Matilde Marcolli, Massachusetts Institute of Technology, Cambridge, MA
Seiberg-Witten Gauge Theory
A publication of the Hindustan Book Agency.
Description
The newly developed field of Seiberg-Witten gauge theory has become a well-established part of the differential topology of four-manifolds and three-manifolds. This book offers an introduction and an up-to-date review of the state of current research.
The first part of the book collects some preliminary notions and then gives an introduction of Seiberg-Witten theory of four-dimensional manifolds. In the second part, the author introduces the dimensional reduction and uses it to describe Seiberg-Witten in three-dimensional manifolds. In both parts, the Seiberg-Witten equations are derived, the moduli spaces of solutions are constructed, and the corresponding invariants of manifolds are
introduced.
In the third part, the author gives an overview of geometric and topological results obtained via Seiberg-Witten theory. Through all these parts of the book, Seiberg-Witten gauge theory is considered as a completely self-contained subject and no a priori knowledge of Donaldson theory is assumed. In fact, all the sections that refer to Donaldson theory can be skipped, and this will not affect the comprehension of the remaining sections.
In the final part of the book, the author describes physical theories that are responsible for the emergence of this new piece of mathematics, the Seiberg-Witten theory.
Contents
Introduction
Seiberg-Witten on four-manifolds
Seiberg-Witten on three-manifolds
Topology and geometry
Seiberg-Witten and physics
Appendix: a bibliographical guide
Details:
Publisher: Hindustan Book Agency
Publication Year: 1999
ISBN: 81-85931-22-4
Paging: 228 pp.
Binding: Hardcover
A. Ramachandra Rao, Indian Statistical Institute, Calcutta, India,
P. Bhimasankaram, Indian Statistical Institute, Hyderabad, India
Linear Algebra: Second Edition
A publication of the Hindustan Book Agency.
Description
The vector space approach to the treatment of linear algebra is useful for geometric intuition leading to transparent proofs; it's also useful for generalization to infinite-dimensional spaces. The Indian School, led by Professors C. R. Rao and S. K. Mitra, successfully employed this approach. This book follows their approach and systematically develops the elementary parts of matrix theory, exploiting the properties of row and column
spaces of matrices.
Developments in linear algebra during the past few decades have brought into focus several techniques not included in basic texts, such as rank-factorization, generalized inverses, and singular value decomposition. These techniques are actually simple enough to be taught at the advanced undergraduate level. When properly used, they provide a better understanding of the topic and give simpler proofs, making the subject
more accessible to students.
This book explains these techniques. It is intended as a textbook for the advanced student of mathematics and/or statistics. It will also be useful for students of physics, computer science, engineering, operations research, and research scientists.
Contents
Preliminaries
Vector spaces
Algebra of matrices
Rank and inverse
Elementary operations and reduced forms
Linear equations
Determinants
Inner product and orthogonality
Eigenvalues
Quadratic forms
References
More hints and solutions
List of symbols
Index
Details:
Publication Year: 2000
ISBN: 81-85931-26-7
Paging: 414 pp.
Binding: Hardcover
Edited by:
Lei Guo, Chinese Academy of Sciences, Beijing, People's Republic of China,
Stephen S.-T. Yau, University of Illinois, Chicago, IL
Lectures on Systems, Control, and Information:
Lectures at the Morningside Center of Mathematics
Description
This volume presents lectures delivered at a workshop held at the Chinese Academy of Sciences (Bejing). The following articles are included: "Nonlinear Systems Control" by R. Brockett, "Adaptive Control of Discrete-Time Nonlinear Systems with Structural Uncertainties" by L.-L. Xie and L. Guo, "Networks and Learning" by P. R. Kumar, "Mathematical Aspects of the Power Control Problem in Mobile Communication Systems" by C. W. Sung and W. S. Wong, and "Brockett's Problem on Nonlinear Filtering Theory" by S. S.-T. Yau.
Basic concepts and current research are both presented in this book. The volume offers a comprehensive and easy-to-follow account of many fundamental issues in this diverse field. It would be a suitable text for a graduate course on wireless communication.
Contents
R. Brockett -- Beijing lectures on nonlinear control systems
L.-L. Xie and L. Guo -- Adaptive control of discrete-time nonlinear systems with structural uncertainties
P. R. Kumar -- Networks and learning
C. W. Sung and W. S. Wong -- Mathematical aspects of the power control problem in mobile communication systems
S. S.-T. Yau -- Brockett's problem on nonlinear filtering theory
Details:
Series: AMS/IP Studies in Advanced Mathematics, Volume: 17
Publication Year: 2000
ISBN: 0-8218-2009-5
Paging: 212 pp.
Binding: Softcover
Edited by:
Salvador Perez-Esteva, Universidad Nacional Autonoma de Mexico,
Carlos Villegas-Blas, Universidad Nacional Autonoma de Mexico,
First Summer School in Analysis and Mathematical Physics:
Quantization, the Segal-Bargmann Transform and Semiclassical Analysis
Description
The first Summer School of Analysis and Mathematical Physics of the Universidad Nacional Aut?noma de M?xico (Cuernavaca) offered graduate and advanced undergraduate students courses on modern topics in the overlap between analysis and physics. This volume contains the expanded notes from the lectures by Brian Hall, Alejandro Uribe, and David Borthwick. The articles introduce readers to mathematical methods of classical and quantum mechanics and the link between these two theories: quantization and semiclassical analysis. Hall writes about holomorphic methods in analysis and mathematical physics and includes exercises. Uribe's lectures covered trace formulae, in particular asymptotic behavior and the relationship between the asymptotics and the geometric properties of the classical system. Borthwick presents an introduction to Kohler quantization, including the moment map, the orbit method, and symmetry and reduction. The exposition in the entire volume is geared to introducing graduate students with a basic knowledge of mathematics into areas of active research.
This volume is a joint publication of the American Mathematical Society and the Sociedad Matematica Mexicana. Members of the SMM may order directly from the AMS at the AMS member price.
Contents
B. C. Hall -- Holomorphic methods in analysis and mathematical physics
A. Uribe -- Trace formulae
D. Borthwick -- Introduction to K?hler quantization
Details:
Series: Contemporary Mathematics, Volume: 260
Publication Year: 2000
ISBN: 0-8218-2115-6
Paging: 132 pp.
Binding: Softcover
Alison M. Etheridge, University of Oxford, England
An Introduction to Superprocesses
Description
Over the past 20 years, the study of superprocesses has expanded into a major industry and can now be regarded as a central theme in modern probability theory. This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis.
A variety of different approaches to the superprocesses emerged over the last ten years. Yet no one approach superseded any others. In this book, readers are exposed to a number of different ways of thinking about the processes, and each is used to motivate some key results. The emphasis is on why results are true rather than on rigorous proof. Specific results are given, including extensive references to current literature
for their general form.
Contents
Superprocesses as diffusion approximations
Qualitative behaviour I
The Le Gall representation
The relationship between our two classes of superprocesses
A countable representation
Qualitative behaviour II
Introducing interactions
Superprocesses and partial differential equations
Some more interacting models
Appendix
Bibliography
Index of notation
Index
Details:
Series: University Lecture Series, Volume: 20
Publication Year: 2000
ISBN: 0-8218-2706-5
Paging: 187 pp.
Binding: Softcover