Edited by: Ricardo Baeza, Universidad de Talca, Chile, John S. Hsia, Ohio State University, Columbus, OH, Bill Jacob, University of California, Santa Barbara, CA, and Alexander Prestel, University of Konstanz, Germany

Algebraic and Arithmetic Theory of Quadratic Forms

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

Edited by: Christopher Heil, Georgia Institute of Technology, Atlanta, GA, Palle E.T. Jorgensen, University of Iowa, Iowa City, IA, and David R. Larson, Texas A&M University, College Station, TX

Wavelets, Frames and Operator Theory

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

Alexander Beilinson and Vladimir Drinfeld, University of Chicago, IL

Chiral Algebras

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

Dusa McDuff, SUNY at Stony Brook, NY,
and Dietmar Salamon, Eidgen Technische Hochschule, Zurich, Switzerland

J-holomorphic Curves and Symplectic Topology

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

Edited by: J. Nesetril, Charles University, Praha, Czech Republic,
and P. Winkler, Bell Labs, Murray Hill, NJ

Graphs, Morphisms and Statistical Physics

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

Edited by: Melvyn B. Nathanson, Herbert H. Lehman College, CUNY, New York, NY

Unusual Applications of Number Theory

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