Part of London Mathematical Society Student Texts
DescriptionContentsResourcesCoursesAbout the Authors
Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988?92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.
Introduction
1. Background results
2. Cyclic cocycles and basic operators
3. Algebras of operators
4. GNS algebra
5. Geometrical examples
6. The algebra of noncommutative differential forms
7. Hodge decomposition and the Karoubi operator
8. Connections
9. Cocycles for a commutative algebra over a manifold
10. Cyclic cochains
11. Cyclic cohomology
12. Periodic cyclic homology
References
List of symbols
Index of notation
Subject index.
PUBLICATION PLANNED FOR: August 2020
FORMAT: HardbackISBN: 9781108479615
FORMAT: PaperbackISBN: 9781108790444
LENGTH: 328 pagesDIMENSIONS: 234 x 156 x 22 mmWEIGHT: 0.59kg
CONTAINS: 60 exercises
This long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics. The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments. Assuming no prior exposure to combinatorics, it explains the basic material for graduate-level students in mathematics and computer science. Optional more advanced material also makes it valuable as a research reference. Suitable for a one-year course or a one-semester introduction, this textbook prepares students to move on to more advanced material. It is organized to emphasize connections among the topics, and facilitate instruction, self-study, and research, with more than 2200 exercises (many accompanied by hints) at various levels of difficulty. Consistent notation and terminology are used throughout, allowing for a discussion of diverse topics in a unified language. The thorough bibliography, containing thousands of citations, makes this a valuable source for students and researchers alike.
Can be used as a text for a one-year sequence, or as a one-semester introduction leading to an advanced course, with a complete solutions manual available online for instructors
Contains more than 2200 exercises at various levels. Especially instructive, interesting, or valuable exercises are marked with a diamond symbol
Includes several thousand references (with pointers to pages where cited) and many exercises, theorems, and proofs that have not previously appeared in textbooks
PUBLICATION PLANNED FOR: August 2020
FORMAT: Hardback ISBN: 9781107058583
DIMENSIONS: 246 x 189 mmCONTAINS: 2200
Part of London Mathematical Society Lecture Note Series
Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.
Brings together applications of orthogonal polynomials to different areas of mathematics
Contains important, up-to-date material not currently available in book form
Highlights the diversity of the field
1. Exceptional Orthogonal Polynomials via Krall Discrete Polynomials Antonio J. Duran
2. A Brief Review of q-series Mourad E. H. Ismail
3. Applications of Spectral Theory to Special Functions Erik Koelink
4. Elliptic Hypergeometric Functions Hjalmar Rosengren
5. Combinatorics of Orthogonal Polynomials and their Moments Jiang Zeng.
PUBLICATION PLANNED FOR: December 2020
FORMAT: PaperbackISBN: 9781108821599
DIMENSIONS: 228 x 152 mmAVAILABILITY
Part of London Mathematical Society Student Texts
This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.
A sleek introduction to the theory of forcing, which allows even those who do not have any background in set theory to understand the subject
Devotes the second part of the book to contemporary topics in the theory of forcing, including open questions
Includes previously unpublished results in the theory of forcing
PUBLICATION PLANNED FOR: October 2020
FORMAT: HardbackISBN: 9781108420150
DIMENSIONS: 228 x 152 mm
Part of London Mathematical Society Lecture Note Series
The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kahler and Sasaki geometry.
Treats very recent developments in differential geometry, geometric analysis and differential topology
High-profile contributors cover an extraordinary breadth of topics in one volume
Clear exposition discussing recent, relevant results
PUBLICATION PLANNED FOR: January 2021
FORMAT: PaperbackISBN: 9781108812818
DIMENSIONS: 228 x 152 mm
Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding.
The first complete reference on the mathematics of origami
Of interest to professionals and students in mathematics, physics and engineering, as well as educators and origami enthusiasts
Contains more than 180 figures to illustrate the constructions described
Numerous 'diversions' provide jumping-off points for readers to deepen and broaden their understanding
PUBLICATION PLANNED FOR: January 2021
FORMAT: HardbackISBN: 9781108478724
FORMAT: PaperbackISBN: 9781108746113
DIMENSIONS: 244 x 170 mm
CONTAINS: 22 b/w illus. 165 colour illus. 2 tables
Part of Cambridge Tracts in Mathematics
The Assouad dimension is a notion of dimension in fractal geometry that has been the subject of much interest in recent years. This book, written by a world expert on the topic, is the first thorough account of the Assouad dimension and its many variants and applications in fractal geometry and beyond. It places the theory of the Assouad dimension in context among up-to-date treatments of many key advances in fractal geometry, while also emphasising its diverse connections with areas of mathematics including number theory, dynamical systems, harmonic analysis, and probability theory. A final chapter detailing open problems and future directions for research brings readers to the cutting edge of this exciting field. This book will be an indispensable part of the modern fractal geometer's library and a valuable resource for pure mathematicians interested in the beauty and many applications of the Assouad dimension.
The first thorough treatment of the Assouad dimension in the context of fractal geometry
Provides a systematic study using consistent notation of the many variants of the Assouad dimension
Discusses several key applications to other fields: number theory, dynamical systems, harmonic analysis, and probability theory
PUBLICATION PLANNED FOR: December 2020
FORMAT: Hardback ISBN: 9781108478656
DIMENSIONS: 228 x 152 mm