Bøker i London Mathematical Society Lecture Note Series-serien

The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the mid-nineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In this book are developed the intriguing and surprising connections that the subject has with descriptive set theory. These have only been discovered recently and the authors present here this novel theory which leads to many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. In order to make the material accessible to logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as well as the relevant parts of descriptive set theory. Thus the book is essentially self-contained and will make an excellent introduction to the subject for graduate students and research workers in set theory and analysis.

This technique is used in the solution of boundary problems for partial differential equations. Its applications include the Dirac theory of quantum mechanics. The author discusses connections to the theory of C*-algebras and the relation of the hyperbolic theory to the propagation of maximal ideals.

These volumes contain selected papers presented at the international conference on group theory held in St Andrews in 1989. The themes of the conference were combinatorial and computational group theory; four leading group theorists (J. A. Green, N. D. Gupta, O. H. Kegel and J. G. Thompson) gave courses whose content is reproduced here.

This volume contains the invited papers presented at the British Combinatorial Conference, held at the University of Surrey in July 1991. The papers will provide excellent reading for all those interested in combinatorics.

Boolean function complexity has seen exciting advances in the last few years. It is a long established area of discrete mathematics which uses combinatorial and occasionally algebraic methods.

A collection of expository surveys given by some distinguished mathematicians during the 1990 International Mathematical Congress.

In this book Professor Kempf gives an introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint. By taking this view he is able to give a clean and lucid account of the subject which will be easily accessible to all newcomers to algebraic varieties, graduate students or experts from other fields alike. Anyone who goes on to study schemes will find that this book is an ideal preparatory text.

This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author. These groups arise as the Grothendieck groups of modules and quadratic forms which are components of the K- and L-groups of polynomial extensions. They are important in the topology of non-compact manifolds such as Euclidean spaces, being the value groups for Whitehead torsion, the Siebemann end obstruction and the Wall finiteness and surgery obstructions. Some of the applications to topology are included, such as the obstruction theories for splitting homotopy equivalences and for fibering compact manifolds over the circle. Only elementary algebraic constructions are used, which are always motivated by topology. The material is accessible to a wide mathematical audience, especially graduate students and research workers in topology and algebra.

This is amongst the first books on the theory of prehomogeneous vector spaces, and represents the author's deep study of the subject.

This is a collection of thirty-five articles on covering topics such as finite projective spaces, generalized polygons, strongly regular graphs, diagram geometries, and polar spaces. Included here are articles from many of the leading practitioners in the field including, for the first time, several distinguished Russian mathematicians.

This two-volume book contains selected papers from the international conference 'Groups 1993 Galway/St Andrews' which was held at University College Galway in August 1993. The wealth and diversity of group theory is represented in these two volumes. Five main lecture courses were given at the conference. These were 'Geometry, Steinberg representations and complexity' by J. L. Alperin (Chicago), 'Rickard equivalences and block theory' by M. Broue (ENS, Paris), 'Cohomological finiteness conditions' by P. H. Kropholler (QMW, London), 'Counting finite index subgroups' by A. Lubotzky (Hebrew University, Jerusalem), 'Lie methods in group theory' by E. I. Zel'manov (University of Wisconsin at Madison). Articles based on their lectures, in one case co-authored, form a substantial part of the Proceedings. Another main feature of the conference was a GAP workshop jointly run by J. Neubuser and M. Schonert (RWTH, Aachen). Two articles by Professor Neubuser, one co-authored, appear in the Proceedings. The other articles in the two volumes comprise both refereed survey and research articles contributed by other conference participants. As with the Proceedings of the earlier 'Groups-St Andrews' conferences it is hoped that the articles in these Proceedings will, with their many references, prove valuable both to experienced researchers and also to new postgraduates interested in group theory.

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 meeting held in 1994 on this topic and it brings together some of the world's best known authorities on stochastic partial differential equations.

These articles give an up-to-date overview of combinatorics that will be extremely useful to both mathematicians and computer scientists.

This book is aimed at graduate students and researchers who have some knowledge of subharmonic functions, or an interest in holomorphic approximation.

The 1993 Durham Symposium on Vector Bundles in Algebraic Geometry brought together some of the leading researchers in the field to explore further these interactions. This book is a collection of survey articles by the main speakers at the symposium and presents to the mathematical world an overview of the key areas of research involving vector bundles.

These proceedings give a state-of-the-art account of the area of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. This volume is an invaluable resource for any researcher in finite fields or related areas.

This book covers the whole spectrum of number theory, and is composed of contributions from some of the best specialists worldwide.

The James space J and the James tree space JT were constructed as counterexamples to several outstanding conjectures in Banach space theory. This book is a compendium of most of the known results about these spaces, frequently taken from the original sources, but presented in a unified and up to date fashion. Generalisations of J and JT are also discussed and other pathological Banach spaces are introduced. Specialists will welcome this book for its drawing together of classical material and recent results. Graduate students should also find that this book offers an excellent introduction to more advanced topics in Banach space theory.

Surveys recent interactions between model theory and algebra, notably group theory. Topics include automorphism groups of algebraically closed fields, aspects of model theory of various classes of groups, and model theory of pseudo-finite fields and of modules. Contains the first comprehensive survey of finite covers.

This volume examines finite geometries and designs, a key area in modern applicable mathematics. It includes state-of-the-art surveys from leading international mathematicians in their fields, and will be a useful reference for researchers in many aspects of combinatorics.

In recent years the application of random matrix techniques to analytic number theory has been responsible for major advances in this area of mathematics. The aim of this book is to provide the necessary grounding as well as to inform the reader of recent progress.

Contains up-to-date contributions from leading international figures in analytic number theory. Topics discussed include the theory of zeta functions, spectral theory of automorphic forms, classical problems in additive number theory such as the Goldbach conjecture, and Diophantine approximations and equations.

This book has its origins in the 1996 Durham Symposium on 'Galois representations in arithmetic algebraic geometry'. Included here are expositions of subjects on the interface between algebraic number theory and arithmetic algebraic geometry which have received substantial attention from many of the best known researchers in this field.

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.

Authoritative lectures from world experts on spectral theory and geometry, arising from a meeting held under the auspices of the ICMS in Edinburgh. Together they survey core material and go beyond to reach deeper results. For graduate students and experts alike, this book will be a highly useful resource.

A comprehensive and self-contained exposition of the algebro-geometric theory of singularities of plane curves, covering both its classical and its modern aspects and presenting new, previously unpublished results. This book will be useful as a reference text for researchers and is also suitable as a textbook for postgraduate courses.

This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.

Its self-contained presentation and 'do-it-yourself' approach makes this the perfect guide for graduate students wishing to access recent literature in the field of mathematical relativity. It introduces all of the key tools and concepts from Lorentzian geometry and provides complete elementary proofs. No previous knowledge of geometry is required.

Written to complement standard texts on commutative algebra, this short book gives complete and relatively easy proofs of important results, including the standard results involving localisation of formal smoothness (M. Andre) and localisation of complete intersections (L. Avramov), some important results of D. Popescu and Andre on regular homomorphisms, and some results from A. Grothendieck's EGA on smooth homomorphisms. The authors make extensive use of the Andre-Quillen homology of commutative algebras, but only up to dimension 2, which is easy to construct, and they deliberately avoid using simplicial methods. The book also serves as an accessible introduction to some advanced topics and techniques. The only prerequisites are a basic course in commutative algebra and the first definitions in homological algebra.

This edited volume contains a mixture of expository and current research material that illustrates the far-reaching impact of 'Monstrous Moonshine' on mathematics and theoretical physics and reflects the range of research activity that has stemmed from the Moonshine conjectures. Potential directions for future development are also discussed.