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This book classifies the maximal subgroups of finite classical groups in low dimension. It features previously unseen results and over 100 tables, making this an essential reference for researchers. It will appeal to graduate students as a textbook on finite simple groups, computational group theory (including Magma) and representation 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.

A collection of articles, written by leading experts, on cutting-edge aspects of algebraic geometry. Up-to-date research is presented in an expository manner, giving a comprehensive picture of current research in this thriving field. Essential reading for researchers and graduate students.

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.

Every four years, leading researchers gather to survey the latest developments in all aspects of group theory. This volume contains selected papers from the 2013 meeting, covering a wide spectrum of modern group theory.

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.

Aimed at both young and established researchers, this book covers several directions of current research lying at the interface between dynamics and analytic number theory. Leading experts present a wide range of topics, including homogeneous dynamics, Diophantine approximation, Ramsey theory, ergodic theory and combinatorics.

An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the connections with other branches of mathematics. Covering topics from growth and amenability of groups, Schroedinger operators, and Poisson boundaries, this book provides a valuable and up-to-date reference for both researchers and graduates.

This volume compiles notes from courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It provides an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity.

This volume summarizes exciting recent developments in geometric and cohomological group theory. It contains research articles and surveys that demonstrate connections with topology, analysis, algebra and logic. The book is an excellent entry point for new researchers and a useful reference work for experts.

The proceedings of the summer school, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. It contains surveys of the current state of the art as well as original research papers. It will therefore benefit both graduate students and researchers in this exciting area.

The nine articles in this book represent a timely snapshot of the state of the art in the different areas of combinatorics. They are written by leading experts in the field and provide expanded accounts of plenary seminars given at the British Combinatorial Conference in July 2017.

This clear and comprehensive book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry. It will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.

In this edited volume leaders in the field of partial differential equations present recent work and current open problems on topics in PDEs arising from geometry and physics. It will serve as a useful reference for researchers and is written in a manner that is accessible to graduate students.

This volume collects eleven peer-reviewed papers on recent developments at the interface of topology and geometric group theory. The authors have given particular attention to clear exposition, making the book especially useful for graduate students and mathematicians in other areas interested in gaining a taste of this rich and active field.