Contemporary Mathematics, Volume: 430
2007; 145 pp; softcover
ISBN-10: 0-8218-3869-5
ISBN-13: 978-0-8218-3869-3
The book contains papers by participants of the Chapel Hill Ergodic Theory Workshops organized in February 2004, 2005, and 2006. Topics covered by these papers illustrate the interaction between ergodic theory and related fields such as harmonic analysis, number theory, and probability theory.
Readership
Graduate students and research mathematicians interested in ergodic theory.
Table of Contents
I. Assani -- Averages along cubes for not necessarily commuting m.p.t.
I. Assani and M. Lin -- On the one-sided ergodic Hilbert transform
Z. Buczolich and R. D. Mauldin -- Concepts behind divergent ergodic averages along the squares
L. A. Bunimovich and A. Yurchenko -- Deterministic walk in Markov environments with constant rigidity
G. Cohen -- On random Fourier-Stieltjes transforms
J.-P. Conze and A. Raugi -- Limit theorems for sequential expanding dynamical systems on [0,1]
M. K. Roychowdhury -- {$m_n$}-odometer and the binary odometer are finitarily orbit equivalent
I. Assani -- Some open problems
AMS/IP Studies in Advanced Mathematics, Volume: 40
2007; 244 pp; hardcover
ISBN-10: 0-8218-4319-2
ISBN-13: 978-0-8218-4319-2
The theory of subRiemannian manifolds is closely related to Hamiltonian mechanics. In this book, the authors examine the properties and applications of subRiemannian manifolds that automatically satisfy the Heisenberg principle, which may be useful in quantum mechanics. In particular, the behavior of geodesics in this setting plays an important role in finding heat kernels and propagators for Schrodinger's equation. One of the novelties of this book is the introduction of techniques from complex Hamiltonian mechanics.
Readership
Graduate students and research mathematicians interested in sub-Riemannian geometry and connections to quantum mechanics.
Table of Contents
Graduate studies in Mathmatics, Volume: 83
2007; 312 pp; hardcover
ISBN-10: 0-8218-3319-7
ISBN-13: 978-0-8218-3319-3
The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.
Readership
Graduate students and research mathematicians interested in several complex variables and complex algebraic geometry.
Table of Contents
Graduate Studies in Mathematics, Volume: 84
2007; approx. 288 pp; hardcover
ISBN-10: 0-8218-4146-7
ISBN-13: 978-0-8218-4146-4
Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools.
Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications.
This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses.
Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques.
Readership
Graduate students and research mathematicians interested in functional analysis and applications, in particular to optimization.
Table of Contents
Cones
Cones in topological vector spaces
Yudin and pull-back cones
Krein operators
$\mathcal{K}$-lattices
The order extension of $L'$
Piecewise affine functions
Appendix: Linear topologies
Bibliography
Index
Mathematical Surveys and Monographs, Volume: 139
2007; 338 pp; hardcover
ISBN-10: 0-8218-4306-0
ISBN-13: 978-0-8218-4306-2
The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc.
The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory.
There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.
Readership
Graduate students and research mathematicians interested in algebraic geometry and coding theory.
Table of Contents
Codes
Curves
Curves over finite fields
Algebraic geometry codes
Summary of results and tables
Bibliography
List of names
Index
2007; 639 pp; hardcover
ISBN-10: 0-8218-4262-5
ISBN-13: 978-0-8218-4262-1
The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems (apart from some general comments at the beginning of each chapter). In the second part, a hint is given for each exercise, which contains the main idea necessary for the solution, but allows the reader to practice the techniques by completing the proof. In the third part, a full solution is provided for each problem.
This book will be useful to those students who intend to start research in graph theory, combinatorics or their applications, and for those researchers who feel that combinatorial techniques might help them with their work in other branches of mathematics, computer science, management science, electrical engineering and so on. For background, only the elements of linear algebra, group theory, probability and calculus are needed.
Readership
Graduate students and research mathematicians interested in graph theory, combinatorics, and their applications.
Table of Contents
Problems
Hints
Solutions
Dictionary of the combinatorial phrases and concepts used
Notation
Index of the abbreviations of textbooks and monographs
Subject index
Author index
Errata
Contemporary Mathematics, Volume: 432
2007; 229 pp; softcover
ISBN-10: 0-8218-4227-7
ISBN-13: 978-0-8218-4227-0
The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic manifolds, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields, such as algebraic geometry, mathematical physics, dynamics, geometric group theory, number theory, and topology. The triannual Ahlford-Bers colloquia serve as a venue to disseminate the relevant work to the wider mathematical community and bring the key participants together to ponder future directions in the field.
The present volume includes a wide range of articles in the fields central to this legacy. The majority of articles present new results, but there are expository articles as well.
Readership
Graduate students and research mathematicians interested in geometric function theory.
Table of Contents
J. W. Anderson, J. Aramoyona, and K. J. Shackleton -- Uniformly exponential growth and mapping class groups of surfaces
C. J. Bishop -- An $A_1$ weight not comparable with any quasiconformal Jacobian
M. Duchin -- Curvature, stretchiness, and dynamics
C. J. Earle -- Some special loci in the Siegel space of genus two
E. Fujikawa -- Another approach to the automorphism theorem for Teichmuller spaces
W. M. Goldman and R. A. Wentworth -- Energy of twisted harmonic maps of Riemann surfaces
P. Hasto, Z. Ibragimov, D. Minda, S. Ponnusamy, and S. Sahoo -- Isometries of some hyperbolic-type path metrics, and the hyperbolic medial axis
J. Hu -- From left earthquakes to right
C. M. Judge -- Small eigenvalues and maximal laminations on complete surfaces of negative curvature
L. Keen and N. Lakic -- A generalized hyperbolic metric for plane domains
R. P. Kent, IV and C. J. Leininger -- Subgroups of mapping class groups from the geometrical viewpoint
Y.-H. Kim -- Determinants of Laplacians, quasifuchsian spaces, and holomorphic extensions of Laplacians
L. V. Kovalev and J. T. Tyson -- Hyperbolic and quasisymmetric structure of hyperspace
K. Matsuzaki -- A classification of the modular transformations of infinite dimensional Teichmuller spaces
M. Mirzakhani -- Random hyperbolic surfaces and measured laminations
S. Mitra -- Extensions of holomorphic motions to quasiconformal motions
R. Schul -- Analyst's traveling salesman theorems. A survey
R. A. Wentworth -- Energy of harmonic maps and Gardiner's formula