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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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466 results in London Mathematical Society Lecture Note Series

Page 14 of 24

Poisson Geometry, Deformation Quantisation and Group Representations
  • Edited by Simone Gutt, John Rawnsley, Daniel Sternheimer
  • Published online:
    04 August 2010
    Print publication:
    21 June 2005
  • Poisson geometry lies at the cusp of noncommutative algebra and differential geometry, with natural and important links to classical physics and quantum mechanics. This book presents an introduction to the subject from a small group of leading researchers, and the result is a volume accessible to graduate students or experts from other fields. The contributions are: Poisson Geometry and Morita Equivalence by Bursztyn and Weinstein; Formality and Star Products by Cattaneo; Lie Groupoids, Sheaves and Cohomology by Moerdijk and Mrcun; Geometric Methods in Representation Theory by Schmid; Deformation Theory: A Powerful Tool in Physics Modelling by Sternheimer.

Surveys in Combinatorics 2005
  • Edited by Bridget S. Webb
  • Published online:
    04 August 2010
    Print publication:
    21 July 2005
  • This volume contains survey articles based on the invited lectures given at the Twentieth British Combinatorial Conference, organised jointly by the University of Durham and the Open University. It was held in July 2005 at the University of Durham. This biennial conference is a well-established international event, with speakers from all over the world. By its nature this volume provides an up-to-date overview of current research activity in several areas of combinatorics, ranging from combinatorial number theory to geometry. The authors are some of the world's foremost researchers in their fields, and here they summarize existing results, and give a unique preview of work currently being written up. The book provides a valuable survey of the present state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science, statistics and engineering.

Number Theory and Algebraic Geometry
  • Edited by Miles Reid, Alexei Skorobogatov
  • Published online:
    04 August 2010
    Print publication:
    26 January 2004
  • Sir Peter Swinnerton-Dyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume provides contemporary insight into several subjects in which Sir Peter's influence has been notable, and is dedicated to his 75th birthday. The opening section reviews some of his many remarkable contributions to mathematics and other fields. The remaining contributions come from leading researchers in analytic and arithmetic number theory, and algebraic geometry. The topics treated include: rational points on algebraic varieties, the Hasse principle, Shafarevich-Tate groups of elliptic curves and motives, Zagier's conjectures, descent and zero-cycles, Diophantine approximation, and Abelian and Fano varieties.

Ordered Permutation Groups
  • A. M. W. Glass
  • Published online:
    04 August 2010
    Print publication:
    07 January 1982
  • As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.

Surveys in Set Theory
  • Edited by A. R. D. Mathias
  • Published online:
    04 August 2010
    Print publication:
    13 October 1983
  • This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

Spectral Generalizations of Line Graphs
  • On Graphs with Least Eigenvalue -2
  • Dragoš Cvetkovic, Peter Rowlinson, Slobodan Simic
  • Published online:
    04 August 2010
    Print publication:
    22 July 2004
  • Line graphs have the property that their least eigenvalue is greater than or equal to –2, a property shared by generalized line graphs and a finite number of so-called exceptional graphs. This book deals with all these families of graphs in the context of their spectral properties. The authors discuss the three principal techniques that have been employed, namely 'forbidden subgraphs', 'root systems' and 'star complements'. They bring together the major results in the area, including the recent construction of all the maximal exceptional graphs. Technical descriptions of these graphs are included in the appendices, while the bibliography provides over 250 references. This will be an important resource for all researchers with an interest in algebraic graph theory.

Model Theory with Applications to Algebra and Analysis
  • Volume 2
  • Edited by Zoé Chatzidakis, Dugald Macpherson, Anand Pillay, Alex Wilkie
  • Published online:
    04 August 2010
    Print publication:
    22 May 2008
  • The second of a two volume set showcasing current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. Each volume contains a series of expository essays and research papers around the subject matter of a Newton Institute Semester on Model Theory and Applications to Algebra and Analysis. The articles convey outstanding new research on topics such as model theory and conjectures around Mordell-Lang; arithmetic of differential equations, and Galois theory of difference equations; model theory and complex analytic geometry; o-minimality; model theory and non-commutative geometry; definable groups of finite dimension; Hilbert's tenth problem; and Hrushovski constructions. With contributions from so many leaders in the field, this book will undoubtedly appeal to all mathematicians with an interest in model theory and its applications, from graduate students to senior researchers and from beginners to experts.

Geometric Aspects of Banach Spaces
  • Essays in Honour of Antonio Plans
  • Edited by E. Martin-Peinador, A. Rodés
  • Published online:
    04 August 2010
    Print publication:
    06 July 1989
  • This volume, dedicated to Professor A. Plans, concentrates on some important and contemporary themes in Banach space theory. The articles are by leading researchers and cover topics such as sequences, operators, eigenvalues, s-numbers and projection constants, so will be of interest to functional analysts and approximation theorists.

Skew Fields
  • P. K. Draxl
  • Published online:
    04 August 2010
    Print publication:
    17 February 1983
  • The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. This material is presented in a classical, though unusual, way. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals. The principal topic discussed in this section is reduced K,-theory. This book will be of interest to graduate students in pure mathematics and to professional mathematicians.

Stochastic Partial Differential Equations
  • Edited by Alison Etheridge
  • Published online:
    04 August 2010
    Print publication:
    13 July 1995
  • Stochastic partial differential equations can be used in many areas of science to model complex systems that evolve over time. Their analysis is currently an area of much research interest. This book consists of papers given at the ICMS Edinburgh meeting held in 1994 on this topic, and it brings together some of the world's best known authorities on stochastic partial differential equations. Subjects covered include the stochastic Navier–Stokes equation, critical branching systems, population models, statistical dynamics, and ergodic properties of Markov semigroups. For all workers on stochastic partial differential equations this book will have much to offer.

Homological Questions in Local Algebra
  • Jan R. Strooker
  • Published online:
    04 August 2010
    Print publication:
    06 September 1990
  • This book presents an account of several conjectures arising in commutative algebra from the pioneering work of Serre and Auslander-Buchsbaum. The approach is via Hochster's 'Big Cohen-Macaulay modules', though the complementary view point of Peskine-Szpiro and Roberts, who study the homology of certain complexes, is not neglected. Various refinements of Hochster's construction, obtained in collaboration with Bartijn, are included. A special feature is a long chapter written by Van den Dries which explains how a certain type of result can be 'lifted' from prime characteristic to characteristic zero. Though this is primarily a research monograph, it does provide introductions to most of the topics treated. Non-experts may therefore find it an appealing guide into an active area of algebra.

Complex Projective Geometry
  • Selected Papers
  • Edited by G. Ellingsrud, C. Peskine, G. Sacchiero, S. A. Stromme
  • Published online:
    06 July 2010
    Print publication:
    30 July 1992
  • Algebraic geometers have renewed their interest in the interplay between algebraic vector bundles and projective embeddings. New methods have been developed for questions such as: what is the geometric content of syzygies and of bundles derived from them? how can they be used for giving good compactifications of natural families? which differential techniques are needed for the study of families of projective varieties? Such problems have often been reformulated over the last decade; often the need for a deeper analysis of the works of classical algebraic geometers was recognised. These questions were addressed at successive conferences held in Trieste and Bergen. New results, work in progress, conjectures and modern accounts of classical ideas were presented. This collection represents a development of the work conducted at the conferences; the Editors have taken the opportunity to mould the papers into a cohesive volume.

Computational and Geometric Aspects of Modern Algebra
  • Edited by Michael Atkinson, Nick Gilbert, James Howie, Steve Linton, Edmund Robertson
  • Published online:
    06 July 2010
    Print publication:
    15 June 2000
  • This book comprises a collection of papers from participants at the IMCS Workshop on Computational and Geometric Aspects of Modern Algebra, held at Heriot-Watt University in 1998. Written by leading researchers, the papers cover a wide range of topics in the vibrant areas of word problems in algebra and geometric group theory. This book represents a timely record of recent work and provides an indication of the key areas of future development.

Moonshine - The First Quarter Century and Beyond
  • Proceedings of a Workshop on the Moonshine Conjectures and Vertex Algebras
  • Edited by James Lepowsky, John McKay, Michael P. Tuite
  • Published online:
    06 July 2010
    Print publication:
    03 June 2010
  • The theory of 'Monstrous Moonshine' has been a major development in mathematics since 1979. Beginning with remarkable conjectures relating finite group theory and number theory that stimulated an outpouring of new ideas, 'Monstrous Moonshine' deeply involves many different areas of mathematics, as well as string theory and conformal field theory in physics. It has changed the landscape of many fields. This volume consists of 17 papers by research leaders, based on talks presented at a workshop held to mark the anniversary of the 'Monstrous Moonshine' conjectures. The papers, which include surveys of many important developments, will give the reader a view of a wide range of current activity and promising directions for future research.

Transcendental Dynamics and Complex Analysis
  • Edited by Philip J. Rippon, Gwyneth M. Stallard
  • Published online:
    06 July 2010
    Print publication:
    26 June 2008
  • After the pioneering work on complex dynamics by Fatou and Julia in the early 20th century, Noel Baker went on to lay the foundations of transcendental complex dynamics. As one of the leading exponents of transcendental dynamics, he showed how developments in complex analysis such as Nevanlinna theory could be applied. His work has inspired many others to take up this increasingly active subject, and will continue to do so. Presenting papers by researchers in transcendental dynamics and complex analysis, this book is written in honour of Noel Baker. The papers describe the state of the art in this subject, with new results on completely invariant domains, wandering domains, the exponential parameter space, and normal families. The inclusion of comprehensive survey articles on dimensions of Julia sets, buried components of Julia sets, Baker domains, Fatou components of functions of small growth, and ergodic theory of transcendental meromorphic functions means this is essential reading for students and researchers in complex dynamics and complex analysis.

The Descriptive Set Theory of Polish Group Actions
  • Howard Becker, Alexander S. Kechris
  • Published online:
    06 July 2010
    Print publication:
    05 December 1996
  • In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces.

Operator Algebras and Applications
  • Volume 1, Structure Theory; K-theory, Geometry and Topology
  • Edited by David E. Evans, Masamichi Takesaki
  • Published online:
    06 July 2010
    Print publication:
    26 January 1989
  • These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.

Lectures on the Combinatorics of Free Probability
  • Alexandru Nica, Roland Speicher
  • Published online:
    06 July 2010
    Print publication:
    07 September 2006
  • Free Probability Theory studies a special class of 'noncommutative'random variables, which appear in the context of operators on Hilbert spaces and in one of the large random matrices. Since its emergence in the 1980s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering. This 2006 book gives a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course (on an advanced undergraduate or beginning graduate level), and is also well-suited for the individual study of free probability.

Coding the Universe
  • A. Beller, R. Jensen, P. Welch
  • Published online:
    06 July 2010
    Print publication:
    07 January 1982
  • Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another model L[a] with the same properties. L[a] is Gödels universe of 'constructible' sets L, together with a set of integers a which code all the cardinality and cofinality structure of M. Some applications are also considered. Graduate students and research workers in set theory and logic will be especially interested by this account.

Representation Theory
  • Selected Papers
  • Edited by I. M. Gelfand
  • Published online:
    06 July 2010
    Print publication:
    18 November 1982
  • The unifying theme of this collection of papers by the very creative Russian mathematician I. M. Gelfand and his co-workers is the representation theory of groups and lattices. Two of the papers were inspired by application to theoretical physics; the others are pure mathematics though all the papers will interest mathematicians at quite opposite ends of the subject. Dr. G. Segal and Professor C-M. Ringel have written introductions to the papers which explain the background, put them in perspective and make them accessible to those with no specialist knowledge in the area.

Page 14 of 24