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.

The NATO ASI/CRM Summer School at Banff offered an in-depth account of the topic of the arithmetic and geometry of algebraic cycles, ranging from introductory courses by leading experts to discussions of the latest developments by all participants. The papers have been organized into three categories: cohomological methods; Chow groups and motives; and arithmetic methods. As a subfield of algebraic geometry, the theory of algebraic cycles has gone through various interactions with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology.

The intital French version of this text was a series of expository lectures that were given at the University of Montreal in November 1975. The book uses the appealing theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms. The presentation is elementary, and the topics are interesting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an...

This volume presents the proceedings of the CRM workshop on graph colouring and applications. The articles span a wide spectrum of topics related the topic including: list-colourings, total colourings, colourings and embeddings of graphs, chromatic polynomials, characteristic polynomials, chromatic scheduling, and graph colouring problems related to frequency assignment. Researchers in combinatorial optimization and graph theory have contributed their work and a list of open problems is included.

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.

This book is the first volume of the proceedings of the Canadian Mathematical Society Annual Seminar on Mathematical Quantum Theory, held in Vancouver in August 1993. The seminar was run as a research-level summer school concentrating on two related areas of contemporary mathematical physics. The subject of the first session, quantum field theory and many-body theory, is covered in the present volume; papers from the second session, on Schr odinger operators, are in Volume 2. Each session featured a series of minicourses, consisting of approximately four one-hour lectures, designed to...

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...

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.

Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers...

The papers in this collection explore the connections between the rapidly developing fields of measure-valued processes, stochastic partial differential equations, and interacting particle systems. Bringing together ideas and tools arising from these different sources, the papers include contributions to major directions of research in these fields, explore the interface between them, and describe newly developing research problems and methodologies. Several papers are devoted to different aspects of measure-valued branching processes (also called superprocesses). Some new classes of these...