Expected publication date is October 18,
2003
Description
The idea of mirror symmetry originated in
physics, but in recent
years, the field of mirror symmetry has exploded
onto the
mathematical scene. It has inspired many
new developments in
algebraic and arithmetic geometry, toric
geometry, the theory of
Riemann surfaces, and infinite-dimensional
Lie algebras among
others.
The developments in physics stimulated the
interest of
mathematicians in Calabi-Yau varieties. This
led to the
realization that the time is ripe for mathematicians,
armed with
many concrete examples and alerted by the
mirror symmetry
phenomenon, to focus on Calabi-Yau varieties
and to test for
these special varieties some of the great
outstanding
conjectures, e.g., the modularity conjecture
for Calabi-Yau
threefolds defined over the rationals, the
Bloch-Beilinson
conjectures, regulator maps of higher algebraic
cycles, Picard-Fuchs
differential equations, GKZ hypergeometric
systems, and others.
The articles in this volume report on current
developments. The
papers are divided roughly into two categories:
geometric methods
and arithmetic methods. One of the significant
outcomes of the
workshop is that we are finally beginning
to understand the
mirror symmetry phenomenon from the arithmetic
point of view,
namely, in terms of zeta-functions and L-series
of mirror pairs
of Calabi-Yau threefolds.
The book is suitable for researchers interested
in mirror
symmetry and string theory.
Contents
Geometric methods
V. V. Batyrev and E. N. Materov -- Mixed
toric residues and
Calabi-Yau complete intersections
L. Chiang and S.-s. Roan -- Crepant resolutions
of mathbb{C}^n/A_1(n)
and flops of n-folders for n=4,5
P. L. Del Angel and S. Muller-Stach -- Picard-Fuchs
equations,
integrable systems and higher algebraic K-theory
S. Hosono -- Counting BPS states via holomorphic
anomaly
equations
J. D. Lewis -- Regulators of Chow cycles
on Calabi-Yau varieties
Arithmetic methods
P. Candelas, X. de la Ossa, and F. Rodriguez-Villegas
-- Calabi-Yau
manifolds over finite fields, II
L. Dieulefait and J. Manoharmayum -- Modularity
of rigid Calabi-Yau
threefolds over mathbb{Q}
Y. Goto -- K3 surfaces with symplectic group
actions
T. Ito -- Birational smooth minimal models
have equal Hodge
numbers in all dimensions
B. H. Lian and S.-T. Yau -- The nth root
of the mirror map
L. Long -- On a Shioda-Inose structure of
a family of K3 surfaces
M. Lynker, V. Periwal, and R. Schimmrigk
-- Black hole attractor
varieties and complex multiplication
F. Rodriguez-Villegas -- Hypergeometric families
of Calabi-Yau
manifolds
R. Schimmrigk -- Aspects of conformal field
theory from Calabi-Yau
arithmetic
J. Stienstra -- Ordinary Calabi-Yau-3 crystals
J. Stienstra -- The ordinary limit for varieties
over mathbb{Z}[x_1,ldots,x_r]
N. Yui -- Update on the modularity of Calabi-Yau
varieties with
appendix by Helena Verrill
N. Yui and J. D. Lewis -- Problems
Details:
Series: Fields Institute Communications,
Volume: 38
Publication Year: 2003
ISBN: 0-8218-3355-3
Paging: approximately 384 pp.
Binding: Hardcover
Expected publication date is October 19,
2003
Description
The articles in this collection present new
results in analysis,
combinatorics, probability, theory of functions,
and partial
differential equations. The material presented
in the book will
be of interest to a broad range of specialists.
In several papers, the authors study the
classical solvability of
the Cauchy-Dirichlet problem for a class
of parabolic systems,
the solvability of the Dirichlet problem
for the quasilinear
second order parabolic systems, estimates
for solutions of
uniformly elliptic systems, and generalizations
of the embedding
theorems. In other papers, the authors describe
a new method for
the computation of correlation dimension,
present generalizations
of the fast Fourier transform method for
wavelet expansions, and
study the spectrum of two-dimensional periodic
magnetic
Schrodinger operator.
Contents
A. A. Arkhipova -- On classical solvability
of the Cauchy-Dirichlet
problem for nondiagonal parabolic systems
in the case of two
spatial variables
A. D. Baranov -- The Bernstein inequality
in the de Branges
spaces and embedding theorems
V. O. Kal'vin -- The oblique derivative problem
in spaces with
asymptotics on edges
V. N. Malozemov and S. M. Masharsky -- Glassman's
formula, fast
Fourier transform, and wavelet expansions
A. I. Nazarov -- Dirichlet problem for quasilinear
parabolic
equations in domains with smooth closed edges
S. I. Repin -- Two-sided estimates for the
deviation from an
exact solution to uniformly elliptic equations
J. V. Romanovsky and L. A. Evdokimov -- Calculation
of
correlation dimension of a time series based
on enumeration of
suboptimal solutions
N. A. Shirokov -- Approximation by entire
functions of an
infinite system of segments
R. G. Shterenberg -- Absolute continuity
of the spectrum of two-dimensional
magnetic periodic Schrodinger operator with
positive electric
potential
Details:
Series: American Mathematical Society Translations--Series
2,
Volume: 209
Publication Year: 2003
ISBN: 0-8218-3405-3
Paging: approximately 232 pp.
Binding: Hardcover
Expected publication date is November 15,
2003
From a review of the Japanese edition:
"The first thing one notices about this
book is that it
includes so many beautiful pictures of surfaces,
which allow the
reader to move comfortably through the material.
The book takes
the reader from historical results through
current research ...
It has distinct charm ... the author's research
is impressive ...
has an inviting style that draws the reader
to the interesting
contents of the book."
-- translated from Sugaku Expositions
Description
The mean curvature of a surface is an extrinsic
parameter
measuring how the surface is curved in the
three-dimensional
space. A surface whose mean curvature is
zero at each point is a
minimal surface, and it is known that such
surfaces are models
for soap film. There is a rich and well-known
theory of minimal
surfaces. A surface whose mean curvature
is constant but nonzero
is obtained when we try to minimize the area
of a closed surface
without changing the volume it encloses.
An easy example of a
surface of constant mean curvature is the
sphere. A nontrivial
example is provided by the constant curvature
torus, whose
discovery in 1984 gave a powerful incentive
for studying such
surfaces. Later, many examples of constant
mean curvature
surfaces were discovered using various methods
of analysis,
differential geometry, and differential equations.
It is now
becoming clear that there is a rich theory
of surfaces of
constant mean curvature.
In this book, the author presents numerous
examples of constant
mean curvature surfaces and techniques for
studying them. Many
finely rendered figures illustrate the results
and allow the
reader to visualize and better understand
these beautiful objects.
The book is suitable for advanced undergraduates,
graduate
students and research mathematicians interested
in analysis and
differential geometry.
Contents
Preliminaries from the theory of surfaces
Mean curvature
Rotational surfaces
Helicoidal surfaces
Stability
Tori
The balancing formula
The Gauss map
Intricate constant mean curvature surfaces
Supplement
Programs for the figures
Postscript
Bibliography
List of sources for the figures
Index
Details:
Series: Translations of Mathematical Monographs,
Volume: 221
Publication Year: 2003
ISBN: 0-8218-3479-7
Paging: approximately 160 pp.
Binding: Softcover
ISBN: 0-8053-8732-3
Publisher: Benjamin Cummings
Copyright: 2003
Format: Cloth; 750 pp
Estimated Availability: 09/19/2003
Description
Spacetime and Geometry: An Introduction to
General Relativity
provides a lucid and thoroughly modern introduction
to general
relativity for advanced undergraduates and
graduate students. It
introduces modern techniques and an accessible
and lively writing
style to what can often be a formal and intimidating
subject.
Readers are led from physics of flat spacetime
(special
relativity), through the intricacies of differential
geometry and
Einstein's equations, and on to exciting
applications such as
black holes, gravitational radiation, and
cosmology. Subtle
points are illuminated throughout the text
by careful and
entertaining exposition. A straightforward
and lucid approach,
balancing mathematical rigor and physical
insight, are hallmarks
of this important text.