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This series has established itself as a valuable source of information for professional mathematicians and research workers in all areas of mathematics. Most of the volumes are short monographs giving an authoritative account of the present state of knowledge of a topic of current interest. The treatment may be informal but importance is attached to clear yet rigorous exposition. The series also accepts conference proceedings and similar collective works that meet its general objectives.

  • Managing Editors: Endre Süli, University of Oxford
  • Associate Editors: Tim Austin, University of Warwick, Roger Heath-Brown, University of Oxford, Colva Roney-Dougal, University of St Andrews, Ulrike Tillmann, University of Oxford, Kasia A. Rejzner, University of York

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465 results in London Mathematical Society Lecture Note Series

Page 9 of 24

Representation Theory of Lie Groups
  • M. F. Atiyah, R. Bott, S. Helgason, D. Kazhdan, B. Kostant, G. Lustztig
  • Published online:
    05 April 2013
    Print publication:
    31 January 1980
  • Lie groups and their representations occupy an important place in mathematics with applications in such diverse fields as differential geometry, number theory, differential equations and physics. In 1977 a symposium was held in Oxford to introduce this rapidly developing and expanding subject to non-specialists. This volume contains the lectures of ten distinguished mathematicians designed to provide the reader with a deeper understanding of the fundamental theory and appreciate the range of results. This volume contains much to interest mathematicians and theoretical physicists from advanced undergraduate level upwards.

Finite Geometries and Designs
  • Proceedings of the Second Isle of Thorns Conference 1980
  • Edited by P. J. Cameron, J. W. P. Hirschfeld, D. R. Hughes
  • Published online:
    05 April 2013
    Print publication:
    16 April 1981
  • Originally published in 1981, this collection of 33 research papers follows from a conference on the interwoven themes of finite Desarguesian spaces, Steiner systems, coding theory, group theory, block designs, generalized quadrangles, and projective planes. There is a comprehensive introduction, which aims to interest the non-specialist in the subject and which indicates how the contributions fit together. This is a field of research pursued both for its intrinsic interest and its applications. These papers include a number of open problems whose statement requires very little mathematical sophistication.

Introduction to Uniform Spaces
  • I. M. James
  • Published online:
    05 April 2013
    Print publication:
    03 May 1990
  • This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.

Rational Points on Curves over Finite Fields
  • Theory and Applications
  • Harald Niederreiter, Chaoping Xing
  • Published online:
    05 April 2013
    Print publication:
    14 June 2001
  • Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.

Brownian Motion, Hardy Spaces and Bounded Mean Oscillation
  • K. E. Petersen
  • Published online:
    05 April 2013
    Print publication:
    19 May 1977
  • This exposition of research on the martingale and analytic inequalities associated with Hardy spaces and functions of bounded mean oscillation (BMO) introduces the subject by concentrating on the connection between the probabilistic and analytic approaches. Short surveys of classical results on the maximal, square and Littlewood-Paley functions and the theory of Brownian motion introduce a detailed discussion of the Burkholder-Gundy-Silverstein characterization of HP in terms of maximal functions. The book examines the basis of the abstract martingale definitions of HP and BMO, makes generally available for the first time work of Gundy et al. on characterizations of BMO, and includes a probabilistic proof of the Fefferman-Stein Theorem on the duality of H11 and BMO.

A Geometric Approach to Homology Theory
  • S. Buonchristiano, C. P. Rourke, B. J. Sanderson
  • Published online:
    05 April 2013
    Print publication:
    01 April 1976
  • The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.

Combinatorial and Geometric Group Theory, Edinburgh 1993
  • Edited by Andrew J. Duncan, N. D. Gilbert, James Howie
  • Published online:
    05 April 2013
    Print publication:
    03 November 1994
  • The ICMS Workshop on Geometric and Combinatorial Methods in Group Theory, held at Heriot-Watt University in 1993, brought together some of the leading research workers in the subject. Some of the survey articles and contributed papers presented at the meeting are collected in this volume. The former cover a number of areas of current interest and include papers by: S. M. Gersten, R. I. Grigorchuk, P. H. Kropholler, A. Lubotzky, A. A. Razborov and E. Zelmanov. The contributed articles, all refereed, range over a wide number of topics in combinatorial and geometric group theory and related topics. The volume represents a summary of the state of knowledge of the field, and as such will be indispensable to all research workers in the area.

Semigroup Theory and its Applications
  • Proceedings of the 1994 Conference Commemorating the Work of Alfred H. Clifford
  • Edited by Karl H. Hofmann, Michael W. Mislove
  • Published online:
    05 April 2013
    Print publication:
    16 May 1996
  • This volume contains survey papers by the invited speakers at the Conference on Semigroup Theory and Its Applications which took place at Tulane University in April, 1994. The authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. Included are papers by Gordon Preston surveying Clifford's work on Clifford semigroups and by John Rhodes tracing the influence of Clifford's work on current semigroup theory. Notable among the areas of application are the paper by Jean-Eric Pin on applications of other areas of mathematics to semigroup theory and the paper by the editors on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable.

Diophantine Equations over Function Fields
  • R. C. Mason
  • Published online:
    05 April 2013
    Print publication:
    26 April 1984
  • 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.

General Theory of Lie Groupoids and Lie Algebroids
  • Kirill C. H. Mackenzie
  • Published online:
    05 April 2013
    Print publication:
    09 June 2005
  • This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry and general connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles, as well as a revised account of the relations between locally trivial Lie groupoids, Atiyah sequences, and connections in principal bundles. As such, this book will be of great interest to all those concerned with the use of Poisson geometry as a semi-classical limit of quantum geometry, as well as to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.

Combinatorics
  • Edited by T. P. McDonough, V. C. Mavron
  • Published online:
    05 April 2013
    Print publication:
    21 November 1974
  • This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation.

Classgroups of Group Rings
  • Edited by Martin J. Taylor
  • Published online:
    05 April 2013
    Print publication:
    12 April 1984
  • This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it achieves a considerable simplification and clarity over previous techniques. A main feature of the book is the introduction of the author's group logarithm, with numerous examples of its application. The main results dealt with are: Ullom's conjecture for Swan modules of p-groups; the self-duality theorem for rings of integers of tame extensions; the fixed-point theorem for determinants of group rings; the existence of Adams operations on classgroups. In addition, the author includes a number of calculations of classgroups of specific families of groups such as generalized dihedral groups, and quaternion and dihedral 2-groups. The work contained in this book should be readily accessible to any graduate student in pure mathematics who has taken a course in the representation theory of finite groups. It will also be of interest to number theorists and algebraic topologists.

Diophantine Analysis
  • Proceedings at the Number Theory Section of the 1985 Australian Mathematical Society Convention
  • Edited by J. H. Loxton, A. J. van Poorten
  • Published online:
    05 April 2013
    Print publication:
    17 July 1986
  • The papers in this volume, which were presented at the 1985 Australian Mathematical Society convention, survey recent work in Diophantine analysis. The contributors are leading mathematicians in the world, and their articles are state of the art accounts, many of which include open problems pointing the way to further research. The contributions will be of general interest to number theorists and of particular interest to workers in transcendence theory, Diophantine approximation and exponential sums.

Probability, Statistics and Analysis
  • Edited by J. F. C. Kingman, G. E. H. Reuter
  • Published online:
    05 April 2013
    Print publication:
    10 February 1983
  • This collection of papers is dedicated to David Kendall (Professor of Mathematical Statistics in the University of Cambridge) on the occasion of his 65th birthday. The content of the contributions indicates the breadth of his interests in mathematics and statistics, and the interrelation between mathematical analysis, the theory of probability, and mathematical statistics. The topics will interest postgraduate and research mathematicians.

A Double Hall Algebra Approach to Affine Quantum Schur–Weyl Theory
  • Bangming Deng, Jie Du, Qiang Fu
  • Published online:
    05 January 2013
    Print publication:
    06 December 2012
  • The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Schur–Weyl duality.

Foundations of Computational Mathematics, Budapest 2011
  • Edited by Felipe Cucker, Teresa Krick, Allan Pinkus, Agnes Szanto
  • Published online:
    05 December 2012
    Print publication:
    15 November 2012
  • The Foundations of Computational Mathematics meetings are a platform for cross-fertilisation between numerical analysis, mathematics and computer science. This volume is a collection of articles based on plenary presentations, given at the 2011 meeting, by some of the world's foremost authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to non-experts who wish to gain some insight into the state of the art in this active and significant field.

Appalachian Set Theory
  • 2006–2012
  • Edited by James Cummings, Ernest Schimmerling
  • Published online:
    05 December 2012
    Print publication:
    15 November 2012
  • This volume takes its name from a popular series of intensive mathematics workshops hosted at institutions in Appalachia and surrounding areas. At these meetings, internationally prominent set theorists give one-day lectures that focus on important new directions, methods, tools and results so that non-experts can begin to master these and incorporate them into their own research. Each chapter in this volume was written by the workshop leaders in collaboration with select student participants, and together they represent most of the meetings from the period 2006–2012. Topics covered include forcing and large cardinals, descriptive set theory, and applications of set theoretic ideas in group theory and analysis, making this volume essential reading for a wide range of researchers and graduate students.

Mathematical Aspects of Fluid Mechanics
  • Edited by James C. Robinson, José L. Rodrigo, Witold Sadowski
  • Published online:
    05 November 2012
    Print publication:
    18 October 2012
  • The rigorous mathematical theory of the equations of fluid dynamics has been a focus of intense activity in recent years. This volume is the product of a workshop held at the University of Warwick to consolidate, survey and further advance the subject. The Navier–Stokes equations feature prominently: the reader will find new results concerning feedback stabilisation, stretching and folding, and decay in norm of solutions to these fundamental equations of fluid motion. Other topics covered include new models for turbulent energy cascade, existence and uniqueness results for complex fluids and certain interesting solutions of the SQG equation. The result is an accessible collection of survey articles and more traditional research papers that will serve both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Operator Methods for Boundary Value Problems
  • Edited by Seppo Hassi, Hendrik S. V. de Snoo, Franciszek Hugon Szafraniec
  • Published online:
    05 November 2012
    Print publication:
    11 October 2012
  • Presented in this volume are a number of new results concerning the extension theory and spectral theory of unbounded operators using the recent notions of boundary triplets and boundary relations. This approach relies on linear single-valued and multi-valued maps, isometric in a Krein space sense, and offers a basic framework for recent developments in system theory. Central to the theory are analytic tools such as Weyl functions, including Titchmarsh-Weyl m-functions and Dirichlet-to-Neumann maps. A wide range of topics is considered in this context from the abstract to the applied, including boundary value problems for ordinary and partial differential equations; infinite-dimensional perturbations; local point-interactions; boundary and passive control state/signal systems; extension theory of accretive, sectorial and symmetric operators; and Calkin's abstract boundary conditions. This accessible treatment of recent developments, written by leading researchers, will appeal to a broad range of researchers, students and professionals.

Dense Sphere Packings
  • A Blueprint for Formal Proofs
  • Thomas Hales
  • Published online:
    05 October 2012
    Print publication:
    06 September 2012
  • The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture.

Page 9 of 24