Contemporary Mathematics, Volume: 419
2006; 319 pp; softcover
ISBN-10: 0-8218-3842-3
ISBN-13: 978-0-8218-3842-6
This volume consists of contributions by speakers at a Conference
on Algebra and Its Applications that took place in Athens, Ohio,
in March of 2005. It provides a snapshot of the diversity of
themes and applications that interest algebraists today. The
papers in this volume include some of the latest results in the
theory of modules, noncommutative rings, representation theory,
matrix theory, linear algebra over noncommutative rings,
cryptography, error-correcting codes over finite rings, and
projective-geometry codes, as well as expository articles that
will provide algebraists and other mathematicians, including
graduate students, with an accessible introduction to areas
outside their own expertise.
The book will serve both the specialist looking for the latest
result and the novice seeking an accessible reference for some of
the ideas and results presented here.
Readership
Graduate students and research mathematicians interested in ring
and module theory; applications to error-correcting codes.
Table of Contents
A. N. Alahmadi, H. S. Al-Hazmi, and P. A. Guil Asensio -- On
countably Sigma-CS modules
E. Babson, B. Huisgen-Zimmermann, and R. Thomas -- Moduli spaces
of graded representations of finite dimensional algebras
G. F. Birkenmeier, J. K. Park, and S. T. Rizvi -- An essential
extension with nonisomorphic ring structures
V. Camillo and S. Lima -- Supplemented principal ideals
V. Camillo and J. J. Simon -- Some properties of rings reflected
in infinite matrix rings
R. M. Dimitric -- Slender monoids
J. Ding and D. Schmidt -- Multivariable public key crytosystems
H. Q. Dinh -- Repeated-root constacyclic codes of length 2^s over
mathbb{Z}_{2^a}
N. V. Dung -- Contravariant finiteness and pure semisimple rings
A. Facchini -- A characterization of additive categories with the
Krull-Schmidt property
K. R. Goodearl -- A Dixmier-Moeglin equivalence for Poisson
algebras with torus actions
P. A. Guil Asensio and I. Herzog -- Pure-injectivity in the
category of flat modules
C. R. Johnson, A. L. Duarte, C. M. Saiago, and D. Sher --
Eigenvalues, multiplicities and graphs
C. R. Johnson and R. L. Smith -- Closure of matrix classes under
Schur complementation, including singularities
T. Y. Lam and R. G. Swan -- Sums of alternating matrices and
invertible matrices
S. H. Mohamed -- Internal exchange rings
D. Mundici -- Representations of sigma-complete MV-algebras and
their associated Dedekind sigma-complete ell-groups
B. L. Osofsky -- Noncommutative linear algebra
C. Otto and M. Penkava -- The moduli space of three-dimensional
Lie algebras
E. R. Puczylowski -- Questions related to Koethe's nil ideal
problem
R. Smarandache and M. Wauer -- Bounds on the pseudo-weight of
minimal pseudo-codewords of projective geometry codes
G. Szeto and L. Xue -- On Galois extensions with automorphism
group as Galois group
M. Tocon -- A *-Litoff theorem for associative pairs
J. Ding, D. Mundici, D. S. Passman, J. B. Srivastava, and L. Vas
-- Open problems
Contemporary Mathematics, Volume: 420
2006; 301 pp; softcover
ISBN-10: 0-8218-3904-7
ISBN-13: 978-0-8218-3904-1
This is a companion volume to the conference in honor of Donald S.
Passman held in Madison, Wisconsin in June 2005. It contains
research papers on Algebras, Group Rings, Hopf Algebras,
Invariant Theory, Lie Algebras and their Enveloping Algebras,
Noncommutative Algebraic Geometry, Noncommutative Rings, and
other topics. The papers represent an important part of the
latest research in these areas.
Readership
Graduate students and research mathematicians interested in
various topics in algebra.
Table of Contents
Y. A. Bahturin and I. P. Shestakov -- Group gradings on
associative superalgebras
K. I. Beidar, S. K. Jain, and A. K. Srivastava -- Essential
extensions of a direct sum of simple modules
J. Bergen -- Adjoint actions of cocommutative Hopf algebras
G. M. Bergman -- Two statements about infinite products that are
not quite true
R. Betz, S. Eckel, P. Pappas, and J. Uyanik -- Cyclic structures
with lag-time generators
O. B. Cristo and C. P. Milies -- Central idempotents in group
algebras
D. R. Farkas and P. A. Linnell -- Congruence subgroups and the
Atiyah conjecture
E. Formanek -- The adjoint of the Bezoutian
A. Giambruno and S. K. Sehgal -- Group algebras whose Lie algebra
of skew-symmetric elements is nilpotent
J. Z. Goncalves and M. Shirvani -- Free symmetric and unitary
pairs in central simple algebras with involution
R. M. Guralnick and M. Lorenz -- Orders of finite groups of
matrices
G. Heide and A. E. Zalesskii -- Passman's problem on adjoint
representations
M. Hertweck and M. Soriano -- On the modular isomorphism problem:
Groups of order 2^6
W. Kimmerle -- On the prime graph of the unit group of integral
group rings of finite groups
L. Krop and D. E. Radford -- Simple modules for the Drinfel'd
double of a class of Hopf algebras
A. I. Lichtman -- The correspondence between groups and
restricted Lie algebras for some relatively free groups
C.-H. Liu -- Semiprime Lie rings of derivations of commutative
rings
I. M. Musson -- Faithful cyclic modules for enveloping algebras
and Sklyanin algebras
D. S. Passman -- Polynomial and inverse forms
D. Riley and H. Usefi -- Restricted Lie algebras with
subexponential growth
M. Ursul -- A few criteria of boundedness of topological rings
What's Happening in the Mathematical Sciences, Volume: 6
2006; 122 pp; softcover
ISBN-10: 0-8218-3585-8
ISBN-13: 978-0-8218-3585-2
The AMS series What's Happening in the Mathematical Sciences
distills the amazingly rich brew of current research in
mathematics down to a few choice samples. This volume leads off
with an update on the Poincare Conjecture, a hundred-year-old
problem that has apparently been solved by Grigory Perelman of St.
Petersburg, Russia. So what did topologists do when the oldest
and most famous problem about closed manifolds was vanquished? As
the second chapter describes, they confronted a suite of problems
concerning the "ends" of open manifolds ... and solved
those, too.
Not to be outdone, number theorists accomplished several
unexpected feats in the first five years of the new century, from
computing a trillion digits of pi to finding arbitrarily long
equally-spaced sequences of prime numbers. Undergraduates made
key discoveries, as explained in the chapters on Venn diagrams
and primality testing. In applied mathematics, the Navier-Stokes
equations of fluid mechanics continued to stir up interest. One
team proved new theorems about the long-term evolution of
vortices, while others explored the surprising ways that insects
use vortices to move around. The random jittering of Brownian
motion became a little less mysterious. Finally, an old and
trusted algorithm of computer science had its trustworthiness
explained in a novel way.
Barry Cipra explains these new developments in his wry and witty
style, familiar to readers of Volumes 1-5, and is joined in this
volume by Dana Mackenzie. Volume 6 of What's Happening will
convey to all readers--from mathematical novices to experts--the
beauty and wonder that is mathematics.
Readership
General mathematical audience.
Table of Contents
B. Cipra -- First of seven millennium problems nears completion
D. Mackenzie -- Classifying hyperbolic manifolds--All's well that
ends well
B. Cipra -- Digits of pi
B. Cipra -- Combinatoricists solve a Venn-erable problem
B. Cipra -- New insights into prime numbers
D. Mackenzie -- From Rubik's Cube to quadratic number fields...and
beyond
B. Cipra -- Vortices and the Navier-Stokes equations
D. Mackenzie -- Fluid dynamics explains mysteries of insect
motion
D. Mackenzie -- Brownian motion, phase transitions, and conformal
maps
B. Cipra -- Smoothed analysis speeds up the simplex method
Courant Lecture Notes, Volume: 14
2006; 217 pp; softcover
ISBN-10: 0-8218-3576-9
ISBN-13: 978-0-8218-3576-0
The theory of hyperbolic equations is a large subject, and its
applications are many: fluid dynamics and aerodynamics, the
theory of elasticity, optics, electromagnetic waves, direct and
inverse scattering, and the general theory of relativity. This
book is an introduction to most facets of the theory and is an
ideal text for a second-year graduate course on the subject.
The first part deals with the basic theory: the relation of
hyperbolicity to the finite propagation of signals, the concept
and role of characteristic surfaces and rays, energy, and energy
inequalities. The structure of solutions of equations with
constant coefficients is explored with the help of the Fourier
and Radon transforms. The existence of solutions of equations
with variable coefficients with prescribed initial values is
proved using energy inequalities. The propagation of
singularities is studied with the help of progressing waves.
The second part describes finite difference approximations of
hyperbolic equations, presents a streamlined version of the Lax-Phillips
scattering theory, and covers basic concepts and results for
hyperbolic systems of conservation laws, an active research area
today.
Four brief appendices sketch topics that are important or
amusing, such as Huygens' principle and a theory of mixed initial
and boundary value problems. A fifth appendix by Cathleen
Morawetz describes a nonstandard energy identity and its uses.
Titles in this series are copublished with the Courant Institute
of Mathematical Sciences at New York University.
Readership
Graduate students and research mathematicians interested in
hyperbolic equations.
Table of Contents
Student Mathematical Library, Volume: 36
2007; 314 pp; softcover
ISBN-10: 0-8218-4132-7
ISBN-13: 978-0-8218-4132-7
This book presents the characteristic zero invariant theory of
finite groups acting linearly on polynomial algebras. The author
assumes basic knowledge of groups and rings, and introduces more
advanced methods from commutative algebra along the way. The
theory is illustrated by numerous examples and applications to
physics, engineering, numerical analysis, combinatorics, coding
theory, and graph theory. A wide selection of exercises and
suggestions for further reading makes the book appropriate for an
advanced undergraduate or first-year graduate level course.
Readership
Undergraduate and graduate students interested in invariant
theory and its applications.
Table of Contents
Introduction
Recollections
Linear representations of finite groups
Rings and algebras
Introduction and Gobel's bound
Rings of polynomial invariants
Permutation representations
Application: Decay of a spinless particle
Application: Counting weighted graphs
The first fundamental theorem of invariant theory and Noether's
bound
Construction of invariants
Noether's bound
Some families of invariants
Application: Production of fibre composites
Application: Gaussian quadrature
Noether's theorems
Modules
Integral dependence and the Krull relations
Noether's theorems
Application: Self-dual codes
Advanced counting methods and the Shephard-Todd-Chevalley theorem
Poincare series
Systems of parameters
Pseudoreflection representations
Application: Counting partitions
Appendix A: Rational invariants
Suggestions for further reading
Index
AMS/IP Studies in Advanced Mathematics, Volume: 38
2007; 576 pp; softcover
ISBN-10: 0-8218-4251-X
ISBN-13: 978-0-8218-4251-5
Since its discovery in the early 1990s, mirror symmetry, or more
generally, string theory, has exploded onto the mathematical
landscape. This topic touches upon many branches of mathematics
and mathematical physics, and has revealed deep connections
between subjects previously considered unrelated. The papers in
this volume treat mirror symmetry from the perspectives of both
mathematics and physics. The articles can be roughly grouped into
four sub-categories within the topic of mirror symmetry:
arithmetic aspects, geometric aspects, differential geometric and
mathematical physics aspects, and geometric analytic aspects. In
these works, the reader will find mathematics addressing, and in
some cases solving, problems inspired and influenced by string
theory.
Titles in this series are copublished with International Press,
Cambridge, MA.
Readership
Graduate students and research mathematicians interested in
theoretical physics and mathematical areas such as geometry and
modular forms.
Table of Contents
Arithmetic aspects
M. J. Bertin -- Mahler's measure and L-series of K3 hypersurfaces
K. Hulek, H. Verrill, and L. V. Dieulefait -- On the modularity
of Calabi-Yau threefolds containing elliptic ruled surfaces
Appendix A. A Modularity Criterion for Integral Galois
Representations and Calabi-Yau Threefolds
S. Kadir -- Arithmetic mirror symmetry for a two-parameter family
of Calabi-Yau manifolds
K. Kimura -- A rational map between two threefolds
E. Lee -- A modular non-rigid Calabi-Yau threefold
M. Lynker and R. Schimmrigk -- Arithmetic of algebraic curves and
the affine algebra A_1^{(1)}
J. Stienstra -- Mahler measure variations, Eisenstein series and
instanton expansions
J. Stienstra -- Mahler measure, Eisenstein series and dimers
D. Wan and C. D. Haessig -- Mirror symmetry for zeta functions
with appendix
N. Yui and Y. Goto -- The L-series of Calabi-Yau orbifolds of CM
type Appendix B. The L-series of Cubic Hypersurface Fourfolds
Geometric aspects
V. Batyrev and M. Kreuzer -- Integral cohomology and mirror
symmetry for Calabi-Yau 3-folds
X. Chen and J. D. Lewis -- The real regulator for a product of K3
surfaces
Y. Kawamata -- Derived equivalence for stratified Mukai flop on G(2,4)
M. Kerr -- A survey of transcendental methods in the study of
Chow groups of zero-cycles
E. Viehweg and K. Zuo -- Geometry and arithmetic of non-rigid
families of Calabi-Yau 3-folds; Questions and examples
Y. Zhang -- Some results on families of Calabi-Yau varieties
Differential geometric and mathematical physical aspects
K. Hori -- Boundary RG flows of mathcal{N}=2 minimal models
S. Hosono -- Central charges, symplectic forms, and
hypergeometric series in local mirror symmetry
C.-H. Liu and S.-T. Yau -- Extracting Gromov-Witten invariants of
a conifold from semi-stable reduction and relative GW-invariants
of pairs
W.-D. Ruan -- Generalized special Lagrangian torus fibrations for
Calabi-Yau hypersurfaces in toric varieties II
Geometric analytic aspects: Picard-Fuchs equations
G. Almkvist and W. Zudilin -- Differential equations, mirror maps
and zeta values
C. F. Doran and J. W. Morgan -- Mirror symmetry and integral
variations of Hodge structure underlying one-parameter families
of Calabi-Yau threefolds
C. van Enckevort and D. van Straten -- Monodromy calculations of
fourth order equations of Calabi-Yau type
B. Forbes -- Open string mirror maps from Picard-Fuchs equations
N. Yui, S.-T. Yau, and J. D. Lewis -- Problems