Bücher der Reihe London Mathematical Society Lecture Note Series

With a mix of expository and original papers this volume is an excellent reference for experienced researchers in geometric variational problems, as well as an ideal introduction for graduate students. It presents all the varied methods and techniques used in attacking geometric variational problems and includes many up-to-date results.

This book introduces the subject of the growth of groups from scratch, starting with basic definitions and culminating in the seminal results of Gromov and Grigorchuk and more. It is valuable reading for researchers from graduate students up who want to be acquainted with contemporary group theory.

The 400-year-old Kepler conjecture about sphere packings is the oldest problem in discrete geometry. In this book, readers will learn about it through a proof that is much more accessible than the original proof of the theorem.

The powerful and far-reaching concept of reversibility is treated for the first time in book form. The authors establish basic principles of reversibility and demonstrate its impact in group theory, geometry, complex analysis and number theory, while describing open research problems throughout. Accessible at the advanced undergraduate level and above.

A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.

Many issues of global importance reveal an urgent need for a new generation trained to understand the mathematics of complex systems. This book presents the essential mathematical aspects of complexity science, suitable for advanced undergraduate/masters-level students and researchers in complexity science and related areas. Includes plentiful examples and real-world applications.

The CDC conjecture (and its numerous variants) is considered one of the major open problems in graph theory. This up-to-date overview of the subject contains all of the techniques, methods and results developed since the 1940s to help mathematicians and computer scientists still working towards a solution.

An account of a significant body of recent work that resolves some long-standing mysteries concerning special values of the Riemann zeta function. It brings together many important results from K-theory, motivic cohomology, and Iwasawa theory, accessible at graduate level and above.

This accessible volume presents articles by leading researchers on different approaches to extension theory and spectral theory by means of the recent notions of boundary triplets and relations. These new operator-theoretic methods for boundary value problems will appeal to a wide range of researchers, students and professionals.

A complete introduction to the theory of variational inequalities with emphasis on the modelling and analysis of contact processes. It represents an invaluable resource for graduate students and practitioners in the theory of contact mechanics. The text contains all the prerequisite mathematical material needed for the analysis.

This volume contains a selection of survey articles and original research papers concerned with the rigorous mathematical theory of fluid mechanics, written by leading researchers. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Schur-Weyl duality has had a profound influence over many areas of mathematics. This text is original in presenting an algebraic approach to the theory in the quantum affine case. Three levels of duality are investigated making this text ideal for researchers and graduate students who wish to master the theory.

The biennial meetings at Sao Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to topics in both pure and applied mathematics. This volume brings together surveys and recent work from the tenth Sao Carlos meeting.

Within algebraic topology, the prominent role of multiplicative cohomology theories has led to a great deal of foundational research on ring spectra and in the 1990s this gave rise to significant new approaches to constructing categories of spectra and ring-like objects in them. These results are presented in this book.

The famous theorem of Feit and Thompson states that every group of odd order is solvable. The first part of the proof appeared in Bender and Glauberman's Local Analysis for the Odd Order Theorem. This book, first published in 2000, provides the character-theoretic second part and thus completes the proof.

This book, first published in 2000, focuses on homological aspects of equivariant modules and discusses interactions between commutative ring theory and representation theory. The book aims to unify two important examples of Auslander-Buchweitz approximations in these areas of algebra. It is primarily aimed at researchers but will also be suitable for graduate students.

Perturbation of the boundary is a rather neglected topic in the study of PDEs for two main reasons. First, on the surface it appears trivial, merely a change of variables and an application of the chain rule. Second, carrying out such a change of variables frequently results in long and difficult calculations. In this book, first published in 2005, the author carefully discusses a calculus that allows the computational morass to be bypassed, and he goes on to develop more general forms of standard theorems, which help answer a wide range of problems involving boundary perturbations. Many examples are presented to demonstrate the usefulness of the author's approach, while on the other hand many tantalizing open questions remain. Anyone whose research involves PDEs will find something of interest in this book.

This accessible volume arises from a series of intensive mathematics workshops where prominent set theorists give one-day lectures that focus on important new directions, methods, tools and results. A wide range of researchers and graduate students will benefit from the material within, which is aimed at non-experts.

A self-contained treatment of the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The book functions as both a useful reference for researchers, and a graduate textbook with plenty of examples and several exercises.

Moduli theory represents a significant topic of modern mathematical research with strong connections to many areas of mathematics (including geometry, topology and number theory) and other disciplines such as theoretical physics. This book presents articles on both fundamental material and advanced research topics, accessible at the graduate level and above.

Focusing on the role that automorphisms and equivalence relations play in the algebraic theory of minimal sets provides an original treatment of some key aspects of abstract topological dynamics. Such an approach is presented in this lucid and self-contained book, leading to simpler proofs of classical results, as well as providing motivation for further study. Minimal flows on compact Hausdorff spaces are studied as icers on the universal minimal flow M. The group of the icer representing a minimal flow is defined as a subgroup of the automorphism group G of M, and icers are constructed explicitly as relative products using subgroups of G. Many classical results are then obtained by examining the structure of the icers on M, including a proof of the Furstenberg structure theorem for distal extensions. This book is designed as both a guide for graduate students, and a source of interesting new ideas for researchers.

A collection of introductory lecture notes and research papers on optimal transportation and its interactions with analysis, geometry, PDE and probability. Both fundamental and advanced aspects of the theory are covered, as well as applications to urban planning and economics. A valuable resource for graduate students and researchers.

This collection, the first of two volumes arising from an LMS-EPSRC Durham Symposium, explores the importance of automorphic forms and Galois representations in number theory. The expository articles and research papers within cover recent progress in anabelian geometry, p-adic Hodge theory, the Langlands program, and p-adic methods in number theory.

This collection, the second of two volumes arising from an LMS-EPSRC Durham Symposium, explores the importance of automorphic forms and Galois representations in number theory. The expository articles and research papers within cover recent progress in anabelian geometry, p-adic Hodge theory, the Langlands program, and p-adic methods in number theory.

In this proceedings volume leading authorities describe the state of the art in number theory, particularly Diophantine and arithmetic geometry. The book gives an excellent overview of the subject for graduate students and it is essential reading for researchers wishing to keep abreast of recent developments.

Hodge theory lies at the heart of modern algebraic geometry and this volume explores the many contexts in which it arises, including theoretical physics. The book will be of value to graduate students and seasoned researchers alike, for its mixture of cutting-edge research and expository articles.

Many geometrical features of manifolds and fibre bundles modelled on Frechet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Frechet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie group structure on the general linear group of a Frechet space, and the non-existence of an exponential map in a Frechet-Lie group. In this book, the authors describe in detail a new approach that overcomes many of these limitations by using projective limits of geometrical objects modelled on Banach spaces. It will appeal to researchers and graduate students from a variety of backgrounds with an interest in infinite-dimensional geometry. The book concludes with an appendix outlining potential applications and motivating future research.

Negative curvature arises in several mathematical areas, including geometry, topology, dynamics, and number theory. This volume contains survey articles around this common theme, which should help mathematicians interested in transitioning between these areas, as well as graduate students entering this interdisciplinary subject.

This survey volume provides an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. It serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

The theory of D-modules applies to many areas, including linear PDEs, group representation, algebraic geometry and mathematical physics. This book is the first devoted specifically to the most important variety, holonomic D-modules. It provides a complete unified treatment of the theory of holonomic D-modules, both regular and irregular.