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Quantum Groups and Lie Theory
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Andrew Pressley (Editor), J W S Cassels (Editor), N J Hitchin (Editor)
Since its genesis in the early 1980s, the subject of quantum groups has grown rapidly. By the late 1990s most of the foundational issues had been resolved and many of the outstanding problems clearly formulated. To take stock and to discuss the most fruitful directions for future research many of the world's leading figures in this area met at the ...
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Maximal Cohen-Macaulay Modules Over Cohen-Macaulay Rings
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Yuji Yoshino, J W S Cassels (Editor), N J Hitchin (Editor)
The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.
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Surveys in Modern Mathematics
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Yulij Ilyashenko (Editor), J W S Cassels (Editor), N J Hitchin (Editor)
This collection of articles from the Independent University of Moscow is derived from the Globus seminars held there. They are given by world authorities, from Russia and elsewhere, in various areas of mathematics and are designed to introduce graduate students to some of the most dynamic areas of mathematical research. The seminars aim to be ...
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Linear Algebraic Monoids
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Mohan S Putcha, N J Hitchin (Editor)
This book provides an introduction to the field of linear algebraic monoids. This subject represents a synthesis of ideas from the theory of algebraic groups, algebraic geometry, matrix theory and abstract semigroup theory. Since every representation of an algebraic group gives rise to an algebraic monoid, the objects of study do indeed arise ...
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Stochastic Partial Differential Equations
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Alison Etheridge (Editor), N J Hitchin (Editor)
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 ...
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Adams Memorial Symposium on Algebraic Topology: Volume 1
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Nigel Ray (Editor), Grant Walker (Editor), N J Hitchin (Editor)
J. Frank Adams had a profound influence on algebraic topology, and his works continue to shape its development. The International Symposium on Algebraic Topology held in Manchester during July 1990 was dedicated to his memory, and virtually all of the world's leading experts took part. This two volume work constitutes the proceedings of the ...
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Commutative Algebra
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James Thomson Knight, N J Hitchin (Editor)
This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and ...
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Synthetic Differential Geometry
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Anders Kock, N J Hitchin (Editor)
Synthetic Differential Geometry is a method of reasoning in differential geometry and differential calculus, based on the assumption of sufficiently many nilpotent elements on the number line, in particular numbers d such that d2=0. The use of nilpotent elements allows one to replace the limit processes of calculus by purely algebraic calculations ...
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Stable Modules and the D(2)-Problem
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F E a Johnson, J W S Cassels (Editor), N J Hitchin (Editor)
This book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems ...
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Surveys in Combinatorics
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Bridget Webb (Editor), N J Hitchin (Editor)
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 ...
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Classification Theory of Polarized Varieties
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Takao Fujita, J W S Cassels (Editor), N J Hitchin (Editor)
A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories ...
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Auslander-Buchweitz Approximations of Equivariant Modules
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Mitsuyasu Hashimoto, J W S Cassels (Editor), N J Hitchin (Editor)
This book focuses on homological aspects of equivariant modules. It presents a new homological approximation theory in the category of equivariant modules, unifying the Cohen-Macaulay approximations in commutative ring theory and Ringel's theory of delta-good approximations for quasi-hereditary algebras and reductive groups. The book provides a ...
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The Q-Schur Algebra
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Stephen Donkin, N J Hitchin (Editor)
This book focuses on the representation theory of q-Schur algebras and connections with the representation theory of Hecke algebras and quantum general linear groups. The aim is to present, from a unified point of view, quantum analogues of certain results known already in the classical case. The approach is largely homological, based on Kempf's ...
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Spectral Theory of Linear Differential Operators and Comparison Algebras
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Heinz Otto Cordes, N J Hitchin (Editor)
The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators. The first part of the book develops the necessary elements of the spectral theory of differential operators as well as the basic properties of elliptic second order differential operators. The ...
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Differentiable Germs and Catastrophes
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Th Brocker, N J Hitchin (Editor), L Lander (Translator)
These notes give a fairly elementary introduction to the local theory of differentiable mappings. Sard's Theorem and the Preparation Theorem of Malgrange and Mather are the basic tools and these are proved first. There follows a number of illustrations including: the local part of Whitney's Theorem on mappings of the plane into the plane, ...
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Number Theory: Paris 1992-3
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Sinnou David (Editor), J W S Cassels (Editor), N J Hitchin (Editor)
This is the fourteenth annual volume arising from the Seminaire de Theorie des Nombres de Paris. As with previous volumes the whole spectrum of number theory is discussed, with many contributions from some of the world's leading figures. The very latest research developments are covered and much of the work presented here will not be found ...
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Algebraic Topology: A Student's Guide
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J Frank Adams, G C Shepherd (Editor), N J Hitchin (Editor)
This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written accounts of each topic. Because a number of the sources are rather inaccessible to students, the ...
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Operator Algebras and Applications: Volume 2
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David E Evans, N J Hitchin (Editor), Masamichi Takesaki (Editor)
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.
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Interaction Models
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Norman L Biggs, N J Hitchin (Editor)
This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt ...
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Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces
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N J Hitchin, G B Segal, R S Ward
This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and ...
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Surveys in Combinatorics, 1993
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Keith Walker (Editor), N J Hitchin (Editor)
This volume comprises the invited lectures given at the 14th British Combinatorial Conference. The lectures survey many topical areas of current research activity in combinatorics and its applications, and also provide a valuable overview of the subject, for both mathematicians and computer scientists.
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Sheaf Theory
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B R Tennison, N J Hitchin (Editor)
Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. It finds its main applications in topology and modern algebraic geometry where it has been used as a tool for solving, with great success, several long-standing problems. This text is based ...
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Characters and Automorphism Groups of Compact Riemann Surfaces
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Thomas Breuer, N J Hitchin (Editor)
This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as factor groups of Fuchsian groups. The author uses modern methods from computational group theory and representation theory, providing classifications of all automorphism groups up to genus 48. The book also classifies the ordinary characters for ...
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Quadratic Forms with Applications to Algebraic Geometry and Topology
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Albrecht Pfister, J W S Cassels (Editor), N J Hitchin (Editor)
This volume has grown out of lectures given by Professor Pfister over many years. The emphasis here is placed on results about quadratic forms that give rise to interconnections between number theory, algebra, algebraic geometry and topology. Topics discussed include Hilbert's 17th problem, the Tsen-Lang theory of quasi algebraically closed fields ...
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Brownian Motion, Hardy Spaces and Bounded Mean Oscillation
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Karl Endel Petersen, J W S Cassels (Editor), N J Hitchin (Editor)
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 ...
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