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The theory of transformation groups is a key mathematical concept, and studies symmetries of various mathematical objects such as topological spaces, manifolds, polyhedra and function spaces. 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.

In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

This collection of research and survey papers sets out the theory of hidden Markov processes, in particular addressing a central problem of the subject: computation of the Shannon entropy rate of an HMP. Connections are drawn between approaches from various disciplines, whilst recent research results and open problems are described.

This collection of articles brings the researcher up to date with recent applications of logic, specifically model theory, to conjectures associated with those of Manin-Mumford and Andre-Oort. Originating from a short course, it combines original papers with background articles on related topics.

This book consists of nine survey papers by internationally renowned mathematicians. It will be of interest to researchers in combinatorics, from graduate students who want an overview of several areas to advanced researchers who want to have an in-depth analysis of recent developments.

This book comprises a collection of papers from leading researchers in the fields of word problems in algebra and geometric group theory. The papers cover a wide range of topics in algebra, representing a timely record of recent work and providing an indication of the key areas of future development.

This first volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Gerhard Hiss and Volodymyr Nekrashevych, survey the latest developments in algebra.

This second volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Eammon O'Brien, Mark Sapir and Dan Segal, survey the latest developments in algebra.

This volume contains articles based on the invited lectures given at the 23rd British Combinatorial Conference, held in July 2011 at the University of Exeter. Each article surveys an area of current research in combinatorial mathematics and will be invaluable to anyone wishing to keep abreast of modern developments.

This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry. It contains articles by K. Altmann, A. V. Pukhlikov, A. R. Iano-Fletcher, A. Corti, and M. Reid.

This book comprises a collection of papers from a conference on Galois theory, bringing together articles from leading experts in the field. Topics are centred around the Inverse Galois Problem, covering the full range of methods and approaches in this area. Invaluable for all whose research involves Galois theory.

This volume, first published in 2000, contains a collection of survey papers by leading researchers covering a wide variety of recent developments in the interactions between descriptive set theory and various aspects of the theory of dynamical systems. It will be of interest to graduate students and researchers working in either of these areas.

A comprehensive introduction to the subject suitable for graduate students and researchers. This book is also an up-to-date survey of the current state of the art and thus will serve as a valuable reference for specialists in the field.

This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.

Quantum chaos and cosmology are areas of theoretical physics where models involving hyperbolic manifolds and the spectral theory of Maass waveforms have exciting applications. In this book leading experts provide a valuable exposition of hyperbolic geometry and its applications to graduate students and researchers.

This comprehensive book describes modern methods in the analysis of reduced models of Bose-Einstein condensation in periodic lattices. Aimed at researchers and graduate students working in applied mathematics and physical sciences where nonlinear waves arise, its unique focus is on localized nonlinear waves in periodic potentials and lattices.

Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 1, which unite the several viewpoints and applications, will prove invaluable.

This complete introduction to the study of arithmetic differential operators over the p-adic integers offers graduate students and researchers an accessible guide to this novel and promising area of mathematics. It starts with the basics and is accessible to anyone with a basic grasp of algebraic number theory.

This volume contains the proceedings of the 18th British Combinatorial Conference, held in 2001. The papers contained here are from the invited speakers and are thus of a quality befitting the event. This book will be a valuable reference both for researchers and graduate students in a variety of branches of combinatorics.

Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.

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.

This book contains papers given at the International Singularity Conference held in 1991 at Lille. Research workers in singularity theory or related subjects will find that this book contains a wealth of valuable information.

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.