Books in the London Mathematical Society Lecture Note Series series

State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.

This book comprises an overview of the material presented at the 1999 Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area. It will be of interest to researchers and will also be useful as a reference text for graduate courses.

This book is devoted to the theory of group representations, a young and promising area of modern algebra. It provides a detailed exposition of several central topics in the field, leading to the most current advances and developments. Much of the included material has never been available in book form before.

Traditionally the Adams-Novikov spectral sequence has been a tool which has enabled the computation of generators and relations to describe homotopy groups. Here a natural geometric description of the sequence is given in terms of cobordism theory and manifolds with singularities. The author brings together many interesting results not widely known outside the USSR, including some recent work by Vershinin. This book will be of great interest to researchers into algebraic topology.

The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related multiplicative functions. They also prove the mean-value theorems of Wirsing and Halasz and study the pointwise convergence of the Ramanujan expansion. Finally, some applications to power series with multiplicative coefficients are included, along with exercises and an extensive bibliography.

This book constitutes the proceedings of a conference held at the University of Birmingham to mark the retirement of Professor A. M. Macbeath. The papers represent work on a broad spectrum of topics in the theory of discrete group actions.

This volume is based on lectures given at a workshop and conference on symplectic geometry at the University of Warwick in August 1990. The contributions to this volume reflect the richness of the subject and include expository papers as well as original research. They will be an essential source for all research mathematicians in symplectic geometry.

An authoritative collection of surveys and papers, ranging over a wide number of topics in combinatorial and geometric group theory and related topics. As a summary of the state of knowledge of the field, this volume will be indispensable to all research workers in the area.

This book describes work, largely that of the author, on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel-Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up to homeomorphism, and surface bundles are characterized up to simple homotopy equivalence. Non-orientable cases are also considered wherever possible, and in the final chapter the results obtained earlier are applied to 2-knots and complex analytic surfaces. This book is essential reading for anyone interested in low-dimensional topology.

This is an introductory text intended to give the non-specialist a comprehensive insight into the science of biotransformations. The book traces the history of biotransformations, clearly spells out the pros and cons of conducting enzyme-mediated versus whole-cell bioconversions, and gives a variety of examples wherein the bio-reaction is a key element in a reaction sequence leading from cheap starting materials to valuable end products.

These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.

This work, first published in 1995, presents developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expressed in terms of hypergeometric series. Dingle's theory of terminants is then employed to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. Numerical results are used to illustrate that a complete asymptotic expansion can be made to agree with exact results for the generalised Euler-Jacobi series to any desired degree of accuracy. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable book.

Based on lectures given at University of Michigan, Harvard University and Seoul National University, this 2003 book is a brief introduction to the main ideas of algebraic and geometric invariant theory. The emphasis is on concrete examples and there are numerous examples and exercises to aid the reader.

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.