ISBN 978-3-319-27369-3
Due: February 11, 2016
The first comprehensive presentation of the whole topic of curves, Jacobians, abelian varieties and proper analytic group varieties over non-archimedian fields
Introduces the powerful tools of formal algebraic geometry as used in arithmetic geometry
The book builds a bridge to the more advanced research on the moduli of degeneration of abelian varieties which is a central object in arithmetic geometry
This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail.
Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
ISBN 978-3-319-27976-3
Due: February 28, 2016
Acts as a perfect book for Graduate-level Fixed-Point Theory
Covers all major Fixed-Point theories in detail
Introduces Fixed-Point Theory and correlates it to several topics in Analysis
This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory.
The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll?Nardzewski surrounding fixed points for families of affine maps.
Joel H. Shapiro is an adjunct professor of Mathematics and Statistics at Portland State University. He received his PhD from the University of Michigan.
This book grew out of a set of lecture notes on gravitational Chern?Simons (CS) theories developed over the past decade for several schools and different audiences including graduate students and researchers.
CS theories are gauge-invariant theories that can include gravity consistently. They are only defined in odd dimensions and represent a very special class of theories in the Lovelock family. Lovelock gravitation theories are the natural extensions of General Relativity for dimensions greater than four that yield second-order field equations for the metric. These theories also admit local supersymmetric extensions where supersymmetry is an off-shell symmetry of the action, as in a standard gauge theory.
Apart from the arguments of mathematical elegance and beauty, the gravitational CS actions are exceptionally endowed with physical attributes that suggest the viability of a quantum interpretation. CS theories are gauge-invariant, scale-invariant and background independent; they have no dimensional coupling constants. All constants in the Lagrangian are fixed rational coefficients that cannot be adjusted without destroying gauge invariance. This exceptional status of CS systems makes them classically interesting to study, and quantum mechanically intriguing and promising.
The Quantum Gravity Puzzle
Geometry: General Overview
First Order Gravitation Theory
Gravity in Higher Dimensions
Chern-Simons Gravities
Additional Features of Chern?Simons Gravity
Black Holes, Particles and Branes
Supersymmetry and Supergravity
Chern?Simons Supergravities
Inonu?Wigner Contractions and Its Extensions
Unconventional Supersymmetries
Local Supersymmetry without Gravitini
Concluding Remarks
Readership: This book provides an introduction to Chern-Simons (super) gravity theories accessible for physics as well as mathematics graduate students and researchers.
200pp Mar 2016
ISBN: 978-981-4730-93-8 (hardcover)
This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
What is Linear Algebra
Introduction to Complex Numbers
The Fundamental Theorem of Algebra and Factoring Polynomials
Vector Spaces
Span and Bases
Linear Maps
Eigenvalues and Eigenvectors
Permutations and the Determinant of a Square Matrix
Inner Product Spaces
Change of Bases
The Spectral Theorem for Normal Linear Maps
Appendices:
Supplementary Notes on Matrices and Linear Systems
The Language of Sets and Functions
Summary of Algebraic Structures Encountered
Some Common Math Symbols and Abbreviations
Readership: Undergraduates in mathematics.
208pp Jan 2016
ISBN: 978-981-4730-35-8 (hardcover)
ISBN: 978-981-4723-77-0 (softcover)