Proceedings of Symposia in Pure Mathematics, Volume: 85
2012; approx. 479 pp; hardcover
ISBN-13: 978-0-8218-7295-6
Expected publication date is November 30, 2012.
The nature of interactions between mathematicians and physicists has been thoroughly transformed in recent years. String theory and quantum field theory have contributed a series of profound ideas that gave rise to entirely new mathematical fields and revitalized older ones. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. A large and rapidly growing number of both mathematicians and physicists are working at the string-theoretic interface between the two academic fields.
Plenary talks
M. Aganagic and S. Shakirov -- Refined Chern-Simons theory and knot homology
P. S. Aspinwall and M. R. Plesser -- Elusive worldsheet instantons in heterotic string compactifications
M. C. N. Cheng and J. F. R. Duncan -- The largest Mathieu group and (mock) automorphic forms
R. Donagi, J. Guffin, S. Katz, and E. Sharpe -- (0,2) quantum cohomology
M. R. Douglas -- Foundations of quantum field theory
S. Gukov and M. Sto?i? -- Homological algebra of knots and BPS states
M. Marcolli -- Motivic structures in quantum field theory
G. W. Moore and Y. Tachikawa -- On 2d TQFTs whose values are holomorphic symplectic varieties
Y. Ruan -- The Witten equation and the geometry of the Landau-Ginzburg model
L.-S. Tseng and S.-T. Yau -- Non-Kahler Calabi-Yau manifolds
S. Schafer-Nameki -- F-theory GUTs: Global aspects and phenomenology
M. Wijnholt -- Higgs bundles and string phenomenology
Contributed talks
D. Baraglia -- Topological T-duality with monodromy
N. Behr and S. Fredenhagen -- Variable transformation defects
E. A. Bergshoeff and F. Riccioni -- The D-brane U-scan
N. Carqueville and M. M. Kay -- An invitation to algebraic topological string theory
A. Francis, T. Jarvis, D. Johnson, and R. Suggs -- Landau-Ginzburg mirror symmetry for orbifolded Frobenius algebras
J. Fullwood and M. van Hoeij -- On Hirzebruch invariants of elliptic fibrations
S. Grigorian -- G2-structure deformations and warped products
M. Hamanaka -- Non-commutative solitons and quasi-determinants
B. Jurke -- Computing cohomology on toric varieties
T. Kragh -- Fibrancy of symplectic homology in cotangent bundles
D. Pomerleano -- Curved string topology and tangential Fukaya categories
T. Rahn -- Target space dualities of heterotic grand unified theories
F. F. Ruffino -- Freed-Witten anomaly and D-brane gauge theories
J. Seo -- Singularity structure and massless dyons of pure Seiberg-Witten theories with SU and Sp gauge groups
A. Sheshmani -- An introduction to the theory of higher rank stable pairs and virtual localization
N. Sibilla -- HMS for punctured tori and categorical mapping class group actions
J. Yagi -- Vanishing chiral algebras and Hohn-Stolz conjecture
Mathematical Surveys and Monographs, Volume: 184
2012; approx. 169 pp; hardcover
ISBN-13: 978-0-8218-9086-8
Expected publication date is December 23, 2012.
This book focuses on gathering the numerous properties and many different connections with various topics in geometric function theory that quasidisks possess. A quasidisk is the image of a disk under a quasiconformal mapping of the Riemann sphere. In 1981 Frederick W. Gehring gave a short course of six lectures on this topic in Montreal and his lecture notes "Characteristic Properties of Quasidisks" were published by the University Press of the University of Montreal. The notes became quite popular and within the next decade the number of characterizing properties of quasidisks and their ramifications increased tremendously. In the late 1990s Gehring and Hag decided to write an expanded version of the Montreal notes. At three times the size of the original notes, it turned into much more than just an extended version. New topics include two-sided criteria. The text will be a valuable resource for current and future researchers in various branches of analysis and geometry, and with its clear and elegant exposition the book can also serve as a text for a graduate course on selected topics in function theory.
Properties of quasidisks
Preliminaries
Geometric properties
Conformal invariants
Injectivity criteria
Criteria for extension
Two-sided criteria
Miscellaneous properties
Some proofs of these properties
First series of implications
Second series of implications
Third series of implications
Fourth series of implications
Bibliography
Index
AMS Chelsea Publishing, Volume: 375
2012; 573 pp; hardcover
ISBN-13: 978-0-8218-5349-8
Expected publication date is December 20, 2012.
This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
Graduate students and research mathematicians interested in formal groups and their applications in other areas of mathematics.
Methods for constructing one-dimensional formal groups
Methods for constructing higher dimensional formal group laws
Curves, p-typical formal group laws, and lots of Witt vectors
Homomorphisms, endomorphisms, and the classification of formal groups by power series methods
Cartier-Dieudonne modules
Applications of formal groups in algebraic topology, number theory, and algebraic geometry
Formal groups and bialgebras
On power series rings
Brief notes on further applications of formal group (law) theory
Bibliography
Notation
Index
Contemporary Mathematics, Volume: 581
2012; 285 pp; softcover
ISBN-13: 978-0-8218-6921-5
Expected publication date is December 1, 2012.
This volume is based on the AMS Special Session on Harmonic Analysis and Partial Differential Equations and the AMS Special Session on Nonlinear Analysis of Partial Differential Equations, both held March 12-13, 2011, at Georgia Southern University, Statesboro, Georgia, as well as the JAMI Conference on Analysis of PDEs, held March 21-25, 2011, at Johns Hopkins University, Baltimore, Maryland. These conferences all concentrated on problems of current interest in harmonic analysis and PDE, with emphasis on the interaction between them.
This volume consists of invited expositions as well as research papers that address prospects of the recent significant development in the field of analysis and PDE. The central topics mainly focused on using Fourier, spectral and geometrical methods to treat wellposedness, scattering and stability problems in PDE, including dispersive type evolution equations, higher-order systems and Sobolev spaces theory that arise in aspects of mathematical physics.
The study of all these problems involves state-of-the-art techniques and approaches that have been used and developed in the last decade. The interrelationship between the theory and the tools reflects the richness and deep connections between various subjects in both classical and modern analysis.
Graduate students and research mathematicians interested in analysis and PDE.
Contemporary Mathematics, Volume: 582
2012; 199 pp; softcover
ISBN-13: 978-0-8218-7563-6
Expected publication date is December 2, 2012.
This volume contains the proceedings of the AMS Special Session on Computational Algebra, Groups, and Applications, held April 30-May 1, 2011, at the University of Nevada, Las Vegas, Nevada, and the AMS Special Session on the Mathematical Aspects of Cryptography and Cyber Security, held September 10-11, 2011, at Cornell University, Ithaca, New York.
Over the past twenty years combinatorial and infinite group theory has been energized by three developments: the emergence of geometric and asymptotic group theory, the development of algebraic geometry over groups leading to the solution of the Tarski problems, and the development of group-based cryptography. These three areas in turn have had an impact on computational algebra and complexity theory.
The papers in this volume, both survey and research, exhibit the tremendous vitality that is at the heart of group theory in the beginning of the twenty-first century as well as the diversity of interests in the field.
Graduate students and research mathematicians interested in combinatorial and computational group theory and their applications to cryptography.
Pure and Applied Undergraduate Texts, Volume: 19
2012; 760 pp; hardcover
ISBN-13: 978-0-8218-9135-3
Expected publication date is January 12, 2013.
This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course.
The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimensions. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems.
The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets.
In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book.
This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations.
Undergraduate and graduate students interested in dynamical systems.
Systems of nonlinear differential equations
Geometric approach to differential equations
Linear systems
The flow: Solutions of nonlinear equations
Phase portraits with emphasis on fixed points
Phase portraits using Scalar functions
Periodic orbits
Chaotic attractors
Iteration of functions
Iteration of functions as dynamics
Periodic points of one-dimensional maps
Itineraries for one-dimensional maps
Invariant sets for one-dimensional maps
Periodic points of higher dimensional maps
Invariant sets for higher dimensional maps
Fractals
Background and terminology
Generic properties
Bibliography
Index
.
Graduate Studies in Mathematics, Volume: 143
2013; approx. 250 pp; hardcover
ISBN-13: 978-0-8218-8771-4
Expected publication date is January 25, 2013.
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations.
The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra.
The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
Graduate students interested in functional analysis and partial differential equations.
Introduction
Banach spaces
Spaces of continuous functions
Bounded linear operators
Hilbert spaces
Compact operators on a Hilbert space
Semigroups of linear operators
Sobolev spaces
Linear partial differential equations
Background material
Summary of notation
Bibliography
Index