and nonlinear differential equations are now being successfully adapted and applied to discrete equations.

This volume presents the papers based upon lectures given at the 1999 Seminaire de Mathemathiques Superieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development since the 1970s, resulting in new motivation for study in surprisingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical...

This volume is comprised of two parts: the first contains articles by S.N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (CRM) seminar entitiled, Topics in Probability on Lie Groups: Boundary Theory. Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on $d$ generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figa-Talamanca using...

Features articles that constitute the proceedings of the Canadian Mathematical Society Annual Seminar on Mathematical Quantum Theory, held in Vancouver in August 1993. This title is suitable for those interested in activity at the frontiers of mathematical quantum theory.

This text contains the proceedings from the workshop, Nonlinear Dynamics and Renormalization Group, held at the Centre de recherches mathematiques (CRM) in Montreal (Canada), as part of the year-long programme devoted to mathematical physics. In the book, active researchers in the fields of nonlinear partial differential equations and renormalization group contribute results on topics such as Ginzburg-Landau equations and blow-up of solutions of the nonlinear Schroedinger equations, quantum resonances, and renormalization group analysis in constructive quantum field theory. This volume offers...

This text is devoted to a topic that has undergone rapid and fruitful development over the last 25 years of the 20th century, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory.

Data mining aims at finding interesting, useful or profitable information in very large databases. This book is based on lectures presented at the workshop on 'Data Mining and Mathematical Programming' (October 10-13, 2006, Montreal). It is suitable for fa

Contains papers presented at the 'Workshop on Singularities in PDE and the Calculus of Variations' at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation.

The central theme of this text is the search for solutions to eigenvalue problems that satisfy additional equations in the spectral parameter, for example, pairs of eigenvalue equations. This problem, which looks very simple at first, has turned out to be both deep and difficult. Moreover, this concept of bispectrality has been shown to be useful in many active areas of current research in mathematics and physics.

This volume contains the proceedings of the third meeting on Symmetries and Integrability of Difference Equations (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art.