Expected publication date is April 9, 2004
Description
This proceedings volume contains papers presented
at the
International Conference on the algebraic
and arithmetic theory
of quadratic forms held in Talca (Chile).
The modern theory of quadratic forms has
connections with a broad
spectrum of mathematical areas including
number theory, geometry,
and K-theory. This volume contains survey
and research articles
covering the range of connections among these
topics.
The survey articles bring readers up-to-date
on research and open
problems in representation theory of integral
quadratic forms,
the algebraic theory of finite square class
fields, and
developments in the theory of Witt groups
of triangulated
categories. The specialized articles present
important
developments in both the algebraic and arithmetic
theory of
quadratic forms, as well as connections to
geometry and K-theory.
The volume is suitable for graduate students
and research
mathematicians interested in various aspects
of the theory of
quadratic forms.
Contents
R. Aravire and B. Jacob -- The Milnor sequence
for W_qmathcal{F}(x)
in characteristic 2 when mathcal{F} is perfect
L. Arenas-Carmona -- Spinor norm for local
skew-Hermitian forms
P. Balmer -- An introduction to triangular
Witt groups and a
survey of applications
W. K. Chan, A. G. Earnest, and B.-K. Oh --
Regularity properties
of positive definite integral quadratic forms
W. K. Chan and M. I. Icaza -- Effective results
on
representations of quadratic forms
W. K. Chan and M. Peters -- Quaternary quadratic
forms and
Hilbert modular surfaces
M. Dickmann and A. Petrovich -- Real semigroups
and abstract real
spectra. I
M. Gaulter -- The role of characteristic
vectors in the neighbour
lattice process
L. J. Gerstein -- On representation by quadratic
mathbb{F}_q[x]-lattices
D. W. Hoffmann -- Diagonal forms of degree
p in characteristic p
D. G. James -- Local densities and the representations
of an
integer by a definite quadratic form
M. Karoubi -- Periodicity of Hermitian K-theory
and Milnor's K-groups
N. A. Karpenko -- Third proof of second gap
in dimensions of
quadratic forms from I^n
M.-H. Kim -- Recent developments on universal
forms
W. Kohnen -- Special Siegel modular forms
and singular series
polynomials of quadratic forms
A. Laghribi -- Quasi-hyperbolicity of totally
singular quadratic
forms
D. B. Leep and T. L. Smith -- Witt kernels
of triquadratic
extensions
D. W. Lewis -- Anti-automorphisms of the
second kind
J. Martinet -- Reduction modulo 2 and 3 of
Euclidean lattices, II
M. Marshall -- The elementary type conjecture
in quadratic form
theory
A. Pfister -- On Hilbert's theorem about
ternary quartics
R. Schulze-Pillot -- Representation by integral
quadratic forms-A
survey
R. Schulze-Pillot and F. Xu -- Representations
by spinor genera
of ternary quadratic forms
T. Watanabe -- A survey and a complement
of fundamental Hermite
constants
Details:
Series: Contemporary Mathematics, Volume:
344
Publication Year: 2004
ISBN: 0-8218-3441-X
Paging: 350 pp.
Binding: Softcover
Expected publication date is April 22, 2004
Description
In the past two decades, wavelets and frames
have emerged as
significant tools in mathematics and technology.
They interact
with harmonic analysis, operator theory,
and a host of other
applications.
This book grew out of a special session on
Wavelets, Frames and
Operator Theory held at the Joint Mathematics
Meetings in
Baltimore and a National Science Foundation-sponsored
workshop
held at the University of Maryland. Both
events were associated
with the NSF Focused Research Group. The
volume includes both
theoretical and applied papers highlighting
the many facets of
these interconnected topics. It is suitable
for graduate students
and researchers interested in wavelets and
their applications.
Contents
A. Aldroubi, C. Cabrelli, and U. M. Molter
-- How to construct
wavelet frames on irregular grids and arbitrary
dilations in
mathbb{R}^d
L. W. Baggett, P. E. T. Jorgensen, K. D.
Merrill, and J. A.
Packer -- An analogue of Bratteli-Jorgensen
loop group actions
for GMRA's
R. L. Benedetto -- Examples of wavelets for
local fields
M. Bownik and Z. Rzeszotnik -- The spectral
function of shift-invariant
spaces on general lattices
P. G. Casazza -- Custom building finite frames
P. G. Casazza and G. Kutyniok -- Frames of
subspaces
D. E. Dutkay -- The local trace function
for super-wavelets
H. Feichtinger and I. Pesenson -- Recovery
of band-limited
functions on manifolds by an iterative algorithm
J. E. Gilbert and J. D. Lakey -- On a characterization
of the
local Hardy space by Gabor frames
A. L. Gonzalez and R. A. Zalik -- Riesz bases,
multiresolution
analyses, and perturbation
D. Han and Y. Wang -- The existence of Gabor
bases and frames
B. D. Johnson -- Co-affine systems in mathbb{R}^d
K. A. Kornelson and D. R. Larson -- Rank-one
decomposition of
operators and construction of frames
D. Labate, G. Weiss, and E. Wilson -- An
approach to the study of
wave packet systems
M. C. Lammers -- Convolution for Gabor systems
and Newton's
method
G. Olafsson and D. Speegle -- Wavelets, wavelet
sets, and linear
actions on mathbb{R}^n
A. M. Powell -- Orthonormalized coherent
states
Q. Sun -- Localization of stability and p-frames
in the Fourier
domain
J. Yang, L. Shen, M. Papadakis, I. Kakadiaris,
D. J. Kouri, and D.
K. Hoffman -- Orthonormal wavelets arising
from HDAFs
Details:
Series: Contemporary Mathematics, Volume:
345
Publication Year: 2004
ISBN: 0-8218-3380-4
Paging: 342 pp.
Binding: Softcover
Expected publication date is May 21, 2004
Description
This long-awaited publication contains the
results of the
research of two distinguished professors
from the University of
Chicago, Alexander Beilinson and Fields Medalist
Vladimir
Drinfeld. Years in the making, this is a
one-of-a-kind book
featuring previously unpublished material.
Chiral algebras form the primary algebraic
structure of modern
conformal field theory. Each chiral algebra
lives on an algebraic
curve, and in the special case where this
curve is the affine
line, chiral algebras invariant under translations
are the same
as well-known and widely used vertex algebras.
The exposition of this book covers the following
topics:
the "classical" counterpart of
the theory, which is an
algebraic theory of non-linear differential
equations and their
symmetries;
the local aspects of the theory of chiral
algebras, including the
study of some basic examples, such as the
chiral algebras of
differential operators;
the formalism of chiral homology treating
"the space of
conformal blocks" of the conformal field
theory, which is a
"quantum" counterpart of the space
of the global
solutions of a differential equation.
The book is intended for researchers working
in algebraic
geometry and its applications to mathematical
physics and
representation theory.
Contents
Introduction
Axiomatic patterns
Geometry of mathcal{D}-schemes
Local theory: Chiral basics
Global theory: Chiral homology
Bibliography
Index and notation
Details:
Series: Colloquium Publications,Volume: 51
Publication Year: 2004
ISBN: 0-8218-3528-9
Paging: approximately 352 pp.
Binding: Hardcover
Expected publication date is May 6, 2004
Description
The theory of J-holomorphic curves has been
of great importance
since its introduction by Gromov in 1985.
Its mathematical
applications include many key results in
symplectic topology. It
was also one of the main inspirations for
the creation of Floer
homology. In mathematical physics, it provides
a natural context
in which to define Gromov-Witten invariants
and quantum
cohomology-two important ingredients of the
mirror symmetry
conjecture.
This book establishes the fundamental theorems
of the subject in
full and rigorous detail. In particular,
the book contains
complete proofs of Gromov's compactness theorem
for spheres, of
the gluing theorem for spheres, and of the
associativity of
quantum multiplication in the semipositive
case. The book can
also serve as an introduction to current
work in symplectic
topology: There are two long chapters on
applications, one
concentrating on classical results in symplectic
topology and the
other concerned with quantum cohomology.
The last chapter
sketches some recent developments in Floer
theory. The five
appendices of the book provide necessary
background related to
the classical theory of linear elliptic operators,
Fredholm
theory, Sobolev spaces, as well as a discussion
of the moduli
space of genus zero stable curves and a proof
of the positivity
of intersections of J-holomorphic curves
in four dimensional
manifolds.
The book is suitable for graduate students
and researchers
interested in symplectic geometry and its
applications,
especially in the theory of Gromov-Witten
invariants.
Contents
Introduction
J-holomorphic curves
Moduli spaces and transversality
Compactness
Stable maps
Moduli spaces of stable maps
Gromov-Witten invariants
Hamiltonian perturbations
Applications in symplectic topology
Gluing
Quantum cohomology
Floer cohomology
Fredholm theory
Elliptic regularity
The Riemann-Roch theorem
Stable curves of genus zero
Singularities and intersections (written
with Laurent Lazzarini)
Bibliography
List of symbols
Index
Details:
Series: Colloquium Publications, Volume:
52
Publication Year: 2004
ISBN: 0-8218-3485-1
Paging: 669 pp.
Binding: Hardcover
Expected publication date is May 5, 2004
Description
The intersection of combinatorics and statistical
physics has
experienced great activity in recent years.
This flurry of
activity has been fertilized by an exchange
not only of
techniques, but also of objectives. Computer
scientists
interested in approximation algorithms have
helped statistical
physicists and discrete mathematicians overcome
language problems.
They have found a wealth of common ground
in probabilistic
combinatorics.
Close connections between percolation and
random graphs, graph
morphisms and hard-constraint models, and
slow mixing and phase
transition have led to new results and perspectives.
These
connections can help in understanding typical
behavior of
combinatorial phenomena such as graph coloring
and homomorphisms.
Inspired by issues and intriguing new questions
surrounding the
interplay of combinatorics and statistical
physics, a DIMACS/DIMATIA
workshop was held at Rutgers University.
These proceedings are
the outgrowth of that meeting. This volume
is intended for
graduate students and research mathematicians
interested in
probabilistic graph theory and its applications.
Contents
S. Boettcher -- Efficient local search near
phase transitions in
combinatorial optimization
C. Borgs, J. T. Chayes, M. Dyer, and P. Tetali
-- On the sampling
problem for H-colorings on the hypercubic
lattice
G. R. Brightwell and P. Winkler -- Graph
homomorphisms and long
range action
A. Daneshgar and H. Hajiabolhassan -- Random
walks and graph
homomorphisms
J. Diaz, M. Serna, and D. M. Thilikos --
Recent results on
parameterized H-colorings
M. Dyer, M. Jerrum, and E. Vigoda -- Rapidly
mixing Markov chains
for dismantleable constraint graphs
D. Galvin and P. Tetali -- On weighted graph
homomorphisms
P. Hell and J. Nesetril -- Counting list
homomorphisms for graphs
with bounded degrees
G. Istrate -- On the satisfiability of random
k-horn formulae
J. Katriel -- The exchange interaction, spin
hamiltonians, and
the symmetric group
M. Loebl -- A discrete non-Pfaffian approach
to the Ising problem
E. Mossel -- Survey: Information flow on
trees
C. Tardif -- Chromatic numbers of products
of tournaments:
Fractional aspects of Hedetniemi's conjecture
X. Zhu -- Perfect graphs for generalized
colouring-circular
perfect graphs
Details:
Series: DIMACS: Series in Discrete Mathematics
and Theoretical
Computer Science, Volume: 63
Publication Year: 2004
ISBN: 0-8218-3551-3
Paging: 193 pp.
Binding: Hardcover
Expected publication date is May 14, 2004
Description
This volume contains the proceedings of the
workshop held at the
DIMACS Center of Rutgers University (Piscataway,
NJ) on Unusual
Applications of Number Theory. Standard applications
of number
theory are to computer science and cryptology.
In this volume,
well-known number theorist, Melvyn B. Nathanson,
gathers articles
from the workshop on other, less standard
applications in number
theory, as well as topics in number theory
with potential
applications in science and engineering.
The material is suitable for graduate students
and researchers
interested in number theory and its applications.
Contents
K. Alladi, G. E. Andrews, and A. Berkovich
-- A four parameter
generalization of Gollnitz's (big) partition
theorem
G. E. Andrews -- The Friedman-Joichi-Stanton
monotonicity
conjecture at primes
I. Anshel, M. Anshel, B. Fisher, and D. Goldfeld
-- A group
theoretic approach to public-key cryptography
M. Beck and S. Robins -- Dedekind sums: A
combinatorial-geometric
viewpoint
P. B. Cohen -- Noncommutative number theory
J.-M. Deshouillers, G. A. Freiman, and A.
A. Yudin -- An
application of structure theory of set addition
to a question in
ergodic theory
J. A. Dias da Silva -- Linear algebra and
additive theory
J. B. Friedlander, J. S. d. Hansen, and I.
E. Shparlinski -- On
the distribution of the power generator modulo
a prime power
C. S. Gunturk -- Number theoretical error
estimates in a
quantization scheme for bandlimited signals
D. Hensley and F. E. Su -- Random walks with
badly approximable
numbers
J. Holden -- Distribution of values of real
quadratic zeta
functions
R. Jin -- Standardizing nonstandard methods
for upper Banach
density problems
B. Kalantari -- On homogeneous linear recurrence
relations and
approximation of zeros of complex polynomials
M. B. Nathanson -- Formal power series arising
from
multiplication of quantum integers
J. Shallit -- Formal languages and number
theory
J. H. Silverman -- Lattices, cryptography,
and the NTRU public
key cryptosystem
H. M. Stark and A. A. Terras -- Zeta functions
of graph coverings
A. Terras -- Comparison of Selberg's trace
formula with its
discrete analogues
C. J. Moreno and A. Wan -- Unusual applications
of quadratic
Gaussian sums
Details:
Series: DIMACS: Series in Discrete Mathematics
and Theoretical
Computer Science, Volume: 64
Publication Year: 2004
ISBN: 0-8218-2703-0
Paging: 264 pp.
Binding: Hardcover