Böcker i London Mathematical Society Lecture Note Series-serien

A book on homotopy theory, written to appeal to both established researchers in the field and graduate students interested in topology and algebra. The techniques used in this book include the use of some new algebraic models of 4-manifolds. There is a full list of references.

Higher-dimensional category theory draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. This is the first book on the subject and lays its foundations, appealing to graduate students and researchers who wish to become acquainted with this modern branch of mathematics.

An introduction to the conformal differential geometry of surfaces and submanifolds. The book discusses those aspects of the geometry of surfaces that only refer to an angle measurement but not to a length measurement. The book presents different methods (models) for thinking about geometry and performing computations.

This first volume contains selected papers from the conference 'Groups St Andrews 2001 in Oxford'. The articles are contributed by leading researchers and cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles.

This second volume of the two-volume book contains selected papers from the conference 'Groups St Andrews 2001 in Oxford'. The 'Groups St Andrews' proceedings volumes are a snapshot of group theory and they often play an important role in future developments in the subject.

This 2003 book is concerned with two fundamental problems in low-dimensional topology. Professor Johnson develops general methods and gives complete solutions in a number of cases. It is ideal for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.

This is the first extensive treatment of the theory of corings and their comodules.

The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems. They are based on summer schools for graduate students and postdocs, and provide complementary and contrasting viewpoints of key topics.

In 2003 the British Combinatorial Conference conference was held at the University of Wales, Bangor. The papers contained here are high quality surveys contributed by the invited speakers, covering topics of significant interest. Ideal for established researchers and graduate students who will find much here to inspire future work.

This volume, first published in 2004, contains the plenary invited talks given at main conference in the subject.

Sir Peter Swinnerton-Dyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume reviews some of his many remarkable contributions to mathematics and other fields, and it includes articles from leading researchers in analytic and arithmetic number theory, and algebraic geometry.

This is a collection of lecture notes from the Summer School 'Cycles Algebriques; Aspects Transcendents, Grenoble 2001'. The lectures were intended for non-specialists so include many illustrative examples. This book will be ideal for graduate students or researchers seeking a modern introduction to the state-of-the-art theory in this subject.

This collection of articles from the Independent University of Moscow is derived from the Globus seminars held there. Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups. The volume as a whole is a fascinating and exciting overview of contemporary mathematics.

The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory.

In recent years there has been a remarkable growth of interest in discrete integrable systems. Connections have been made with other topics such as numerical methods, cellular automata and mathematical physics. This volume comprises state-of-the-art articles from almost all the leading workers in this important and rapidly developing area.

In this book, the general theory of stable groups is developed from the beginning, concentrating on the model- and group-theoretic aspects. It brings together the various extensions of the original finite rank theory under a unified perspective and provides a coherent exposition of the knowledge in the field.

This volume contains the invited lectures given at the Sixteenth British Combinatorial Conference, held in July 1997 at Queen Mary and Westfield College. It provides a valuable survey of the present state of knowledge in combinatorics.

This is an essentially self-contained monograph in an intriguing field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications.

This book presents thirteen papers by leading researchers in computational mathematics. A wide range of topics are covered, illustrating the diversity of the field and its applications. This book will be of interest to researchers and graduate students in all areas of mathematics involving numerical and symbolic computations.

This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.

This book provides a general introduction to Tits buildings, their geometries and the related classical linear groups. It also surveys recent developments in model theory, in particular explaining amalgamation methods which have produced examples and counterexamples in group theory and geometry. Suitable for graduate students and researchers.

This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. It will be invaluable to mathematicians wanting to see how pure mathematics can be applied, and also engineers and computer scientists wishing to implement such systems.

The British Combinatorial Conference is one of the most well known meetings for combinatorialists. This volume collects the invited talks from the 1999 conference held at the University of Kent, spanning a broad range of combinatorial topics. All researchers into combinatorics will find this volume an outstanding and up-to-date resource.

This two-volume book contains selected papers from the international conference 'Groups St Andrews 1997 in Bath'. The articles cover a wide spectrum of modern group theory. Proceedings of earlier 'Groups St Andrews' conferences have had a major impact on the development of group theory and these volumes should be equally important.

The theory of von Neumann algebras has undergone rapid development since the work of Tonita, Takesaki and Conner. These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the subject and demonstrate the important role of the theory of crossed products. Part I deals with general continuous crossed products and proves the commutation theorem and the duality theorem. Part II discusses the structure of Type III von Neumann algebras and considers crossed products with modular actions. Restricting the treatment to the case of o-finite von Neumann algebras enables the author to work with faithful normal states.

These lecture notes are devoted to an area of current research interest that bridges functional analysis and function theory. The unifying theme is the notion of subharmonicity with respect to a uniform algebra. The topics covered include the rudiments of Choquet theory, various classes of representing measures, the duality between abstract sub-harmonic functions and Jensen measures, applications to problems of approximation of plurisubharmonic functions of several complex variables, and Cole's theory of estimates for conjugate functions. Many of the results are published here for the first time in monograph form.

This book is concerned with the relations between graphs, error-correcting codes and designs, in particular how techniques of graph theory and coding theory can give information about designs. A major revision and expansion of a previous volume in this series, this account includes many examples and new results as well as improved treatments of older material. So that non-specialists will find the treatment accessible the authors have included short introductions to the three main topics. This book will be welcomed by graduate students and research mathematicians and be valuable for advanced courses in finite combinatorics.

Recursion theory - now a well-established branch of pure mathematics, having grown rapidly over the last 35 years - deals with the general (abstract) theory of those operations which we conceive as being `computable' by idealized machines.

Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a different setting, namely that of positive characteristic, enables the various families of equations to be resolved in that circumstance. Finally, by applying the inequality in a different manner, simple bounds are determined on their solutions in rational functions of the general superelliptic equation. This book represents a self-contained account of a new approach to the subject, and one which plainly has not reached the full extent of its application. It also provides a more direct on the problems than any previous book. Little expert knowledge is required to follow the theory presented, and it will appeal to professional mathematicians, research students and the enthusiastic undergraduate.

This book describes a fresh approach to the classification of of convex plane polygons and of convex polyhedra according to their symmetry properties, based on ideas of topology and transformation group theory. Although there is considerable agreement with traditional treatments, a number of new concepts emerge that present classical ideas in a quite new way.