Expected publication date is January 13, 2005
Description
This two-part volume gives a comprehensive overview of the theory
of probability measures on the unit circle, viewed especially in
terms of the orthogonal polynomials defined by those measures. A
major theme involves the connections between the Verblunsky
coefficients (the coefficients of the recurrence equation for the
orthogonal polynomials) and the measures, an analog of the
spectral theory of one-dimensional Schrodinger operators.
Among the topics discussed along the way are the asymptotics of
Toeplitz determinants (Szego's theorems), limit theorems for the
density of the zeros of orthogonal polynomials, matrix
representations for multiplication by z (CMV matrices), periodic
Verblunsky coefficients from the point of view of meromorphic
functions on hyperelliptic surfaces, and connections between the
theories of orthogonal polynomials on the unit circle and on the
real line.
The book is suitable for graduate students and researchers
interested in analysis.
Contents
Part 1: The Basics
Szego's theorem
Tools for Geronimus' theorem
Matrix representations
Baxter's theorem
The strong Szego theorem
Verblunsky coefficients with rapid decay
The density of zeros
Bibliography
Author index
Subject index
Part 2: Rakhmanov's theorem and related issues
Techniques of spectral analysis
Periodic Verblunsky coefficients
Spectral analysis of specific classes of Verblunsky coefficients
The connection to Jacobi matrices
Reader's guide: Topics and formulae
Perspectives
Twelve great papers
Conjectures and open questions
Bibliography
Author index
Subject index
Details:
Series: Colloquium Publications, Volume: 54
Publication Year: 2004
ISBN: 0-8218-3757-5
Paging: approximately 1096 pp.
Binding: Hardcover
Expected publication date is January 19, 2005
Description
This volume is the proceedings of the 2002 Clay Mathematics
Institute School on Geometry and String Theory. This month-long
program was held at the Isaac Newton Institute for Mathematical
Sciences in Cambridge, England, and was organized by both
mathematicians and physicists: A. Corti, R. Dijkgraaf, M.
Douglas, J. Gauntlett, M. Gross, C. Hull, A. Jaffe and M. Reid.
The early part of the school had many lectures that introduced
various concepts of algebraic geometry and string theory with a
focus on improving communication between these two fields. During
the latter part of the program there were also a number of
research level talks.
This volume contains a selection of expository and research
articles by lecturers at the school and highlights some of the
current interests of researchers working at the interface between
string theory and algebraic geometry. The topics covered include
manifolds of special holonomy, supergravity, supersymmetry, D-branes,
the McKay correspondence and the Fourier-Mukai transform.
The book is suitable for graduate students and research
mathematicians interested in relations between mathematical
physics and algebraic geometry.
Titles in this series are published by the AMS for the Clay
Mathematics Institute (Cambridge, MA).
Contents
M. R. Douglas -- The geometry of string theory
B. S. Acharya -- M theory, G_2-manifolds and four dimensional
physics
S. K. Donaldson -- Conjectures in Kahler geometry
J. P. Gauntlett -- Branes, calibrations and supergravity
S. Gukov -- M-theory on manifolds with exceptional holonomy
N. Hitchin -- Special holonomy and beyond
D. Joyce -- Constructing compact manifolds with exceptional
holonomy
A. Kovalev -- From Fano threefolds to compact G_2-manifolds
A. Craw -- An introduction to motivic integration
A. Ishii -- Representation moduli of the McKay quiver for finite
Abelian subgroups of SL(3,mathbb{C})
F. Kirwan -- Moduli spaces of bundles over Riemann surfaces and
the Yang-Mills stratification revisited
C. Madonna and V. V. Nikulin -- On a classical correspondence
between K3 surfaces II
B. Szendroi -- Contractions and monodromy in homological mirror
symmetry
N. Dorey -- Lectures on supersymmetric gauge theory
A. Kapustin -- The geometry of A-branes
R. C. Myers -- Low energy D-brane actions
List of Participants
Details:
Series: Clay Mathematics Proceedings,Volume: 3
Publication Year: 2004
ISBN: 0-8218-3715-X
Paging: approximately 408 pp.
Binding: Softcover
Expected publication date is January 14, 2005
Description
The calculus of variations is a beautiful subject with a rich
history and with origins in the minimization problems of calculus.
Although it is now at the core of many modern mathematical
fields, it does not have a well-defined place in most
undergraduate mathematics curricula. This volume should
nevertheless give the undergraduate reader a sense of its great
character and importance.
Interesting functionals, such as area or energy, often give rise
to problems whose most natural solution occurs by differentiating
a one-parameter family of variations of some function. The
critical points of the functional are related to the solutions of
the associated Euler-Lagrange equation. These differential
equations are at the heart of the calculus of variations and its
applications to other subjects. Some of the topics addressed in
this book are Morse theory, wave mechanics, minimal surfaces,
soap bubbles, and modeling traffic flow. All are readily
accessible to advanced undergraduates.
This book is derived from a workshop sponsored by Rice University.
It is suitable for advanced undergraduates, graduate students and
research mathematicians interested in the calculus of variations
and its applications to other subjects.
Contents
F. Jones -- Calculus of variations: What does "variations"
mean?
R. Forman -- How many equilibria are there? An introduction to
Morse theory
S. J. Cox -- Aye, there's the rub. An inquiry into why a plucked
string comes to rest
F. Morgan -- Proof of the double bubble conjecture
M. Wolf -- Minimal surfaces, flat cone spheres and moduli spaces
of staircases
B. L. Keyfitz -- Hold that light! Modeling of traffic flow by
differential equations
Details:
Series: Student Mathematical Library,Volume: 26
Publication Year: 2004
ISBN: 0-8218-3720-6
Paging: 153 pp.
Binding: Softcover
Expected publication date is January 16, 2005
Description
Mathematical modelling is a subject without boundaries. It is the
means by which mathematics becomes useful to virtually any
subject. Moreover, modelling has been and continues to be a
driving force for the development of mathematics itself. This
book explains the process of modelling real situations to obtain
mathematical problems that can be analyzed, thus solving the
original problem.
The presentation is in the form of case studies, which are
developed much as they would be in true applications. In many
cases, an initial model is created, then modified along the way.
Some cases are familiar, such as the evaluation of an annuity.
Others are unique, such as the fascinating situation in which an
engineer, armed only with a slide rule, had 24 hours to compute
whether a valve would hold when a temporary rock plug was removed
from a water tunnel.
Each chapter ends with a set of exercises and some suggestions
for class projects. Some projects are extensive, as with the
explorations of the predator-prey model; others are more modest.
The text was designed to be suitable for a one-term course for
advanced undergraduates. The selection of topics and the style of
exposition reflect this choice. The authors have also succeeded
in demonstrating just how enjoyable the subject can be.
This is an ideal text for classes on modelling. It can also be
used in seminars or as preparation for mathematical modelling
competitions.
Contents
Crystallization dynamics
Will the valve hold?
How much will that annuity cost me?
Dimensional analysis
Predator-prey systems
A control problem in fishery management
Formal justice
Traffic dynamics: A microscopic model
Traffic dynamics: Macroscopic modelling
Bibliography
Details:
Series: Student Mathematical Library, Volume: 27
Publication Year: 2005
ISBN: 0-8218-3650-1
Paging: 196 pp.
Binding: Softcover
Expected publication date is January 13, 2005
Description
The power that analysis, topology and algebra bring to geometry
has revolutionized the way geometers and physicists look at
conceptual problems. Some of the key ingredients in this
interplay are sheaves, cohomology, Lie groups, connections and
differential operators. In Global Calculus, the appropriate
formalism for these topics is laid out with numerous examples and
applications by one of the experts in differential and algebraic
geometry.
Ramanan has chosen an uncommon but natural path through the
subject. In this almost completely self-contained account, these
topics are developed from scratch. The basics of Fourier
transforms, Sobolev theory and interior regularity are proved at
the same time as symbol calculus, culminating in beautiful
results in global analysis, real and complex. Many new
perspectives on traditional and modern questions of differential
analysis and geometry are the hallmarks of the book.
The book is suitable for a first year graduate course on global
analysis.
Contents
Sheaves and differential manifolds: Definitions and examples
Differential operators
Integration on differential manifolds
Cohomology of sheaves and applications
Connections on principal and vector bundles; Lifting of symbols
Linear connections
Manifolds with additional structures
Local analysis of elliptic operators
Vanishing theorems and applications
Appendix
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics, Volume: 65
Publication Year: 2005
ISBN: 0-8218-3702-8
Paging: 316 pp.
Binding: Hardcover
Expected publication date is January 13, 2005
Description
This new version of the author's prizewinning book, Algebraic
Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a
modern and self-contained introduction to the theory of quadratic
forms over fields of characteristic different from two. Starting
with few prerequisites beyond linear algebra, the author charts
an expert course from Witt's classical theory of quadratic forms,
quaternion and Clifford algebras, Artin-Schreier theory of
formally real fields, and structural theorems on Witt rings, to
the theory of Pfister forms, function fields, and field
invariants. These main developments are seamlessly interwoven
with excursions into Brauer-Wall groups, local and global fields,
trace forms, Galois theory, and elementary algebraic K-theory, to
create a uniquely original treatment of quadratic form theory
over fields. Two new chapters totaling more than 100 pages have
been added to the earlier incarnation of this book to take into
account some of the newer results and more recent viewpoints in
the area.
As is characteristic of this author's expository style, the
presentation of the main material in this book is interspersed
with a copious number of carefully chosen examples to illustrate
the general theory. This feature, together with a rich stock of
some 280 exercises for the thirteen chapters, greatly enhances
the pedagogical value of this book, both as a graduate text and
as a reference work for researchers in algebra, number theory,
algebraic geometry, algebraic topology, and geometric topology.
Contents
Foundations
Introduction to Witt rings
Quaternion algebras and their norm forms
The Brauer-Wall group
Clifford algebras
Local fields and global fields
Quadratic forms under algebraic extensions
Formally real fields, real-closed fields, and pythagorean fields
Quadratic forms under transcendental extensions
Pfister forms and function fields
Field invariants
Special topics in quadratic forms
Special topics on invariants
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics, Volume: 67
Publication Year: 2005
ISBN: 0-8218-1095-2
Paging: 550 pp.
Binding: Hardcover