IRMA Lectures in Mathematics and Theoretical Physics
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Edited by:
Vladimir G. Turaev
This series is devoted to the publication of proceedings of conferences or workshops sponsored by the Institut de Recherche Mathématique Avanceé, Strasbourg, France, research monographs and other mathematical writings judged appropriate by the editor. The main focus will be proceedings of the international meetings between mathematicians and theoretical physicists (known under the French abbreviation "RCP") held at IRMA twice a year since about 30 years.
These meetings are aimed at creating and strengthening bridges between active mathematicians and physicists in the areas of current strong development. The goal is to promote the recent advances in these disciplines and to make them accessible to wide circles of professional mathematicians and students of mathematics and physics.
The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics.
Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern--Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large N limits ranging from approximation methods in quantum mechanics to modular forms and string/gauge theory duality.
Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of important themes of research at the forefront of mathematics and theoretical physics.
Modeling, in particular with partial differential equations, plays an ever growing role in the applied sciences. Hence its mathematical understanding is an important issue for today's research.
This book provides an introduction to three different topics in partial differential equations arising from applications. The subject of the first course by Michel Chipot (Zurich) is equilibrium positions of several disks rolling on a wire. In particular, existence and uniqueness of and the exact position for an equilibrium are discussed.
The second course by Josselin Garnier (Toulouse) deals with problems arising from acoustics and geophysics where waves propagate in complicated media, the properties of which can only be described statistically. It turns out that if the different scales presented in the problem can be separated, there exists a deterministic result.
The third course by Otared Kavian (Versailles St.-Quentin) is devoted to so-called inverse problems where one or several parameters of a partial differential equation need to be determined by using, for instance, measurements on the boundary of the domain. The question that arises naturally is what information is necessary to determine the unknown parameters. This question is answered in different settings.
The text is addressed to students and researchers with a basic background in partial differential equations.
This volume contains nine refereed research papers in various areas from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme.
Topics covered include irregular connections, rank reduction and summability of solutions of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems, multiple zeta values, quasi-polynomial formalism, Padé approximants related to analytic integrability, hybrid systems.
The interactions between computer algebra, dynamical systems and combinatorics discussed in this volume should be useful for both mathematicians and theoretical physicists who are interested in effective computation.
The book contains seven refereed research papers on locally compact quantum groups and groupoids by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg from February 21 to February 23, 2002. Topics covered are: various constructions of locally compact quantum groups and their multiplicative unitaries; duality theory for locally compact quantum groups; combinatorial quantization of flat connections associated with SL(2,c); quantum groupoids, especially coming from Depth 2 Extensions of von Neumann algebras, C*-algebras and Rings. Many mathematical results are motivated by problems in theoretical physics. Historical remarks set the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research in which great progress has been achieved in the last few years, with new ties to many other areas of mathematics and physics.
This book contains eleven refereed research papers on deformation quantization by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg in May 2001.
Topics covered are: star-products over Poisson manifolds, quantization of Hopf algebras, index theorems, globalization and cohomological problems. Both the mathematical and the physical approach ranging from asymptotic quantum electrodynamics to operads and prop theory will be presented. Historical remarks and surveys set the results presented in perspective.
Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research that has seen enourmous acticity in the last years, with new ties to many other areas of mathematics and physics.
