Algebraic and Geometric Methods in Mathematical Physics Proceedings
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MATHEMATICAL PHYSICS STUDIES
Series Editor:
M. FLATO, Universite de Bourgogne, Dijon, France
VOLUME 19
Algebraic and Geometric Methods in Mathematical Physics Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
edited by
Anne Boutet de Monvel Universite Paris 7, Paris, France
and
Vladimir Marchenko Institute for Low Temperature Physics, Kharkov, Ukraine
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-4663-5 ISBN 978-94-017-0693-3 (eBook) DOI 10.1007/978-94-017-0693-3
Printed on acid-free paper
All Rights Reserved © 1996 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1996
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
Soleil de pierre et quatre murs de chaux La veiIIe encore on avait chaud et l'on a froid maintenant devant "la porte" ouverte sur Ie soleil d'Ukraine. Kaciveli 1993.
Table of Contents
Preface
ix
List of participants
xi
Analysis and Spectral Theory 1 A.Beilinson and V.Drinfeld, Quantization of Hitchin's Fibration and Langland's Program. . . . . . . . . . . . . . . . . . .. 3 A.Boutet de Monvel and V.Georgescu, Boundary Values of the Resolvent of a Self-Adjoint Operator: 9 Higher Order Estimates . . . . . . . . . . . . . . . L.Boutet de Monvel, Index Theorems and Microsupport 53 G.Lebeau, Equation des Ondes Amorties. . . . . . . . . 73 N .Lerner , Oscillatory Integrals Controlling the Drift of Spectral Projections for Pseudo-Differential Operators . . . . . . .. 111 G.Nenciu, Linear Adiabatic Theory: Exponential Estimates and Applications. . . . . . . . . . . . . . . . . . . . . . . . . .. 127 Mathematical Problems of Quantum Field Theory and Statistical Physics 143 A.Beauville, Vector Bundles on Riemann Surfaces and Conformal 145 Field Theory . . . . . . . . . . . . . . . . . . . . . . A.Belavin, Introduction to the Conformal Field Theory . . . . 167 L.Chekhov, Discretized Moduli Spaces and Matrix Models 187 L.Pastur, Spectral arid Probabilistic Aspects of Matrix Models 207 D.Petrina, On Approximation of General Hamiltonians by Hamiltonians of the Theories of Superconductivity and Superfluidity . . . . . . . . . . . . . . . . . . . . . 243 Nonlinear Equations and Integrable Systems E.Belokolos, Initial and Boundary Value Problems for the SineGordon Equation . . . . . . . . . . . . . . . . . . . . . . . . Yu.Daletskii, Algebra of Compositions and Nonlinear Equations. N.Gonchar, Nonlinear Equations for Equilibrium Costs and their Solvability . . . . . . . . . . . . . . . . . . . . . . . . . . . .
261 263 277 293
Vlll
E.Khruslov, Soliton Asymptotics of Non-Decreasing Solutions of Nonlinear Evolutionary Equations . . . . . . . . . . . . . . V.Marchenko, Operator Algebras, Nonlinear Equations and Da
