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# Algebraic and Geometric Methods in Mathematical Physics: Proceedings Of The Kaciveli Summer School…

## byAnne Boutet de MonvelEditorV.a. Marchenko

### Paperback | December 4, 2010

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This volume contains the expository lectures and a selection of short communications presented at the Summer School Algebraic and Geometric Methods in Mathematical Physics, held in Kaciveli, Crimea, Ukraine, in September 1993. The contributions, by leading experts in the various fields, review the state of the art in many important branches of modern mathematical physics. Special emphasis is given to certain aspects of quantum groups and conformal field theory, spectral theory of differential and pseudodifferential operators, nonlinear integrable PDEs and related problems of algebra, geometry and analysis. A number of topics of current interest is also discussed, such as nonlinear problems of mathematical economics, direct and inverse problems of spectral theory, mathematical statistical mechanics, etc. Audience: Researchers and graduate students in group representations, spectral theory, nonlinear equations, integrable systems, mathematical quantum field theory and statistical mechanics.

### Details & Specs

Title:Algebraic and Geometric Methods in Mathematical Physics: Proceedings Of The Kaciveli Summer School…Format:PaperbackDimensions:478 pagesPublished:December 4, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048146631

ISBN - 13:9789048146635

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Table of Contents

Preface. List of Participants. Analysis and Spectral Theory. Quantization of Hitchin''s Fibration and Langland''s Program; A. Beilinson, V. Drinfeld. Boundary Values of the Resolvent of a Self-Adjoint Operator: Higher Order Estimates; A. Boutet de Monvel, V. Georgescu. Index Theorems and Microsupport; L. Boutet de Monvel. Equation des Ondes Amorties; G. Lebeau. Oscillatory Integrals Controlling the Drift of Spectral Projections for Pseudo-Differential Operators; N. Lerner. Linear Adiabatic Theory: Exponential Estimates and Applications; G. Nenciu. Mathematical Problems of Quantum Field Theory and Statistical Physics. Vector Bundles on Riemann Surfaces and Conformal Field Theory; A. Beauville. Introduction to the Conformal Field Theory; A. Belavin. Discretized Moduli Spaces and Matrix Models; L. Chekhov. Spectral and Probabilistic Aspects of Matrix Models; L. Pastur. On Approximation of General Hamiltonians by Hamiltonians of the Theories of Superconductivity and Superfluidity; D. Petrina. Nonlinear Equations and Integrable Systems. Initial and Boundary Value Problems for the Sine-Gordon Equation; E. Belokolos. Algebra of Compositions and Nonlinear Equations; Yu. Daletskii. Nonlinear Equations for Equilibrium Costs and their Solvability; N. Gonchar. Soliton Asymptotics of Non-Decreasing Solutions of Nonlinear Evolutionary Equations; E. Khruslov. Operator Algebras, Nonlinear Equations and Darboux-like Transform; V. Marchenko. Trivial S-matrices, Wigner-von Neumann Resonances and Positon Solutions of the Integrable Nonlinear Evolution Equations; V. Matveev. Minimal Surfaces in the Hyperbolic Space and Radial-Symmetric Solutions of the Cosh-Laplace Equation; V. Novokshenov. Spectral Properties of Non-Selfadjoint Hill''s Operators with Smooth Potentials; J.-J. Sansuc, V. Tkachenko. Short Communications. Complex Deformations of Riemann Surfaces, Frequency Maps and Instability Problems; R. Bikbaev. A Propagation Estimate for the Dirac Hamiltonian in the Field of an Electromagnetic Wave; A. Boutet de Monvel, R. Purice. The Commutativity of the Singularly Perturbed Self-Adjoint Operators; N. Dudkin. Approximate-Iterative Method for Solving Nonlinear Differential and Integral Equations; V. Dzyadyk. Regular Representations of Affine Kac&endash;Moody Algebras; B. Feigin, S. Parkhomenko. On Boundary Value Problems for Operator Differential Equations; M. Gorbachuk, V. Gorbachuk. Singularly Perturbed Operators of Type - &Dgr; + &lgr;&dgr;; V. Koshmanenko. Inverse Scattering Problems for Hyperbolic Equations and their Applications; L. Nizhnik. Sine-Gordon Equation in Laboratory Coordinates and Inverse Problem on the Semi-Axis; A. Sakhnovic. Gibbs States and Regularized Dynamics of the Chern&endash;Simons Charged Particle System; W. Skrypnik. Almost-Periodic Sturm Liouville Operators with Homogeneous Spectrum; M. Sodin, P. Yuditski. On Higher-Order Difference Operators; V. Yurko. Invariant Measures for Infinite-Dimensional Dynamical Systems with Applications to a Nonlinear Schrödinger Equation; P. Zhidkov.