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Scattering Theory For Hyperbolic Operators

Avbryt Send e-post. The main conjectures themselves have also been proved since then. The Author's Notes gives detailed explanations of these developments, together with open problems. The topics range over crystal bases of quantum groups, its algebro-geometric analogue known as geometric crystal, generalizations of Robinson-Schensted type correspondence, fermionic formula related to Bethe ansatz, applications of crystal bases to soliton celluar automata, Yang-Baxter maps, and integrable discrete dynamics.

All the papers are friendly written with many illustrative examples and intimately related to each other. This volume will serve as a good guide for researchers and graduate students who are interested in this fascinating subject.

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Bowditch Title: A course on geometric group theory This volume is intended as a self-contained introduction to the basic notions of geometric group theory, the main ideas being illustrated with various examples and exercises. One goal is to establish the foundations of the theory of hyperbolic groups. There is a brief discussion of classical hyperbolic geometry, with a view to motivating and illustrating this. The notes are based on a course given by the author at the Tokyo Institute of Technology, intended for fourth year undergraduates and graduate students, and could form the basis of a similar course elsewhere.

Many references to more sophisticated material are given, and the work concludes with a discussion of various areas of recent and current research.

Nikulin Title: Del Pezzo and K3 surfaces The present volume is a self-contained exposition on the complete classification of singular del Pezzo surfaces of index one or two. The method of the classification used here depends on the intriguing interplay between del Pezzo surfaces and K3 surfaces, between geometry of exceptional divisors and the theory of hyperbolic lattices. The topics involved contain hot issues of research in algebraic geometry, group theory and mathematical physics. This book, written by two leading researchers of the subjects, is not only a beautiful and accessible survey on del Pezzo surfaces and K3 surfaces, but also an excellent introduction to the general theory of Q-Fano varieties.

Noboru Nakayama, the author of this book, studies the birational classification of algebraic varieties and of compact complex manifolds. This book is a collection of his works on the numerical aspects of divisors of algebraic varieties. The notion of Zariski-decomposition introduced by Oscar Zariski is a powerful tool in the study of open surfaces. In the higher dimensional generalization, we encounter interesting phenomena on the numerical aspects of divisors. The author treats the higher dimensional Zariski-decomposition systematically.

The abundance conjecture predicts that the numerical Kodaira dimension of a minimal variety coincides with the usual Kodaira dimension.

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The Kodaira dimension is an invariant of the canonical divisor of a variety. The numerical analogue used to be defined only for nef divisors, but it is now extended to arbitrary divisors in this book. Explained in details are many important results on the numerical Kodaira dimension related to the abundance, to the addition theorem for fiber spaces, and to the deformation invariance.

Crandall and P. Lions in to study first-order partial differential equations of nondivergence form, typically, Hamilton-Jacobi equations. This text is an introduction to the viscosity solution theory as indicated by the title. After a brief history of weak solutions, it presents several uniqueness comparison principle and existence results, which are main issues. For further topics, it chooses generalized boundary value problems and regularity results. In Appendix, which is the hardest part, it provides proofs of several important propositions.

Koike's current mathematical interests still lie in the viscosity solution theory and its applications. Kato and N. Tsuzuki Title: Period mappings and differential equations. 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. The books ends with a theory of p-adictriangle groups. 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.

Marc van Leeuwen is famous in the field of manipulation of Young tableaux and its related topics. Prokhorov Title: Lectures on complements on log surfaces Dr.

Scattering Theory for Hyperbolic Operators, Volume 21 - 1st Edition

Yuri Prokhorov, the author of this book, is an expert in birational geometry in the field of algebraic geometry. There is currently much ongoing research on this subject, a very active area in algebraic geometry. 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.

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This book contains information and encouragement necessary to attack the problem of the higher dimensional case. Orlik and H. 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.

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.

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.

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 L p weighted a priori estimates. 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 C 1 solutions to the Cauchy problem with small and decaying initial data. Key words and phrases: Quasilinear hyperbolic system, Cauchy problem, C 1 solution, blow-up, life span.

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 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.

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.

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.

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He dedicates this paper to Dr. Matsuo's daughter who was born a few days ago. After the discovery of the Jones polynomial at the middle of '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.

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. 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.


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