Edited by
H. W. Braden, University of Edinburgh, Scotland
and I. M. Krichever, L. D Landau Institute of Theoretical Physics, Moscow, Russia
Integrability: The Seiberg-Witten and Witham Equations
This volume presents selected papers on Integrability: the Seiberg-Witten and Whitham Equations and reviews the general algebro-geometric and geometric structures underlying integrability and aims to clarify the appearance of integrable structures in Seiberg-Witten theory.
Contents: Baker-Akhiezer Functions and Integrable Systems ・ Integrable Systems, Algebratic Geometry and Seiberg-Witten Theory ・Seiberg-Witten Theory and Integrable Systems ・Seiberg-Witten Curves and Integrable Systems ・Integrability in Seiberg-Witten Theory ・WDVV Equations and Seiberg-Witten Theory ・
Deformations of the Root Systems and New Solutions to Generalized WDVV Equations ・Picard-Fuchs Equations, Hauptmoduls and Integrable Systems ・Painlev Type Equations and Hitchin Systems ・ World-sheet Instantons and Virasoro Algebra ・Dispersionless Integrable Systems and their Solutions ・N-Component Integrable Systems and Geometric Asymptotics ・Systems of Hydrodynamic Type from Poisson Commuting Hamiltonians ・Integral Systems and Equations of Hydrodynamic Type from the End of the 19th to the
End of the 20th Century
Readership: Graduates and researchers interested in mathematics and ordinary differential equations.
August, 2000 / 288 pp / Cloth / 90-5699-281-3 /
Yau.S.-T./Chan,R.(ed)
Two Special Issues for Sir Michael Atiyah
Sir Michael Atiyah was born on April 22, 1929.
AJM has dedicated this and the December issue to celebrate his 70th birthday.
Papers in this issue:
(
Lectures by Sir Michael Atiyah.
R. Bott, A Letter from R. Bott.
Simon Donaldson, Geometry in Oxford C. 1980-85.
Lars Garding, A Happy Collaboration.
G. Lusztig, Recollections about My Teacher, Michael Atiyah.
L. Nirenberg, Memories of Sir Michael Atiyah.
G.B. Segal, Being a Graduate Student of Michael Atiyah.
E. Witten, Michael Atiyah and the Physics/Geometry Interface.
S. K. Donaldson, Moment Maps and Diffeomorphisms.
Sergei Gelfand and David Kazhdan, Conjectural Algebraic Formulas for Representations of $GL_n$.
V. Guillemin and C. Zara, Equivariant de Rham Theory and Graphs.
N. J. Hitchin, The Moduli Space of Complex Lagrangian Submanifolds.
Ruth Lawrence and Don Zagier, Modular Forms and Quantum Invariants of 3-Manifolds.
B. H. Lian, K. Liu, and S. T. Yau, Mirror Principle II.
G. Lusztig, Aperiodicity in Quantum Affine $\frak g\frak l_n$.
Y. I. Manin, Three Constructions of Frobenius Manifolds: A Comparative Study.
B. Mazur, Visualizing Elements of Order Three in the Shafarevich-Tate Group.
W. Schmid and K. Vilonen, On the Geometry of Nilpotent Orbits.
C. H. Taubes, Moduli Spaces and Fredholm Theory for Pseudoholomorphic Subvarieties Associated to
Self-Dual, Harmonic 2-Forms.
R. S. Ward, Two Integrable Systems Related to Hyperbolic Monopoles.
Yau.S.-T./Chan,R.(ed)
A Special Issue for Prof. Kunihiko Kodaira
Prof. Kunihiko Kodaira was born on March 16, 1915.
AJM has dedicated this issue to commemorate his 85th birthday.
Papers in this issue:
Walter Baily, Preface to Kodaira's Issue.
Reese Harvey and Blaine Lawson, Student Reminicenses of Kodaira at Stanford.
F. Hirzebruch, Kunihiko Kodaira: Mathematician, Friend, and Teacher.
S. Iyanaga, Kunihiko Kodaira as I have seen him.
Joseph Kohn, Remembering Professor K. Kodaira.
Ichiro Satake, Personal Reminiscences of Professor Kodaira.
Walter Baily, Exceptional Moduli Problems II.
Lionel Bayle and Arnaud Beauville, Birational Involutions of P2.
Fedor Bogomolov and Yuri Tschinkel, Lagrangian Subvarieties of Abelian Fourfolds.
Jean-Paul Brasselet and Tatsuo Suwa, Nash Residues of Singular Holomorphic Foliations.
Yasushi Gomi, Iku Nakamura, and Ken-ichi Shinoda, Hilbert Schemes of G-Orbits in Dimension Three.
Reese Harvey and Blaine Lawson, Singularities and Chern-Weil Theory, I: The Local Macpherson Formula.
Guangfeng Jiang and Mutsuo Oka, Lines on Non-Degenerate Surfaces.
Yasuyuki Kachi and Janos Kolleer, Characterizations of Pn in Arbitrary Characteristic.
Michael Kapovich, John J. Millson, and Thomas Treloar, The Symplectic Geometry of Polygons in Hyperbolic
3-Space.
Schi Kawai, A Note on the Cosegre Class of a Subvariety.
Yujiro Kawamata, On Effective Non-Vanishing and Base-Point-Freeness.
Stephen D. Miller and Gregory Moore, Landau-Siegel Zeroes and Black Hole Entropy.
Keiji Oguiso and Thomas Peternell, Projectivity via the Dual Kahler Cone -- Huybrechts' Criterion.
D. H. Phong and Jacob Sturm, On a Conjecture of Demailly and Koller.
Tetsuji Shioda, Some New Observation on Invariant Theory of Plane Quartics.
S.-T. Yau, Review of Geometry and Analysis.
Kang Zuo, On the Negativity of Kernels of Kodaira-Spencer Maps on Hodge Bundles and Applications.
edited by
Giuseppe Dito Universit・de Bourgogne, Dijon, France
Daniel Sternheimer CNRS and Universit・de Bourgogne, Dijon, France
Conference Moshe Flato 1999
Quantization, Deformations, and Symmetries Volume I and Volume II
MATHEMATICAL PHYSICS STUDIES Volume 21/22
These two volumes constitute the Proceedings of the `Confnfence Moshe Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity.
With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena.
Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.
Hardbound Volume I, ISBN 0-7923-6540-2
July 2000, 440 pp.
Hardbound Volume II, ISBN 0-7923-6541-0
July 2000, 356 pp.
Hardbound Set Volumes I+II, ISBN 0-7923-6542-9
July 2000
Vladimir B. Vasil'ev
Dept. of Mathematical Analysis, Novgorod State University, Russia
Wave Factorization of Elliptic Symbols:
Theory and Applications
Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains
This monograph is devoted to the development of a new approach to studying elliptic differential and integro-differential (pseudodifferential) equations and their boundary problems in non-smooth domains. This
approach is based on a special representation of symbols of elliptic operators called wave factorization. In canonical domains, for example, the angle on a plane or a wedge in space, this yields a general solution, and then leads to the statement of a boundary problem. Wave factorization has also been used to obtain explicit formulas for solving some problems in diffraction and elasticity theory.
Audience: This volume will be of interest to mathematicians, engineers, and physicists whose work involves partial differential equations, integral equations, operator theory, elasticity and viscoelasticity, and
electromagnetic theory. It can also be recommended as a text for graduate and postgraduate students for courses in singular integral and pseudodifferential equations.
Contents
Preface. 1. Distributions and their Fourier transforms. 2. Multidimensional complex analysis. 3. Sobolev-Slobodetskii spaces. 4. Pseudodifferential operators and equations in half-space. 5. Wave factorization. 6. Diffraction on a quadrant. 7. The problem of indentation of a wedge-shaped punch. 8.
Equations in an infinite plane angle. 9. General boundary value problems. 10. The Laplacian in a plane infinite angle. 11. Problems with potentials. Appendix 1: The multidimensional Riemann problem. Appendix 2:
Symbolic calculus, Noether property, index, regularization. Appendix 3: The Mellin transform. References. Index.
Hardbound, ISBN 0-7923-6531-3
August 2000, 192 pp.