Selected Titles in This Series

16 Rudi Weikard and Gilbert Weinstein, Editors, Differential Equations and Mathematical Physics, 2000 15 Ling Hsiao and Zhouping Xin, Editors, Some Current Topics on Nonlinear Conservation Laws, 2000 14 Jun-ichi Igusa, An Introduction to the Theory of Local Zeta Functions, 2000 13 Vasilios Alexiades and George Siopsis, Editors, Trends in Mathematical Physics, 1999 12 Sheng Gong, The Bieberbach Conjecture, 1999 11 Shinichi Mochizuki, Foundations of p-adic Teichmüller Theory, 1999 10 Duong H. Phong, Luc Vinet, and Shing-Tung Yau, Editors, Mirror Symmetry III, 1999 9 Shing-Tung Yau, Editor, Mirror Symmetry I, 1998 8 Jürgen Jost, Wilfrid Kendall, Umberto Mosco, Michael Röckner, and Karl-Theodor Sturm, New Directions in Dirichlet Forms, 1998 7 D. A. Buell and J. T. Teitelbaum, Editors, Computational Perspectives on Number Theory, 1998 6 Harold Levine, Partial Differential Equations, 1997 5 Qi-keng Lu, Stephen S.-T. Yau, and Anatoly Libgober, Editors, Singularities and Complex Geometry, 1997 4 Vyjayanthi Chari and Ivan B. Penkov, Editors, Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras, 1997 3 Xia-Xi Ding and Tai-Ping Liu, Editors, Nonlinear Evolutionary Partial Differential Equations, 1997 2.2 William H. Kazez, Editor, Geometrie Topology, 1997 2.1 William H. Kazez, Editor, Geometrie Topology, 1997 1 B. Greene and S.-T. Yau, Editors, Mirror Symmetry II, 1997 This page intentionally left blank Differential Equations and Mathematical Physics This page intentionally left blank https://doi.org/10.1090/amsip/016 AM S/1 P Studies in Advanced Mathematics

Volume 16

Differential Equations and Mathematical Physics

Proceedings of an International Conference held at the University of Alabama in Birmingham, Maren 16-20, 1999

Rudi Weikard and Gilbert Weinstein, Editors

American Mathematical Society · International Press Shing-Tung Yau, Managing Editor

2000 Mathematics Subject Classification. Primary 34-06, 35-06.

Library of Congress Cataloging-in-Publication Data Differential equations and mathematical physics : proceedings of an international Conference held at the University of Alabama in Birmingham, March 16-20, 1999 / Rudi Weikard and Gilbert Weinstein, editors. p. cm. — (AMS/IP studies in advanced mathematics, ISSN 1089-3288 ; v. 16) Includes bibliographical references ISBN 0-8218-2157-1 1. Differential equations—Numerical Solutions—Congresses. 2. Mathematical physics— Congresses. I. Weikard, Rudi, 1958- IL Weinstein, Gilbert, 1957- III. International Con• ference on Differential Equations and Mathematical Physics (8th : 1999 : University of Alabama in Birmingham) IV. Series. QC20.7.D5D544 2000 515M5—dc21 00-025797

Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by Services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Assistant to the Publisher, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to [email protected]. Excluded from these provisions is material in articles for which the author holds Copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.)

© 2000 by the American Mathematical Society and International Press. All rights reserved. The American Mathematical Society and International Press retain all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at URL: http://www.ams.org/ Visit the International Press home page at URL: http://www.intlpress.com/ 10 9 8 7 6 5 4 3 2 1 05 04 03 02 01 00 Contents

Preface xi

List of Plenary Speakers xiii

List of Special Sessions xv

List of Participants xvii

A. A. BALINSKY AND W. D. EVANS On the Brown-Ravenhall Relativistic Hamiltonian and the Stability of Matter 1

ROBERT BARTNIK Assessing Accuracy in a Numerical Einstein Solver 11

RAFAEL D. BENGURIA AND M. CRISTINA DEPASSIER Variational Principle for the Limit Cycle of Rayleigh's Equation 21

BEVERLY K. BERGER Approach to the Singularity in Spatially Inhomogeneous Cosmologies 27

M. SH. BIRMAN AND T. A. SUSLINA On the Absolute Continuity of the Periodic Schrödinger and Dirac Operators with Magnetic Potential 41

T. BODINEAU AND Â. HELFFER Correlations, Spectral Gap, and Log-Sobolev Inequalities for Unbounded Spin Systems 51

RAYMOND BRUMMELHUIS, MARY BETH RUSKAI AND ELISABETH WERNER One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields 67

DONGHO CHAE AND OLEG YU. IMANUVILOV Construction of a Solution to the Semilinear Elliptic Equation in Chern-Simons Gauge Theory 77 viii CONTENTS

Ì . CHRIST, Á. KISELEV AND Y. LAST Approximate Eigenvectors and Spectral Theory 85

DEMETRIOS CHRISTODOULOU The Initial Value Problem in the Large and Spacetime Singularities 97

LÄSZLO ERDÖS AND JAN PHILIP SOLOVEJ On the Kernel of Spinc Dirac Operators on §3 and R3 111

RICHARD FROESE AND IRA HERBST Realizing Holonomic Constraints in Classical and Quantum Mechanics 121

FRITZ GESZTESY AND HELGE HOLDEN Á Combined Sine-Gordon and Modified Korteweg-de Vries Hierarchy and its Algebro-geometric Solutions 133

M. GRIESEMER Á Minimax Principle for Eigenvalues in Spectral Gaps 175

GEORGE A. HAGEDORN AND ALAIN JOYE Semiclassical Dynamics and Exponential Asymptotics 181

RAINER HEMPEL AND KARSTEN LIENAU Genericity of the Band-Gap Structure of Periodic Media in the Large Coupling Limit 197

ANDREAS M. HINZ Distribution of Eigenvalues in the Dense Point Spectrum of Schrödinger Operators 207

P. D. HISLOP On the Distribution of Scattering Resonances for Asymptotically Hyperbolic Manifolds 217

THOMAS HUPFER, HAJO LESCHKE, AND SIMONE WARZEL The Multiformity of Lifshits Tails Caused by Random Landau Hamiltonians with Repulsive Impurity Potentials of Different Decay at Infinity 233

WITOLD KARWOWSKI AND VOLODYMYR KOSHMANENKO Schrödinger Operator Perturbed by Dynamics of Lower Dimension 249

YAROSLAV V. KURYLEV AND MATT! LASSAS Hyperbolic Inverse Problem with Data on a Part of the Boundary 259

YANYAN LI Best Sobolev Inequalities on Riemannian Manifolds 273

ELLIOTT H. LIEB AND MICHAEL LÖSS Self-Energy of Electrons in Non-Perturbative QED 279

ELLIOTT H. LIEB AND The Ground State Energy of a Dilute Böse Gas 295 CONTENTS ix

MAYUMI OHMIYA Trace Formulae and Completely Integrable Hamiltonians 307

YEHUDA PINCHOVER On the Maximum and Anti-maximum Principles 323

THOMAS C. SIDERIS The Null Condition and Global Existence of Nonlinear Elastic Waves 339

HEINZ SIEDENTOP The Hartree-Fock Approximation in Quantum Electrodynamics - Positivity of the Energy 347

J.A. SMOLLER AND J.B. TEMPLE Shock-Wave Cosmology 351

STEPHEN BRUCE SONTZ On Some Reverse Inequalities in the Segal-Â argmann Space 361

GERALD TESCHL On the Initial Value Problem of the Toda and Kac-van Moerbeke Hierarchies 375

V. TKACHENKO Á Class of Non-Selfadjoint HiH's Operators with Analytic Potentials 385

MICHAEL M. TOM Regularized Long Wave-KP Models 393

CHRISTIANE TRETTER Spectral Issues for Block Operator Matrices 407

JEFF A. VIACLOVSKY Some Fully Nonlinear Equations in Conformal Geometry 425

RICARDO WEDER LP — Lv Estimates for the Schrödinger Equation and Inverse Scattering 435

G. WOLANSKI Stationary States of Vlasov System 449 This page intentionally left blank Preface

At which point do individual Conferences become a series? We think that the crucial element to look for is whether the participants naturally expect the next Conference, and — preferably — also look forward to it. In this respect, we certainly hope that the UAB-GIT Conferences have long become a series. Thus, we would for the most part only be repeating prefaces to previous volumes, were we to describe the purpose, scope, and contents of this Conference, the 8th Inter• national Conference on Differential Equations and Mathematical Physics, held in Birmingham, Alabama, March 16-20, 1999. It should nevertheless be noted that this Conference series started in 1981 as a meeting on spectral and scattering the- ory with 90 participants from North America and Europe. It has since grown, not only in the number of participants and countries, but also by encompassing many other disciplines, such as Statistical physics, general relativity, geometric analysis, fluid dynamics, and elasticity, among others. This Conference featured 172 talks, and was attended by over 200 participants from 25 countries: Australia (2), Aus- tria (3), Canada (6), Chile (4), the Czech Republic (2), (2), Egypt (1), Finland (3), France (7), Germany (24), Israel (7), Italy (3), Japan (10), Mexico (7), Norway (2), Poland (1), PR China (1), Russia (5), South Korea (1), Sweden (5), Switzerland (1), Turkey (1), United Kingdom (11), Ukraine (2), United States (95). Previous Conferences in the series were held in Birmingham in 1981, 1983, 1986, 1990, 1994, as well as in Atlanta in 1992, and 1997. We attempted to run an entirely electronic Conference. Advertising, announce- ments, and Communications on all aspects of the Conference were essentially con- ducted over the electronic medium, thus saving paper and lowering cost. There were three notable exceptions: we mailed out posters advertising the Conference, we printed out programs and various handouts for participants, and this volume appears in print. It is conceivable that in the not-too-distant future, even these may be eliminated. With more and more people using the web and email, the value of bulletin board posters may become marginal. Programs, abstracts, and local Information may eventually be made available in e-book format. And publish- ers may eventually give up on the idea of printing Conference proceedings, leaving Organizers with the only remaining Option of Publishing the proceedings on the in• ternet. We also tried to automate many tasks. Rudi Weikard wrote most of the Perl Scripts to collect, organize, and process data from the participants; Gilbert Weinstein wrote most of the HTML code for the Conference web site. Our ex- perience was that in most cases, the time required to program the automation

XI Xll PREFACE was more or less equivalent to the time the manual task would have taken. Thus our recommendation to other Conference Organizers is: do not attempt to auto- mate any Conference with fewer than 200 participants unless you plan on running a series of Conferences, or you particularly enjoy programing. If you feel inclined to sift through our partially inadequate code, you are welcome to most of the Conference files with the personal Information stripped at the following ftp site: ftp://ftp.math.uab.edu/pub/uabgit99/electronic On behalf of the Conference participants, we acknowledge with gratitude the generous financial support provided by the US National Science Foundation, under grant number DMS 9812460, the Department of Mathematics at UAB, and the Alabama Alliance for Minority Participation. We thank the organizing committee composed of Eric Carlen (GIT), Yulia Karpeshina (UAB), Roger Lewis (UAB), and Marius Nkashama (UAB), for valuable support. In particular, we wish to thank Eric Carlen for making available to participants of this Conference, funds leftover from the 1997 Conference in Atlanta. We also wish to thank our students, directed by our colleague Günter Stolz, who helped with the registration, refreshments, and entertainment. Finally, we thank the Conference participants without whose attendance — real rather than Virtual — the Conference could not have been a success. See you next time in Atlanta.

Rudi Weikard and Gilbert Weinstein Birmingham, Alabama November 1999 List of Plenary Speakers

S.Y. ALICE CHANG, , USA On the Chern-Gauss Bonnet Integral on 4-manifolds

DEMETRIOS CHRISTODOULOU, Princeton University, USA The Initial Value Problem in the Large and Spacetime Singularities

ELLIOTT LIEB, Princeton University, USA Photons and Stability ïf Matter: How heavy is an electron?

ADRIAN I. NACHMAN, University of Rochester, USA The Inverse Boundary Value Problem of Calderon

S. P. NOVIKOV, University of Maryland at College Park, USA Topological Phenomena in Metals

ROBERT L. PEGO, University of Maryland, USA Solitary waves on FPU lattices

THOMAS SIDERIS, University of California, Santa Barbara, USA The null condition and global existence of nonlinear elastic waves

BARRY SIMON, California Institute of Technology, USA The A-amplitude Approach to Inverse Spectral Theory

JOEL SMOLLER, , USA Cosmology with á shock-wave

JAKOB YNGVASON, University of Vienna, Austria The ground state energy of á dilute Böse gas

Xlll This page intentionally left blank List of Special Sessions

General Relativity Organizer: GREG GALLOWAY, University of Miami, USA Speakers: Robert Bartnik, John Beem, Beverly Berger, Piotr Chrusciel, Paul Ehr• lich, Alex Freire, Ralph Howard, Gourgen Oganessyan, Brian Smith, Eric Woolgar Integrable Systems Organizer: FRITZ GESZTESY, University of Missouri, USA Speakers: E. Belokolos, B. Birnir, O. Bogoyavlenskij, V. Enolskii, H. Holden, O. Knill, Y. Mishev, M. Ohmiya, A. Rybkin, G. Teschl, A. Treibich Inverse Problems Organizer: JOHN SYLVESTER, University of Washington, USA Speakers: Tuncay Aktosun, Matti Lassas, Steve McDowall, Petri Ola, Rakesh, Paul Sacks, John Sylvester, Ziqi Sun PDEs in Geometry Organizer: YANYAN LI, Rutgers University, USA Speakers: J. Cao, D. Chae, Y.Y. Li, A. Shadi Tahvildar-Zadeh, J. Viaclovsky, J. Wei, P. Yang Quantum Mechanics Organizer: HEINZ SIEDENTOP, University of Regensburg, Germany Speakers: V. Bach, A. Balinsky, B. Helffer, L. Erdos, M. J. Esteban, G. M. Graf, M. Griesemer, D. Hundertmark, F. Hiroshima, H. Leschke, H. Siedentop, J. P. Solovej This page intentionally left blank List of Participants and Speakers

TUNCAY AKTOSUN, North Dakota State University, USA Recovery of the phase of á reflection coefficient IVAN AVRAMIDI, University of Iowa, USA Heat kernel asymptotics of Gilkey-Smith boundary-value problem STEFAN BÖCKER, Ruhr-University of Bochum, Germany VOLKER BACH, TU Berlin, Germany Spectral Analysis of Atoms and Molecules interacting with the Electromagnetic Field ALEXANDER BALINSKY, Cardiff University, Wales, UK On the Positivity of the No-Pair Hamiltonian PEDRO BALODIS, University of Regensburg, Germany On the asymptotic exactness of Thomas-Fermi theory in the thermodynamic limit

ROBERT BARTNIK, University of Canberra, Australia Characteristic-based evolution for the Einstein equations JOHN BEEM, University of Missouri-Columbia, USA Cauchy horizon generators and properties

EUGENE BELOKOLOS, Institute of Magnetism, NAN, Ukraine Integrable Systems and reducible Abelian functions

MOHAMED BEN RHOUMA, University of Missouri-Columbia, USA Continuation of Periodic Orbits

RAFAEL BENGURIA, P. Universidad Catolica de Chile, Chile Limit cycle of Rayleigh 's equation, á variational approach

CHRISTER BENNEWITZ, Univ. of Lund, Sweden

BEVERLY K. BERGER, Oakland University, USA Approach to the Singularity in Spatially Inhomogeneous Cosmologies

BJOERN BIRNIR, University of California, Santa Barbara, USA An Index for Integrable PDEs

ANJAN BISWAS, Valley City State University, North Dakota, USA Integro-Differential Perturbations of Optical Solitons with Nonlinear Damping

XVll xviii LIST OF PARTICIPANTS AND SPEAKERS

XAVIER BLANC, Ecole Nationale des Ponts et Chaussees, France Thomas-Fermi type theories for polymers and solid films

OLEG BOGOYAVLENSKIJ, Queen's University, Canada Extended Integrability and Bi-Hamiltonian Systems

ABDELKADER BOUZOUINA, Univ. of Cardiff, UK Long time semi-classical Egorov Theorem

FERNANDO BRAMBILA, UNAM, Mexico Lax-Phillips scattering theory, generalizations and inverse problems

ALEXANDER BRENNER, Technion-Israel Institute Of Technology, Israel Multiparameter elliptic Operators and related spectral asymptotics

B. MALCOLM BROWN, Cardiff University, UK Spectral Concentration and Resonances for Sturm-Liouville Problems

RICHARD C. BROWN, University of Alabama, USA Some Separation Crüeria and Inequalüies Associated with Linear Second Order Differential and Partial Differential Operators

Luc Á BUGLIARO, Universität Regensburg, Germany Lieb-Thirring inequalüies and stability of non-relativistic QED

ALMUT BURCHARD, University of Virginia, USA Minimal and Random Spanning Trees in two dimensions

VICTOR BURENKOV, Cardiff University, UK Estimates of regularized Solutions ïf convolution-type equation in the Spaces offunc- tions with fractional order of smoothness

JIANGUO CAO, University of Notre Dame, USA Cheeger isoperimetric constants of Gromov-hyperbolic spaces and applications

ERIC CARLEN, Georgia Institute of Technology, USA

RADU CASCAVAL, University of Memphis, USA ISABELLE CATTO, CNRS & Universite de Paris-Dauphine, France Thermodynamic limits for Hartree and Hartree-Fock type modeis

DONGHO CHAE, Seoul National University, South Korea Non-topological multivortex Solutions in the self-dual Chern-Simons theory

S.Y. ALICE CHANG, Princeton University, USA On the Chern- Gauss Bonnet Integral on ^-manifolds

THIERRY CHATELAIN, University of Misssouri, USA About two Schiffers conjectures

MAYA CHHETRI, Mississippi State University, USA Positivity of nonnegative Solutions for cooperative semipositone Systems

DEMETRIOS CHRISTODOULOU, Princeton University, USA The initial value problem in the large and singularities of space-time

PIOTR CHRUSCIEL, Universite Francois Rabelais, Tours, France The Classification of regulär statte vaeuum black holes LIST OF PARTICIPANTS AND SPEAKERS XIX

JOHN CLANCY, Indiana University, USA Osterwalder-Schrader Positivity in Chern-Simons QED STEPHEN CLARK, University of Missouri-Rolla, USA

JOSEPH CONLON, University of Michigan, USA Homogenisation of elliptic pde with random coefficients

VICTOR H. CORTES, P. Universidad Catolica de Chile, Chile Long-living State for Time Dependent Schrödinger Operator JAIME CRUZ, Universidad de las Americas-Puebla, Mexico Perturbations of the Embedded Eigenvalue of Schrödinger Operators with á Wigner- Von Neumann Potential Louis DALE, University of Alabama at Birmingham, USA DAVID DAMANIK, Goethe-Universität, Frankfurt, Germany Uniform spectral properties of one-dimensional quasicrystals, IL RAFAEL RENE DEL RIO CASTILLO, IIMAS-UNAM, Mexico Mixed Spectra

JAROSLAV DITTRICH, Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Czech Republic Massive Scalar Field in an Oscillating Region

ATSUSHI DOUMEKI, Kanazawa University, Japan Semiclassical estimate for the eigenvalue Splitting for the Kac Operator

JULIAN EDWARD, Florida International University, USA Scattering theory for perturbations of quotients of Rn by finite subgroups of Gl(n).

PAUL EHRLICH, University of Florida, USA Volume Comparison on Pseudo-Riemannian Manifolds

DANIEL ELTON, University of Sussex, UK Spectral properties of the equation (V + %A) ÷ u = u

VICTOR ENOLSKII, Institute of Magnetism NASU, Kiev, Ukraine Kleinian sigma function theory from the viewpoint of completely integrable theory

LASZLO ERDOS, Georgia Institute of Technology, USA Linear Boltzmann Equation as the Weak Coupling Limit of á Random Schrödinger Equation

MARIA J. ESTEBAN, CNRS & University Paris-Dauphine, France Nonrelativistic limit for the Dirac-Fock equations

DESMOND EVANS, Cardiff University, Wales, UK On the stability of relativistic one-electron molecules

PAVEL EXNER, Czech Academy of Sciences, Czech Republic Anomalous bound states of the two-dimensional Pauli Operator

CLAUDIO FERNANDEZ, Pontificia Universidad Catolica de Chile, Chile Resonances in á one dimensional model

ANNE-MARIE FILIP, Ryerson Polytechnic University, Canada XX LIST OF PARTICIPANTS AND SPEAKERS

SOEREN FOURNAIS, Univ. of Aarhus, Denmark ALEX FREIRE, University of Tennessee, Knoxville, USA Weak compactness and global existence for wave maps

STEPHEN A. FULLING, Texas A&M University, USA Wigner-Kirkwood Expansions in the Energy Domain: Stalking Structural Consis- tency across the Asymptotic Landscape

GREG GALLOWAY, University of Miami, USA

FRITZ GESZTESY, University of Missouri - Columbia, USA

TEPPER L. GILL, Howard University, USA S*-Algebras GIAN MICHELE GRAF, ÅÔÇ Zürich, Switzerland Groundstates of super Symmetrie matrix modeis

SANDRO GRAFFI, Universita di Bologna, Italy

EDWARD GREEN, North Georgia College & State University, USA Unified Field Theory based on an Enlarged Coordinate Transformation Group and its Consistent Hamiltonian

MARCEL GRIESEMER, University of Alabama at Birmingham, USA Á minimax principle for eigenvalues in spectral gaps

GUDRUN GUDMUNDSDOTTIR, Lund University, Sweden

STEPHEN GUSTAFSON, , Canada Dynamic Stability of Magnetic Vortices

GEORGE HAGEDORN, Virginia Tech, USA Raising and Lowering Operators for Semiclassical Wave Packets

DESMOND HARRIS, Cardiff University, Wales, UK

BERNARD HELFFER, Universite Paris-Sud, France Witten Laplacians and Log-Sobolev inequalities

RAINER HEMPEL, TU Braunschweig, Germany Strong magnetic fields of compact support, Dirichlet boundaries, and eigenvalues in gaps

IRA HERBST, University of Virginia, USA Constraints in Classical and Quantum Mechanics

LOTFI HERMI, University of Missouri-Columbia, USA On Extending an Inequality of Payne-Ñ olya-Weinberg er Using Spherical Harmonics

DON HINTON, University of Tennessee, USA Liapunov and Opial Inequalities with Applications

ANDREAS HINZ, Technical University Munich, Germany Distribution of eigenvalues in the dense point spectrum of Schrödinger Operators

FUMIO HIROSHIMA, University of Bonn, Germany Ground States of á System Interacting with á Quantized Radiation Field: Existence, Uniqueness and Expression LIST OF PARTICIPANTS AND SPEAKERS XXI

PETER HISLOP, University of Kentucky, USA The Distribution of Scattering Poles MICHAEL HITRIK, University of Lund, Sweden Bounds on scattering poles in one dimension

GEORG HOEVER, University of Regensburg, Germany On the spectrum of two-dimensional Schrödinger Operators with spherically Sym• metrie radially periodic magnetic fields FRANK HOEVERMANN, TU München, Germany Á Semiclassical Limit for Particles in Perturbed Periodic Potentials

THOMAS HOFFMANN-OSTENHOF, Schrödinger Institute and Inst, for Theoreticai Chemistry, Austria Spectral Properties of á Böhm Aharanov Hamiltonian

HELGE HOLDEN, Norwegian University of Science and Technology, Norway Darboux transformations and hyperelliptic curves

RALPH HOWARD, University of South Carolina, USA The strueture of Cauchy sections of event horizons

DIRK HUNDERTMARK, Princeton University, USA Sharp Lieb-Thirring Bounds

THOMAS HUPFER, Universität Erlangen-Nürnberg, Germany

WATARU ICHINOSE, Shinshu University, Japan On the convergence of the Feynman path integral approximated through broken line paths

NEZAM IRANIPARAST, Western Kentucky University, USA Á CIV Boundary Value Problem for the Wave Equation

BARBARA JANAUSCHEK, LMU München, MPI für Plasmaphysik, Germany ALAIN JOYE, Institut Fourier, Universite Grenoble-1, France Semiclassical Dynamics with Exponentially Small Error Estimates

YULIA KARPESHINA, University of Alabama at Birmingham, USA

WITOLD KARWOWSKI, Wroclaw University, Poland Schrödinger Operator Perturbed by Dynamics of á Null Set System

RYOICHI KAWAI, University of Alabama at Birmingham, USA

ANDREI KHODAKOVSKY, California Institute of Technology, USA Inverse scattering problem with partial Information on the potential

ROWAN KILLIP, California Institute of Technology, USA The a.c. spectrum with L2 potentials.

ALEXANDER KISELEV, University of Chicago, USA Approximate eigenvectors and spectral theory

OLIVER KNILL, University of Texas, USA Nonlinear integrable Vlasov dynamical Systems

IAN KNOWLES, University of Alabama at Birmingham, USA xxii LIST OF PARTICIPANTS AND SPEAKERS

ALEXANDER KOZHEVNIKOV, University of Haifa, Israel Analyticity of the Semigroup Generated by the Operator of á Viscous Compressible Fluid KAZUHIRO KURATA, Tokyo Metropolitan University, Japan Some Optimization Problems for the first Dirichlet Eigenvalue of Elliptic Operators JAN LANG, University of Missouri-Columbia, USA The approximation numbers of Hardy-type Operators

MATTI LASSAS, University of Helsinki, Finland An inverse problem for á hyperbolic equation on Riemannian manifold TUAN LE, University of Alabama at Birmingham, USA

DANIEL LENZ, J. W. Goethe Universität, Frankfurt, Germany Uniform spectral properties of one-dimensional quasicrystals, I

HAJO LESCHKE, Universität Erlangen-Nürnberg, Germany Poissonian obstacles with Gaussian walls discriminate between classical and quan- tum Lifshits tailing in magnetic fields

MICHAEL LEVITIN, Heriot-Watt University, UK Commutators, spectral trace identities, and applications I ROGER LEWIS, University of Alabama at Birmingham, USA

YANYAN LI, Rutgers University, New Brunswick, USA On the best constant in the Sobolev inequality ELLIOTT LIEB, Princeton University, USA Photons and Stability ïf Matter: How heavy is an electron? PETER LINDQVIST, Norwegian University of Science and Technology, Norway The p-harmonic ground state is superharmonic

JOSEPH LUTGEN, Mainz, Germany On Singular Sturm-Liouville Problems Nonlinear in the Spectral Parameter and the Discrete Spectrum of the Radial Dirac Operator

KONSTANTIN MAKAROV, University of Missouri-Columbia, USA The Spectral Shift Operator MARCO MARLETTA, University of Leicester, UK The Friedrichs Extension of Differential Operators

UWE F. MAYER, Vanderbilt University, USA Classical Solutions for diffusion-induced grain-boundary motion

STEPHEN MCDOWALL, University of Rochester, USA Infinite order boundary determination of electromagnetic parameters.

IVOR MCGILLIVRAY, University of Bristol, USA On the large time behaviour of the pinned Wiener sausage

MARCO MERKLI, University of Toronto, Canada Á Time-Dependent Theory of Quantum Resonances

RONALD MICKENS, Clark Atlanta University, USA Analytic Approximation to the Periodic Solution of á Modified van der Pol Equation LIST OF PARTICIPANTS AND SPEAKERS xxiii

YORDAN MISHEV, RIMS, Kyoto University, Japan On Functional Fay Identity and Related Cubic Identities KlYOSHl MOCHIZUKI, Tokyo Metropolitan University, Japan 171 p N Life span and asymptotic behavior of Solutions to ut = Au + a(x)u in R ALEXANDER MOTOVILOV, University of Bonn & Dubna Joint Institute for Nuclear Research, Russia Factorization theorem for the transfer functions of 2 ÷ 2 matrix Hamiltonians and Operator Interpretation of resonances ADRIAN I. NACHMAN, University of Rochester, USA The Inverse Boundary Value Problem of Calderon BRUNO NACHTERGAELE, University of California, Davis, USA Interface states of quantum lattice modeis FUMIHIKO NAKANO, Princeton University, USA Absence of transport under the time-modulated fields in 1D disordered Systems

MARIUS NKASHAMA, University of Alabama at Birmingham, USA S. P. NOVIKOV, University of Maryland at College Park, USA Topological Phenomena in Metals GOURGEN OGANESSYAN, University of Canberra, Australia Á Canonical Characteristic Gauge for the Einstein Field Equations. MAYUMI OHMIYA, Doshisha University, Japan Trace formulae and the finite dimensional completely integrable System PETRI OLA, University of Oulu, Finland Recovering singularities from backscattering PETER V. Ï'NEIL , University of Alabama at Birmingham, USA

KEVSER OZDEN KOKLU, Yildiz Technical University, Turkey Green Function of differential equation with even order and Operator coefficient in half axis ALEXANDER PANCHENKO, University of Delaware, USA On Reconstruction of Nonsmooth First-Order Coefficients MICHAEL PANG, University of Missouri, Columbia, USA Lower Gradient Bound for Solutions of Schrödinger Equations

ROBERT PEACOCK, University of Alabama at Birmingham, USA ROBERT L. PEGO, University of Maryland, USA Solitary waves on FPU lattices

MARIA PEREL, St. Petersburg University, Russia Highly Localised Solutions to the Wave Equation

SANTIAGO PEREZ-OYARZUN, Pontificia Universidad Catolica de Chile, Chile YEHUDA PINCHOVER, Technion, Haifa, Israel On perturbations of Green functions, maximum and anti-maximum principles, and eigenfunctions estimates for elliptic Operators xxiv LIST OF PARTICIPANTS AND SPEAKERS

ROBERTO QUEZADA, UAM-Iztapalapa, Mexico City, Mexico Conservative semigroups of completely positive maps LIZABETH RACHELE, Tufts University, USA Inverse Problems for Elastic Media RAKESH, University of Delaware, USA Coefficient Recovery from transmission data for the 1D wave equation NORBERT ROEHRL, University of Regensburg, Germany Instability of the Electron-Positron Field MARY BETH RUSKAI, University of Massachusetts Lowell, USA One-dimensional regularizations of the Coulomb potential ALEXEI RYBKIN, University of Alaska, Fairbanks, USA On á new representation of the KdV invariants ANDREA SACCHETTI, University of Modena, Italy Wannier-Bloch oscillators PAUL SACKS, Iowa State University, USA Inverse spectral problems for radially Symmetrie potentials TIMUR SADYKOV, Stockholm University, Stockholm, Sweden The Multiple Mellin-Barnes Integrals as Solutions of Multidimensional Hypergeo- metric Differential Equations in the Nonresonance Case YOSHIMI SAITO, University of Alabama at Birmingham, USA MAYUMI SAKATA, University of Alabama at Birmingham, USA KARL MICHAEL SCHMIDT, Ludwig-Maximilians-Universität München, Germany Á remark on the essential spectra of Dirac Systems ELMAR SCHROHE, U Potsdam, Germany Heat kernel expansions and noncommutative residues on manifolds with boundary B.-WOLFGANG SCHULZE, U Potsdam, Germany Pseudo-differential calculus on Spaces with edge and corner singularities MICHAEL SEVER, The Hebrew University, Jerusalem, Israel Zero Pressure Gas Dynamics SHIN-ICHI SHIMADA, Setsunan University, Japan Eigenfunction expansions for the Aharonov-Bohm hamiltonians RATNASINGHAM SHIVAJI, Mississippi State University, USA An existence result for á dass of superlinear p-laplacian semipositone Systems THOMAS SIDERIS, University of Calfornia, Santa Barbara, USA The null condition and global existence of nonlinear elastic waves HEINZ SIEDENTOP, Universität Regensburg, Germany Stability of Matter for the Hartree-Fock Functional of the Relativistic Electron- Positron Field SAMULI SILTANEN, Helsinki University of Technology, Finland LIST OF PARTICIPANTS AND SPEAKERS xxv

BARRY SIMON, Caltech, USA The A-amplitude approach to Inverse Spectral Theory ROBERT SIMS, University of Alabama at Birmingham, USA

ROMAN SMIRNOV, University of Waterloo, Canada On separability of the Toda lattice

BRIAN SMITH, University of Alabama at Birmingham, USA On the connectedness of the space of initial data for the Einstein equations

JOEL SMOLLER, University of Michigan, USA Cosmology with á shock-wave

ALEXANDER SOBOLEV, University of Sussex, UK New proof of the Âethe-Sommerfeld conjecture in dimension three

MICHAEL SOLOMYAK, The Weizmann Institute of Science, Rehovot, Israel Eigenvalue estimates for the weighted Laplacian on metric trees

JAN PHILIP SOLOVEJ, Copenhagen, Denmark Zero Energy Eigenfunctions of the Three Dimensional Pauli Operator

STEPHEN SONTZ, UAM-Iztapalapa, Mexico On Some Reverse Inequalities in the S egal-Â argmann space

MILENA STANISLAVOVA, University of Missouri-Columbia, USA Dynamics of the four-dimensional rigid body in á quadratic potential field GÜNTER STOLZ, University of Alabama at Birmingham, USA ZIQI SUN, Wichita State, USA Inverse Boundary Value Problems for Quasilinear Elliptic Partial Differential Equa• tions

TATYANA SUSLINA, St. Petersburg State University, Russia The periodic Dirac Operator is absolutely continuous

ALINA SUZKO, Joint Institute for Nuclear Research, Russia Darboux transformations for tw ï-dimensional discrete Schrödinger equation

JOHN SYLVESTER, University of Washington, USA Á Stable Layer Stripping Algorithm

ABDOLREZA SHADI TAHVILDAR-ZADEH, Princeton University, USA Global existence of the equivariant Yang-Mills heat flow in four space dimensions

PETER TAKAC, Universität Rostock, Germany Bifurcations to Vortex Solutions in Superconductors Near the Critical Temperature

GERALD TESCHL, University of Vienna, Austria On the Toda and Kac-van Moerbeke hierarchies

LAWRENCE THOMAS, University of Virginia, USA Regularity of Spherical Harmonie Maps and ó-modeis Defined on Lattices

VADIM TKACHENKO, Ben-Gurion University of the Negev, Israel Nonselfadjoint periodic Operators with finite-band spectrum xxvi LIST OF PARTICIPANTS AND SPEAKERS

MICHAEL TOM, Louisiana State University, Baton Rouge, USA Regularized Long Wave-KP modeis ARMANDO TREIBICH, University of Artois, France Beyond the exceptional Covers and their canonical hyper-elliptic potentials CHRISTIANE TRETTER, University of Regensburg, Germany Spectral properties of some classes of block Operator matrices EDUARD TSEKANOVSKII, Niagara University, USA Stieltjes functions and inverse nonselfadjoint spectral problems

TETSUO TSUCHIDA, Kyushu University, Japan Uniqueness for an inverse boundary value problem for Dirac Operators

NAOMASA UEKI, Himeji Institute of Technology, Japan Lifschitz tails in Gaussian random magnetic fields

CORNELIS VAN DER MEE, University of Cagliari, Italy Inverse Scattering of Symmetrie Hamiltonian Systems on the Line

DMITRI VASSILIEV, University of Sussex, UK The Dirac equation without spinors

IVAN VESELIC, Ruhr University at Bochum, Germany Wegner estimate for the Anderson model with indefinite potential JEFF VIACLOVSKY, Princeton University, USA Fully Nonlinear Equations in Conformal Geometry

CARLOS VILLEGAS-BLAS, Universidad Nacional Autonoma de Mexico, Mexico The S egal-Â argmann Transform and Canonical Transformations

VITALI VOUGALTER, Georgia Tech, USA

BJÖRN G. WALTHER, Royal Institute of Technology, Sweden On Large Time Regularity and Decay Estimates for Solutions to the (Non-Relativ- istic) Schrödinger Equation and Other Oscillatory Integrals JAMES R. WARD, University of Alabama at Birmingham, USA

SIMONE WARZEL, Universität Erlangen-Nürnberg, Germany Upper bounds on the density of states for continuum Schrödinger Operators with Gaussian random potentials and magnetic fields

RICARDO WEDER, National University of Mexico, Mexico Lp-Lq Estimates for the Schrödinger Equation and Inverse Scattering

JUNCHENG WEI, Chinese University of Hong Kong, PR China On the effect of domain shape on the existence of large Solutions for á superlinear problem

RUDI WEIKARD, University of Alabama at Birmingham, USA

GILBERT WEINSTEIN, University of Alabama at Birmingham, USA

DENIS WHITE, Univ of Toledo, USA Meromorphic continuation of the scattering matrix: Stark effect case LIST OF PARTICIPANTS AND SPEAKERS xxvii

GERSHON WOLANSKI, Technion, Haifa, Israel Steady states of the Vlasov-Einstein System

ERIC WOOLGAR, University of Alberta, Canada Asymptotically Locally Anti-de Sitter Black Holes OSANOBU YAMADA, Ritsumeikan University, Japan Spectral Theory of Dirac Operators with the Variable Mass PAUL YANG, USC and Princeton University, USA Conformally invariant equations

JAKOB YNGVASON, University of Vienna, Austria The ground state energy of á dilute Böse gas

E. M. E. ZAYED, Zagazig Universty, Egypt An inverse problemfor á general bounded domain in three dimensions with piecewise smooth mixed boundary conditions YANNI ZENG, University of Alabama at Birmingham, USA

GREGORY ZHISLIN, NIRFI, Russia The structure of the discrete spectrum of two particle pseudorelativistic Systems

HENGHUI ZOU, University of Alabama at Birmingham, USA This page intentionally left blank