580pp Oct 2017
ISBN: 978-981-3207-32-5 (hardcover)
This book is a comprehensive treatise on the partial toroidal and minimal compactifications of the ordinary loci of PEL-type Shimura varieties and Kuga families, and on the canonical and subcanonical extensions of automorphic bundles. The results in this book serve as the logical foundation of several recent developments in the theory of p-adic automorphic forms; and of the author's work with Harris, Taylor, and Thorne on the construction of Galois representations without duality conditions, which is a major breakthrough in the Langlands program.
This book is important for active researchers and graduate students who need to understand the above-mentioned recent works, and is written with such users of the theory in mind, providing plenty of explanations and background materials, which should be helpful for people working in similar areas. It also contains precise internal and external references, and an index of notation and terminologies. These are useful for readers to quickly locate materials they need.
Introduction
Theory in Characteristic Zero
Flat Integral Models
Ordinary Loci
Partial Toroidal Compactifications
Partial Minimal Compactifications
Ordinary Kuga Families
Automorphic Bundles and Canonical Extensions
Readership: Graduate students and researchers who are interested in the applications of Shimura varieties in algebraic number theory.
800pp Jan 2018
ISBN: 978-981-3203-17-4 (hardcover)
ISBN: 978-981-3203-18-1 (softcover)
This volume is not only intended for mathematicians who deal with applications of functional analysis, but also for those having only a moderate background in mathematics in their areas of work.
The materials covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of mathematics applications, as well as the simplicity of presentation, differentiates this book from others. The method and style of presentation of materials make it digestible and easily understood by readers.
This second edition includes new and updated 300 examples and more than 500 problems to help readers understand and master the theories presented. In addition, necessary improvements for bringing the contents more up to date with current fundamental and applied developments in Chapters 1?10 were made. Now, Chapter 9 covers nonlinear and stochastic problems and Chapter 10, devoted to elements of numerical functional analysis, has been completely revised and broadened.
Preface to the Second Edition
Preface to the First Edition
Sets. Spaces. Functions
Measure Theory
Integrals
Topological Spaces
Spaces of Operators and Functionals
Linear Operators
Linear Operators in Hilbert Spaces
Spectral Theory of Linear Operators
Nonlinear and Stochastic Problems of Functional Analysis
Elements of Numerical Functional Analysis
Appendices, Bibliographical Notes
Readership: Undergraduate and graduate students as well as researchers in applied mathematics, and engineers.
200pp Feb 2018
ISBN: 978-1-78634-018-4 (hardcover)
This invaluable book provides both an introduction to the rudiments of perturbative string theory and a more detailed introduction to the more current topic of D-brane dynamics. The approach taken is pedagogical, with much of the technical detail streamlined. It is the concise nature of this rapid, but highly coherent, introduction to the subject that distinguishes it from other books on string theory or D-brane dynamics. The third edition has been revised to include a new chapter on the recent topic of string theory in electromagnetic fields. The material is based on courses in theoretical high-energy physics delivered by the author at various summer schools, so its level of appropriateness has been tested and has been resoundingly well received.
Preface to Second Edition
Preface to First Edition
A Brief History of String Theory
Classical String Theory
Quantization of the Bosonic String
Superstrings
Ramond?Ramond Charges and T-Duality
D-Branes and Gauge Theory
D-Brane Dynamics
Ramond?Ramond Couplings of D-Branes
String Theory in Electromagnetic Fields
Solutions to Exercises
Bibliography
Index
Readership: Graduate students and professionals in the field of high-energy or particle physics.
500pp Feb 2018
ISBN: 978-981-3209-96-1 (hardcover)
ISBN: 978-981-3209-97-8 (softcover)
This textbook introduces advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Topics covered include error analysis, computer arithmetic, solution of systems of linear equations, least squares problems, eigenvalue problems, polynomial interpolation and approximation, numerical differentiation and integration, nonlinear equations and ordinary differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the MATLAB programming language. This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.
Preliminaries:
What is Numerical Analysis?
Numerical Linear Algebra:
Methods for Systems of Linear Equations
Least Squares Problems
Eigenvalue Problems
Data Fitting and Function Approximation:
Polynomial Interpolation
Approximation of Functions
Differentiation and Integration
Nonlinear and Differential Equations:
Zeros of Nonlinear Functions
Initial Value Problems
Two-Point Boundary Value Problems
Appendices:
Review of Calculus
Review of Linear Algebra
Readership: Advanced undergraduate and graduate students in numerical analysis, approximations and expansions, linear and multilinear algebra/matrix theory and ordinary differential equations.