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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 10 of 24

Mathematical Models in Contact Mechanics
  • Mircea Sofonea, Andaluzia Matei
  • Published online:
    05 October 2012
    Print publication:
    13 September 2012
  • This text provides a complete introduction to the theory of variational inequalities with emphasis on contact mechanics. It covers existence, uniqueness and convergence results for variational inequalities, including the modelling and variational analysis of specific frictional contact problems with elastic, viscoelastic and viscoplastic materials. New models of contact are presented, including contact of piezoelectric materials. Particular attention is paid to the study of history-dependent quasivariational inequalities and to their applications in the study of contact problems with unilateral constraints. The book fully illustrates the cross-fertilisation between modelling and applications on the one hand and nonlinear mathematical analysis on the other. Indeed, the reader will gain an understanding of how new and nonstandard models in contact mechanics lead to new types of variational inequalities and, conversely, how abstract results concerning variational inequalities can be applied to prove the unique solvability of the corresponding contact problems.

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.

Applicable Differential Geometry
  • M. Crampin, F. A. E. Pirani
  • Published online:
    05 August 2012
    Print publication:
    26 March 1987
  • This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechanics, gauge fields theories, relativity and gravitation. The order of presentation corresponds to that used for the relevant material in theoretical physics: the geometry of affine spaces, which is appropriate to special relativity theory, as well as to Newtonian mechanics, is developed in the first half of the book, and the geometry of manifolds, which is needed for general relativity and gauge field theory, in the second half. Analysis is included not for its own sake, but only where it illuminates geometrical ideas. The style is informal and clear yet rigorous; each chapter ends with a summary of important concepts and results. In addition there are over 650 exercises, making this a book which is valuable as a text for advanced undergraduate and postgraduate students.

Lectures on Mechanics
  • Jerrold E. Marsden
  • Published online:
    05 August 2012
    Print publication:
    30 April 1992
  • The use of geometric methods in classical mechanics has proven to be a fruitful exercise, with the results being of wide application to physics and engineering. Here Professor Marsden concentrates on these geometric aspects, and especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water molecule. This book, based on the 1991 LMS Invited Lectures, will be valued by pure and applied mathematicians, physicists and engineers who work in geometry, nonlinear dynamics, mechanics, and robotics.

Non-equilibrium Statistical Mechanics and Turbulence
  • John Cardy, Gregory Falkovich, Krzysztof Gawedzki
  • Edited by Sergey Nazarenko, Oleg V. Zaboronski
  • Published online:
    05 June 2012
    Print publication:
    11 December 2008
  • Methods of non-equilibrium statistical mechanics play an increasingly important role in modern turbulence research, yet the range of relevant tools and methods is so wide and developing so fast that until now there has not been a single book covering the subject. As an introduction to modern methods of statistical mechanics in turbulence, this volume rectifies that situation. The book comprises three harmonised lecture courses by world class experts in statistical physics and turbulence: John Cardy introduces Field Theory and Non-Equilibrium Statistical Mechanics; Gregory Falkovich discusses Turbulence Theory as part of Statistical Physics; and Krzysztof Gawedzki examines Soluble Models of Turbulent Transport. To encourage readers to deepen their understanding of the theoretical material, each chapter contains exercises with solutions. Essential reading for students and researchers in the field of theoretical turbulence, this volume will also interest any scientist or engineer who applies knowledge of turbulence and non-equilibrium physics to their work.

Circuit Double Cover of Graphs
  • Cun-Quan Zhang
  • Published online:
    05 May 2012
    Print publication:
    26 April 2012
  • The famous Circuit Double Cover conjecture (and its numerous variants) is considered one of the major open problems in graph theory owing to its close relationship with topological graph theory, integer flow theory, graph coloring and the structure of snarks. It is easy to state: every 2-connected graph has a family of circuits covering every edge precisely twice. C.-Q. Zhang provides an up-to-date overview of the subject containing all of the techniques, methods and results developed to help solve the conjecture since the first publication of the subject in the 1940s. It is a useful survey for researchers already working on the problem and a fitting introduction for those just entering the field. The end-of-chapter exercises have been designed to challenge readers at every level and hints are provided in an appendix.

Random Matrices: High Dimensional Phenomena
  • Gordon Blower
  • Published online:
    05 March 2012
    Print publication:
    08 October 2009
  • This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.

Transformation Groups
  • Proceedings of the Conference in the University of Newcastle upon Tyne, August 1976
  • Edited by Czes Kosniowski
  • Published online:
    05 March 2012
    Print publication:
    17 February 1977
  • The theory of transformation groups studies symmetries of various mathematical objects such as topological spaces, manifolds, polyhedra and function spaces. It is thus a central concept in many branches of mathematics. This volume contains 25 of the papers submitted at the conference on transformation groups held at the University of Newcastle upon Tyne in August 1976.

Proceedings of Groups - St. Andrews 1985
  • Edited by E. F. Robertson, Colin Matthew Campbell
  • Published online:
    05 March 2012
    Print publication:
    08 January 1987
  • This book contains selected papers from the international conference Groups - St Andrews 1985. Five leading group theorists - Bachmuth, Baumslag, Neuman, Roseblade and Tits - have presented survey articles based on short lecture courses given at the conference and the rest of the book comprises both survey and research articles contributed by other conference speakers. The many articles with their wealth of references demonstrate the richness and vitality of modern group theory and its many connections with other area of mathematics. The book will prove invaluable to both experienced researchers and new postgraduates whose interests involve group theory.

Trends in Stochastic Analysis
  • Edited by Jochen Blath, Peter Mörters, Michael Scheutzow
  • Published online:
    05 March 2012
    Print publication:
    09 April 2009
  • Presenting important trends in the field of stochastic analysis, this collection of thirteen articles provides an overview of recent developments and new results. Written by leading experts in the field, the articles cover a wide range of topics, ranging from an alternative set-up of rigorous probability to the sampling of conditioned diffusions. Applications in physics and biology are treated, with discussion of Feynman formulas, intermittency of Anderson models and genetic inference. A large number of the articles are topical surveys of probabilistic tools such as chaining techniques, and of research fields within stochastic analysis, including stochastic dynamics and multifractal analysis. Showcasing the diversity of research activities in the field, this book is essential reading for any student or researcher looking for a guide to modern trends in stochastic analysis and neighbouring fields.

Geometric Analysis of Hyperbolic Differential Equations: An Introduction
  • S. Alinhac
  • Published online:
    05 February 2012
    Print publication:
    20 May 2010
  • Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.

Arithmetic Differential Operators over the p-adic Integers
  • Claire C. Ralph, Santiago R. Simanca
  • Published online:
    05 February 2012
    Print publication:
    26 January 2012
  • The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers.

Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology
  • Edited by Jens Bolte, Frank Steiner
  • Published online:
    05 January 2012
    Print publication:
    15 December 2011
  • Hyperbolic geometry is a classical subject in pure mathematics which has exciting applications in theoretical physics. In this book leading experts introduce hyperbolic geometry and Maass waveforms and discuss applications in quantum chaos and cosmology. The book begins with an introductory chapter detailing the geometry of hyperbolic surfaces and includes numerous worked examples and exercises to give the reader a solid foundation for the rest of the book. In later chapters the classical version of Selberg's trace formula is derived in detail and transfer operators are developed as tools in the spectral theory of Laplace–Beltrami operators on modular surfaces. The computation of Maass waveforms and associated eigenvalues of the hyperbolic Laplacian on hyperbolic manifolds are also presented in a comprehensive way. This book will be valuable to graduate students and young researchers, as well as for those experienced scientists who want a detailed exposition of the subject.

How Groups Grow
  • Avinoam Mann
  • Published online:
    05 January 2012
    Print publication:
    15 December 2011
  • Growth of groups is an innovative new branch of group theory. This is the first book to introduce the subject from scratch. It begins with basic definitions and culminates in the seminal results of Gromov and Grigorchuk and more. The proof of Gromov's theorem on groups of polynomial growth is given in full, with the theory of asymptotic cones developed on the way. Grigorchuk's first and general groups are described, as well as the proof that they have intermediate growth, with explicit bounds, and their relationship to automorphisms of regular trees and finite automata. Also discussed are generating functions, groups of polynomial growth of low degrees, infinitely generated groups of local polynomial growth, the relation of intermediate growth to amenability and residual finiteness, and conjugacy class growth. This book is valuable reading for researchers, from graduate students onward, working in contemporary group theory.

Non-abelian Fundamental Groups and Iwasawa Theory
  • Edited by John Coates, Minhyong Kim, Florian Pop, Mohamed Saïdi, Peter Schneider
  • Published online:
    05 January 2012
    Print publication:
    15 December 2011
  • Number theory currently has at least three different perspectives on non-abelian phenomena: the Langlands programme, non-commutative Iwasawa theory and anabelian geometry. In the second half of 2009, experts from each of these three areas gathered at the Isaac Newton Institute in Cambridge to explain the latest advances in their research and to investigate possible avenues of future investigation and collaboration. For those in attendance, the overwhelming impression was that number theory is going through a tumultuous period of theory-building and experimentation analogous to the late 19th century, when many different special reciprocity laws of abelian class field theory were formulated before knowledge of the Artin–Takagi theory. Non-abelian Fundamental Groups and Iwasawa Theory presents the state of the art in theorems, conjectures and speculations that point the way towards a new synthesis, an as-yet-undiscovered unified theory of non-abelian arithmetic geometry.

Forcing with Random Variables and Proof Complexity
  • Jan Krajíček
  • Published online:
    05 November 2011
    Print publication:
    23 December 2010
  • This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.

Foundations of Computational Mathematics, Minneapolis 2002
  • Edited by Felipe Cucker, Ron DeVore, Peter Olver, Endre Süli
  • Published online:
    05 November 2011
    Print publication:
    25 March 2004
  • The Foundations of Computational Mathematics meetings are a platform for cross-fertilization between numerical analysis, mathematics and computer science. This volume, first published in 2004, contains the plenary presentations, given by some of the leading authorities in the world, and topics surveyed range from optimization to computer algebra, image processing to differential equations, quantum complexity to geometry. The volume will be essential reading for all those wishing to be informed of the state-of-the-art in computational mathematics.

Spaces of Kleinian Groups
  • Edited by Yair N. Minsky, Makoto Sakuma, Caroline Series
  • Published online:
    05 November 2011
    Print publication:
    19 June 2006
  • The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory, computer explorations and projective structures. Researchers in these and related areas will find much of interest here.

Fundamentals of Hyperbolic Manifolds
  • Selected Expositions
  • Edited by R. D. Canary, A. Marden, D. B. A. Epstein
  • Published online:
    05 November 2011
    Print publication:
    13 April 2006
  • Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

Variational Problems in Differential Geometry
  • Edited by Roger Bielawski, Kevin Houston, Martin Speight
  • Published online:
    05 November 2011
    Print publication:
    20 October 2011
  • The field of geometric variational problems is fast-moving and influential. These problems interact with many other areas of mathematics and have strong relevance to the study of integrable systems, mathematical physics and PDEs. The workshop 'Variational Problems in Differential Geometry' held in 2009 at the University of Leeds brought together internationally respected researchers from many different areas of the field. Topics discussed included recent developments in harmonic maps and morphisms, minimal and CMC surfaces, extremal Kähler metrics, the Yamabe functional, Hamiltonian variational problems and topics related to gauge theory and to the Ricci flow. These articles reflect the whole spectrum of the subject and cover not only current results, but also the varied methods and techniques used in attacking variational problems. With a mix of original and expository papers, this volume forms a valuable reference for more experienced researchers and an ideal introduction for graduate students and postdoctoral researchers.

Page 10 of 24