Expected publication date is August 14, 2002
Description
Recent developments in topology and analysis
have led to the
creation of new lines of investigation in
differential geometry.
The 2000 Barrett Lectures present the background,
context and
main techniques of three such lines by means
of surveys by
leading researchers.
The first chapter (by Alice Chang and Paul
Yang) introduces new
classes of conformal geometric invariants,
and then applies
powerful techniques in nonlinear differential
equations to derive
results on compactifications of manifolds
and on Yamabe-type
variational problems for these invariants.
This is followed by
Karsten Grove's lectures, which focus on
the use of isometric
group actions and metric geometry techniques
to understand new
examples and classification results in Riemannian
geometry,
especially in connection with positive curvature.
The chapter
written by Jon Wolfson introduces the emerging
field of
Lagrangian variational problems, which blends
in novel ways the
structures of symplectic geometry and the
techniques of the
modern calculus of variations.
The lectures provide an up-do-date overview
and an introduction
to the research literature in each of their
areas. This very
readable introduction should prove useful
to graduate students
and researchers in differential geometry
and geometric analysis.
Contents
S.-Y. A. Chang and P. C. Yang -- Partial
differential equations
related to the Gauss-Bonnet-Chern integrand
on 4-manifolds
K. Grove -- Geometry of, and via, symmetries
J. G. Wolfson -- Lagrangian cycles and volume
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: University Lecture Series, Volume:
27
Publication Year: 2002
ISBN: 0-8218-3210-7
Paging: 85 pp.
Binding: Softcover
Description
This book is an elementary introduction to
p-adic analysis from
the number theory perspective. With over
100 exercises included,
it will acquaint the non-expert to the basic
ideas of the theory
and encourage the novice to enter this fertile
field of research.
The main focus of the book is the study of
p-adic L-functions and
their analytic properties. It begins with
a basic introduction to
Bernoulli numbers and continues with establishing
the Kummer
congruences. These congruences are then used
to construct the p-adic
analog of the Riemann zeta function and p-adic
analogs of
Dirichlet's L-functions. Featured is a chapter
on how to apply
the theory of Newton polygons to determine
Galois groups of
polynomials over the rational number field.
As motivation for
further study, the final chapter introduces
Iwasawa theory.
The book treats the subject informally, making
the text
accessible to non-experts. It would make
a nice independent text
for a course geared toward advanced undergraduates
through
beginning graduate students.
Titles in this series are copublished with
International Press,
Cambridge, MA.
Contents
Historical introduction
Bernoulli numbers
p-adic numbers
Hensel's lemma
p-adic interpolation
p-adic L-functions
p-adic integration
Leopoldt's formula for L_p(1,chi)
Newton polygons
An introduction to Iwasawa theory
Bibliography
Index
Details:
Publisher: American Mathematical Society,
International Press
Distributor: American Mathematical Society
Series: AMS/IP Studies in Advanced Mathematics,
Volume: 27
Publication Year: 2002
ISBN: 0-8218-3262-X
Paging: 149 pp.
Binding: Hardcover
Reviews of the Previous Edition:
"It is remarkable to see just how far
the subject has
developed since 1968 ... contains an absolute
wealth of material
... this approach is a real success ... results
are obtained with
a minimum of fuss, so that the story unfolds
rather quickly and
holds the reader's interest ... a copious
supply of well-structured
exercises ... most certainly a valuable addition
to the
literature ... carefully written and well-presented
state of the
art account of local fields, which contains
much ... of interest
to the expert and non-expert alike ... its
appeal should go well
beyond the usual public of number theorists."
-- Bulletin of the London Mathematical Society
Description
This book offers a modern exposition of the
arithmetical
properties of local fields using explicit
and constructive tools
and methods. It has been ten years since
the publication of the
first edition, and, according to Mathematical
Reviews, 1,000
papers on local fields have been published
during that period.
This edition incorporates improvements to
the first edition, with
60 additional pages reflecting several aspects
of the
developments in local number theory.
The volume consists of four parts: elementary
properties of local
fields, class field theory for various types
of local fields and
generalizations, explicit formulas for the
Hilbert pairing, and
Milnor K-groups of fields and of local fields.
The first three
parts essentially simplify, revise, and update
the first edition.
The book includes the following recent topics:
Fontaine-Wintenberger
theory of arithmetically profinite extensions
and fields of
norms, explicit noncohomological approach
to the reciprocity map
with a review of all other approaches to
local class field
theory, Fesenko's p-class field theory for
local fields with
perfect residue field, simplified updated
presentation of
Vostokov's explicit formulas for the Hilbert
norm residue symbol,
and Milnor K-groups of local fields. Numerous
exercises introduce
the reader to other important recent results
in local number
theory, and an extensive bibliography provides
a guide to related
areas.
The book is geared toward graduate students
and research
mathematicians interested in local number
theory and its
applications in arithmetic algebraic geometry.
Contents
Complete discrete valuation fields
Extensions of discrete valuation fields
The norm map
Local class field theory I
Local class field theory II
The group of units of local number fields
Explicit formulas for the Hilbert symbol
Explicit formulas for the Hilbert pairing
on formal groups
The Milnor K-groups of a local field
Bibliography
List of notations
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Translations of Mathematical Monographs,
Volume: 121
Publication Year: 2002
ISBN: 0-8218-3259-X
Paging: 345 pp.
Binding: Hardcover
Expected publication date is November 6,
2002
Description
Many important functions of mathematical
physics are defined as
integrals depending on parameters. The Picard-Lefschetz
theory
studies how analytic and qualitative properties
of such integrals
(regularity, algebraicity, ramification,
singular points, etc.)
depend on the monodromy of corresponding
integration cycles. In
this book, V. A. Vassiliev presents several
versions of the
Picard-Lefschetz theory, including the classical
local monodromy
theory of singularities and complete intersections,
Pham's
generalized Picard-Lefschetz formulas, stratified
Picard-Lefschetz
theory, and also twisted versions of all
these theories with
applications to integrals of multivalued
forms.
The author also shows how these versions
of the Picard-Lefschetz
theory are used in studying a variety of
problems arising in many
areas of mathematics and mathematical physics.
In particular, he discusses the following
classes of functions:
volume functions arising in the Archimedes-Newton
problem of
integrable bodies;
Newton-Coulomb potentials;
fundamental solutions of hyperbolic partial
differential
equations;
multidimensional hypergeometric functions
generalizing the
classical Gauss hypergeometric integral.
The book is geared toward a broad audience
of graduate students,
research mathematicians and mathematical
physicists interested in
algebraic geometry, complex analysis, singularity
theory,
asymptotic methods, potential theory, and
hyperbolic operators.
Contents
Introduction
Local monodromy theory of isolated singularities
of functions and
complete intersections
Stratified Picard-Lefschetz theory and monodromy
of hyperplane
sections
Newton's theorem on the non-integrability
of ovals
Lacunas and local Petrovskiicondition for
hyperbolic differential
operators with constant coefficients
Calculation of local Petrovskiicycles and
enumeration of local
lacunas close to real singularities
Homology of local systems, twisted monodromy
theory, and
regularization of improper integration cycles
Analytic properties of surface potentials
Multidimensional hypergeometric functions,
their ramification,
singularities, and resonances
Bibliography
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Mathematical Surveys and Monographs,Volume:
97
Publication Year: 2002
ISBN: 0-8218-2948-3
Paging: approximately 352 pp.
Binding: Hardcover
Expected publication date is September 4,
2002
Description
Because of its many applications to mathematics and mathematical
physics, the representation theory of infinite-dimensional Lie
and quantized enveloping algebras comprises an important area of
current research. This volume includes articles from the
proceedings of an international conference, "Infinite-Dimensional
Lie Theory and Conformal Field Theory", held at the
University of Virginia. Many of the contributors to the volume
are prominent researchers in the field.
This conference provided an opportunity for mathematicians and
physicists to interact in an active research area of mutual
interest. The talks focused on recent developments in the
representation theory of affine, quantum affine, and extended
affine Lie algebras and Lie superalgebras. They also highlighted
applications to conformal field theory, integrable and disordered
systems.
Some of the articles are expository and accessible to a broad
readership of mathematicians and physicists interested in this
area; others are research articles that are appropriate for more
advanced readers.
Contents
S. Berman, Y. Billig, and J. Szmigielski -- Vertex operator
algebras and the representation theory of toroidal algebras
V. Chari and M. Kleber -- Symmetric functions and representations
of quantum affine algebras
B. L. Cox -- Two realizations of toroidal mathfrak{sl}_2(mathbb C)
C. Dong, H. Li, and G. Mason -- Vertex Lie algebras, vertex
Poisson algebras and vertex algebras
A. J. Feingold and M. D. Weiner -- Type A fusion rules from
elementary group theory
J. Fuchs and C. Schweigert -- Lie algebra automorphisms in
conformal field theory
Y. Hara, M. Jimbo, H. Konno, S. Odake, and J. Shiraishi -- On
Lepowsky-Wilson's mathcal{Z}-algebra
G. Hatayama, A. Kuniba, M. Okado, T. Takagi, and Y. Yamada --
Scattering rules in soliton cellular automata associated with
crystal bases
B. M. McCoy -- Algebra versus analysis in statistical mechanics
and quantum field theory
A. Milas -- Weak modules and logarithmic intertwining operators
for vertex operator algebras
A. Schilling and S. O. Warnaar -- Conjugate Bailey pairs
M. Vazirani -- Irreducibility of affine Hecke algebra modules
induced from Specht modules
W. Wang -- Algebraic structures behind Hilbert schemes and wreath
products
W. Zhao -- Some generalizations of genus zero two-dimensional
conformal field theory
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume: 297
Publication Year: 2002
ISBN: 0-8218-2716-2
Paging: 334 pp.
Binding: Softcover