MSJ Memoirs

Mathematical Society of Japan

This monograph series is intended to publish lecture notes, graduate textbooks and long research papers* in pure and applied mathematics. Each volume should be an integrated monograph. Proceedings of conferences or collections of independent papers are not accepted.

Articles for the series can be submitted to one of the editors in the form of hard copy. When the article is accepted, the author(s) is (are) requested to send a camera-ready manuscript.
* limited to contributions by MSJ members

List of Publications
Vol.12 Author: Yves André
(with appendices by F. Kato and N. Tsuzuki)
Title: Period mappings and differential equations. Form C to C_p
Tohoku-Hokkaido lectures in Arithmetic Geometry
The theorey of period mappings has played a central role in nineteen-century mathematics as a fertile place of interaction between algebraic and differential geometry, differential equations, and group theory, from Gauss and Riemann to Klein and Poincaré. This text is an introduction to the p-adic counterpart of this theory, which is much more recent and still mysterious. It should be of interest both to some complex geometers and to some arithmetic geometers.
Starting with an introduction to p-adic analytic geometry (in the sense of Berkovich), it then presents the Rapoport-Zink theory of period mappings, emphasizing the relation with Picard-Fuchs differential equtions. a new theory of fundamental groups, orbifolds, and uniformizing equations (in the p-adic context) accounts for the group-theoretic aspects of these period mappings. The books ends with a theory of p-adictriangle groups.
Dr. André's current mathematical interests lie in arithmetic geometry and in the theory of motives.
2003, 246p, ISBN4-931469-22-1
Vol.11 Authors: John R. Stembridge, Jean-Yves Thibon and Marc A. A. van Leeuwen
Title: Interaction of combinatorics and representation theory
This volume consisting of two research papers and one survey paper is a good guide to look into a new emerging field, which stems from the interaction of combinatorics and representation theory.
Dr. John Stembrige is famous for his study on combinatorics in Lie algebra representations, Coxeter/Weyl groups, and other topics. Also he is the author of the Maple package software ``SF'' (Schur functions), ``coxeter/weyl'', and ``posets''.
Dr. Jean-Yves Thibon is one of the most active researchers in this field and is famous for many collaborated works with Alain Lascoux and Bernard Leclerc and other famous researchers.
Dr. Marc van Leeuwen is famous in the field of manipulation of Young tableaux and its related topics. He is one of the authors of the software package ``LiE'' for Lie group computation.
2001, 145p, ISBN4-931469-14-0
Vol.10 Author: Yuri G. Prokhorov
Title: Lectures on complements on log surfaces
Dr. Yuri Prokhorov, the author of this book, is an expert in birational geometry in the field of algebraic geometry. This book is the first significant expository lecture for ``complements''; this notion was introduced by Vyacheslav Shokurov quite recently and is important in understanding singularities of a pair consisting of an algebraic variety and a divisor on it. There is currently much ongoing research on this subject, a very active area in algebraic geometry.
This book helps the reader to understand the ``complement'' concept and provides the basic knowledge about the singularities of a pair. The author gives a simple proof of the boundedness of the complements for two dimensional pairs under some restrictive condition, where this boundedness has been conjectured by Shokurov for every dimension. This book contains information and encouragement necessary to attack the problem of the higher dimensional case.
2001, 130p, ISBN4-931469-12-4
Vol.9 Authors: Peter Orlik and Hiroaki Terao
Title: Arrangements and hypergeometric integrals
An affine arrangement of hyperplanes is a finite collection of one-codimensional affine linear spaces in Cn. P. Orlik and H. Terao are leading specialists in the theory of arrangements and the co-authors of the well-known book ``Arrangements of Hyperplanes''. In this monograph, they give an introductory survey which also contains the recent progress in the theory of hypergeometric functions. The main argument is done from the arrangement-theoretic point of view. This will be a nice text for a student to begin the study of hypergeometric functions.
2001, 112p, ISBN4-931469-10-8
Vol.8 Author: Eric M. Opdam
Title: Lecture notes on Dunkl operators for real and complex reflection groups
Eric M. Opdam studied a generalization of the system of differential equations satisfies by the Harish-Chandra spherical functions, and with Gerrit Heckman established the theory of Heckman-Opdam hypergeometric functions by the use of a trigonometric extension of Dunkl operators.
In this note he introduces this theory, and includes a recent result on the harmonic analysis of the hypergeometric functions and also an application of Dunkl operators to the study of reflection groups.
2000, 90p, ISBN4-931469-08-6
Vol.7 Author: Vladimir Georgiev
Title: Semilinear hyperbolic equations
Most of the standard theorems of global in time existence for solutions of the nonlinear evolution equations in mathematical physics depend heavily upon estimates for the solution's total energy. Typically, to prove the global existence of a smooth solution, one argues that a certain amount of energy would necessarily be dissipated in the development of a singularity, which is limited by virtue of small data assumptions so far, except for some semilinear evolution equations with good sign.
Under the small data assumption, the main observation is devoted to the investigation of the dissipative mechanism of linearized equations, which is described by the decay estimate of solutions mathematically. V. Georgiev is one of the most excellent mathematicians who created outstanding a priori estimates about hyperbolic equations in mathematical physics, which yield solutions of the corresponding nonlinear hyperbolic equations under small data assumption.
The aim of this lecture note is to explain how to derive sharp a priori estimates which enable us to prove a global in time existence of solutions to semilinear wave equation and non-linear Klein-Gordon equation.
The core of the lecture note is Section 8, which is devoted to Fourier transform on manifolds with constant negative curvature. Combining this with the interpolation method and psudodifferential operator approach enables us to obtain better Lp weighted a priori estimates.
Key words: semilinear wave equation, Fourier transform on hyperboloid, Sobolev spaces on hyperboloid, Klein - Gordon equation
2000, 209p, ISBN4-931469-07-8
Vol.6 Author: Kong De-xing
Title: Cauchy problem for quasilinear hyperbolic systems
This book is concerned with Cauchy problem for quasilinear hyperbolic systems. By introducing the concepts weak linear degeneracy and matching condition, we give a systematic presentation on the global existence, the large time behaviour and the blow-up phenomenon, particularly, the life span of C1 solutions to the Cauchy problem with small and decaying initial data. Some successful applications of our general theory are given to the quasilinear canonical system related to the Monge-Amp\`ere equation, the system of nonlinear three-wave interaction in plasma physics, the nonlinear wave equation with higher order dissipation, the system of one-dimensional gas dynamics with nonlinear dissipation, the system of motion of an elastic string, the system of plane elastic waves for hyperelastic materials and so on.
Key words and phrases: Quasilinear hyperbolic system, Cauchy problem, C1 solution, blow-up, life span.
2000, 213p, ISBN4-931469-06-X
Vol.5 Authors: Daryl Cooper, Craig D. Hodgson and Steven P. Kerckhoff
Title: Three-dimensional orbifolds and cone-manifolds
This volume provides an excellent introduction of the statement and main ideas in the proof of the orbifold theorem announced by Thurston in late 1981. It is based on the authors' lecture series entitled ``Geometric Structures on 3-Dimensional Orbifolds" which was featured in the third MSJ Regional Workshop on ``Cone-Manifolds and Hyperbolic Geometry" held on July 1-10, 1998, at Tokyo Institute of Technology. The orbifold theorem shows the existence of geometric structures on many 3-orbifolds and on 3-manifolds with symmetry. The authors develop the basic properties of orbifolds and cone-manifolds, extends many ideas from the differential geometry to the setting of cone-manifolds and outlines a proof of the orbifold theorem.
2000, 170p, ISBN4-931469-05-1
Vol.4 Authors: Atsushi Matsuo and Kiyokazu Nagatomo
Title: Axioms for a vertex algebra and the locality of quantum fields
Dr. A. Matsuo has been working on various mathematical structures related to two-dimensional conformal field theory. He is famous for his study on the Knizhnik-Zamolodchkov equation and its analogues. He is recently interested in searching for examples of vertex algebras having interesting symmetries.
Dr. K. Nagatomo is working on the theory of vertex oeprator algebras and related topics. His interests include applications of the representation theory of infinite dimensional algebras to completely integrable systems. He dedicates this paper to Dr. Matsuo's daughter who was born a few days ago.
1999, 110p, ISBN4-931469-04-3
Vol.3 Author: Tomotada Ohtsuki
Title: Combinatorial quantum method in 3-dimensional topology
This book is based on a series of lectures by the author in the workshop "Combinatorial Quantum Method in 3-dimensional Topology" held in Oiwake Seminar House of Waseda University in the end of September, 1996.
After the discovery of the Jones polynomial at the middle of 1980's, many new invariants of knots and 3-manifolds, what we call quantum invariants, have been found. At the present we have two key words to understand quantum invariants of knots; "the Kontsevich invariant" and "Vassiliev invariants". Correspondingly we have also two notions for 3-manifold invariants; "The LMO invariant" and "finite type invariants". The aim of this book is to explain about construction and basic properties of these invariants and how to understand quantum invariants via these invariants.
1999, 83p, ISBN4-931469-03-5
Vol.2 Authors: Masako Takahashi, Mitsuhiro Okada and Mariangiola Dezani-Ciancaglini (Eds.)
Title: Theories of types and proofs
This is an excellent collection of refereed articles on theories of types and proofs. The articles are written by noted experts in the area. In addition to the value of the individual articles, the collection is notable for covering a range of related topics. The collection begins with useful primer on the subject that will make the subsequent articles more accessible to potential readers. Following the primer, there are good articles on traditional topics in type assignment systems. These are followed by explanations of applications to program analysis and a series of articles on application to logic. The collection includes articles on intuitionistic logic, a standard use of type-theoretic notions, and concludes with an article on linear logic.
1998, 295p, ISBN4-931469-02-7
Vol.1 Authors: Ivan Cherednik, Peter J. Forrester and Denis Uglov
Title: Quantum many-body problems and representation theory
Dr. I. Cherednik is famous for introducing the double affine Hecke algebras, which is the main topics in his article ``Lectures on affine Knizhnik-Zamolodchikov equations, . . .''. This focuses on the equivalence of the affine Knizhnik-Zamolodchikov equations and the quantum many-body problems. It also serves as an introduction to the new theory of the spherical and the hypergeometric functions based on the affine and the double affine Hecke algebras.
Dr. P. J. Forrester is an expert in random matrix theory and Coulomb systems. Dr. Forrester has also been a pioneer in the application of Jack symmetric functions to statistical physics. The article ``Random Matrices, Log-Gases and the Calogero-Sutherland Model'' deals precisely with these three areas.
Dr. D. Uglov is actively working in the quantum many-body problems and the related representation theory. The article `` Symmetric functions and the Yangian decomposition . . .'' is an exposition of his recent works on these topics.
1998, 241p, ISBN4-931469-01-9
Editorial Board
Fukaya, Kenji • Funaki, Tadahisa • Ishii, Shihoko
Kashiwara, Masaki (Chief Editor) • Kobayashi, Ryoichi
Kusuoka, Shigeo • Mabuchi, Toshiki • Maeda, Yoshiaki
Miwa, Tetsuji (Managing Editor) • Miyaoka, Yoichi
Nishiura, Yasumasa • Noumi, Masatoshi • Ohta, Masami
Okamoto, Kazuo • Ozawa, Tohru • Taira, Kazuaki
Tsuboi, Takashi • Wakimoto, Minoru

MSJ Memoirs is published occasionally (3-5 volumes each year) by the Mathematical Society of Japan. Each volume may be ordered separately. Please spacify volume when ordering an individual volume.

© 2003 by the Mathematical Society of Japan. All rights reserved.

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