Expected publication date is December 13,
2002
Description
Convexity is a simple idea that manifests
itself in a surprising
variety of places. This fertile field has
an immensely rich
structure and numerous applications. Barvinok
demonstrates that
simplicity, intuitive appeal, and the universality
of
applications make teaching (and learning)
convexity a gratifying
experience. The book will benefit both teacher
and student: It is
easy to understand, entertaining to the reader,
and includes many
exercises that vary in degree of difficulty.
Overall, the author
demonstrates the power of a few simple unifying
principles in a
variety of pure and applied problems.
The notion of convexity comes from geometry.
Barvinok describes
here its geometric aspects, yet he focuses
on applications of
convexity rather than on convexity for its
own sake. Mathematical
applications range from analysis and probability
to algebra to
combinatorics to number theory. Several important
areas are
covered, including topological vector spaces,
linear programming,
ellipsoids, and lattices. Specific topics
of note are optimal
control, sphere packings, rational approximations,
numerical
integration, graph theory, and more. And
of course, there is much
to say about applying convexity theory to
the study of faces of
polytopes, lattices and polyhedra, and lattices
and convex bodies.
The prerequisites are minimal amounts of
linear algebra,
analysis, and elementary topology, plus basic
computational
skills. Portions of the book could be used
by advanced
undergraduates. As a whole, it is designed
for graduate students
interested in mathematical methods, computer
science, electrical
engineering, and operations research. The
book will also be of
interest to research mathematicians, who
will find some results
that are recent, some that are new, and many
known results that
are discussed from a new perspective.
Contents
Convex sets at large
Faces and extreme points
Convex sets in topological vector spaces
Polarity, duality and linear programming
Convex bodies and ellipsoids
Faces of polytopes
Lattices and convex bodies
Lattice points and polyhedra
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics,Volume:
54
Publication Year: 2002
ISBN: 0-8218-2968-8
Paging: 366 pp.
Binding: Hardcover
Expected publication date is January 12,
2003
Description
This work celebrates the work of Eberhard
Hopf, a founding father
of ergodic theory, a mathematician who produced
many beautiful,
elegantly written, and now classical results
in integral
equations and partial differential equations.
Hopf's results
remain at the core of these fields, and the
title includes Hopf's
original mathematical papers, still notable
for their elegance
and clarity of the writing, with accompanying
summaries and
commentary by well-known mathematicians.
Today, ergodic theory and P.D.E. continue
to be active, important
areas of mathematics. In this volume the
reader will find the
roots of many ergodic theory concepts and
theorems. Hopf authored
fundamental results for P.D.E., such as the
maximum principle of
elliptic equations and the complete solution
of Burger's equation.
The familiar properties of elliptic equations
were proved for the
first time in his earliest work and are included
here. His
bifurcation theorem, still used over and
over again, is a
particular gem. The proof of the Wiener-Hopf
Theorem is a
stunning application of deep analysis.
The volume is presented in two main parts.
The first section is
dedicated to classical papers in analysis
and fluid dynamics, and
the second to ergodic theory.
These works and all the others in the Selected
Works carry
commentaries by a stellar group of mathematicians
who write of
the origin of the problems, the important
results that followed.
Many a mathematical researcher and graduate
student will find
these collected works to be an excellent
resource.
Contents
Part I
E. Hopf -- Elementare Bemerkungen uber die
Losungen partieller
Differentialgleichungen zweiter Ordnung vom
elliptischen Typus
J. B. Serrin -- Commentary
E. Hopf -- A remark on linear elliptic differential
equations of
second order
J. B. Serrin -- Commentary
E. Hopf -- Zum analytischen Charakter der
Losungen regularer
zweidimensionaler Variationsprobleme
H. Weinberger -- Commentary
N. Wiener and E. Hopf -- Uber eine Klasse
singularer
Integralgleichungen
H. Widom -- Commentary
E. Hopf -- Uber den funktionalen, insbesondere
den analytischen
Charakter der Losungen elliptscher Differentialgleichungen
zweiter Ordnung
H. Weinberger -- Commentary
E. Hopf -- Abzweigung einer periodischen
Losung von einer
stationaren Losung eines Differentialsystems
M. Golubitsky and P. H. Rabinowitz -- Commentary
E. Hopf -- Repeated branching through loss
of stability. An
example
E. Hopf -- A mathematical example displaying
features of
turbulence
R. Temam -- Commentary
E. Hopf -- On S. Bernstein's theorem on surfaces
$z(x,y)$ of
nonpositive curvature
L. Nirenberg -- Commentary
E. Hopf -- The partial differential equation
$u_t + uu_x =
\mu_{xx}$
P. D. Lax -- Commentary
E. Hopf -- Uber die Anfangswertaufgabe fur
die hydrodynamischen
Grundgleichungen
J. B. Serrin -- Commentary
E. D. Conway and E. Hopf -- Hamilton's theory
and generalized
solutions of the Hamilton-Jacobi equation
C. S. Morawetz -- Commentary
Part II
E. Hopf -- Statistik der geodatischen Linien
in
Mannigfaltigkeiten negativer Krummung
E. Hopf -- Statistik der Losungen geodatischer
Probleme vom
unstabilen Typus. II
Ya. G. Sinai -- Commentary
E. Hopf -- Closed surfaces without conjugate
points
Ya. G. Sinai -- Commentary
E. Hopf -- Statistical hydromechanics and
functional calculus
Ya. G. Sinai -- Commentary
E. Hopf -- On the ergodic theorem for positive
linear operators
D. Ornstein -- Commentary
Acknowledgments
Details:
Series: Collected Works Volume: 17
Publication Year: 2003
ISBN: 0-8218-2077-X
Paging: 396 pp.
Binding: Hardcover
Expected publication date is December 26,
2002
Description
This book publishes papers originally presented
at a conference
on the Mathematical Aspects of Orbifold String
Theory, hosted by
the University of Wisconsin-Madison. It contains
a great deal of
information not fully covered in the published
literature and
showcases the current state of the art in
orbital string theory.
The subject of orbifolds has a long prehistory,
going back to the
work of Thurston and Haefliger, with roots
in the theory of
manifolds, group actions, and foliations.
The recent explosion of
activity on the topic has been powered by
applications of
orbifolds to moduli problems and quantum
field theory. The
present volume presents an interdisciplinary
look at orbifold
problems. Topics such as stacks, vertex operator
algebras,
branes, groupoids, K-theory and quantum cohomology
are discussed.
The book reflects the thinking of distinguished
investigators
working in the areas of mathematical physics,
algebraic geometry,
algebraic topology, symplectic geometry and
representation theory.
By presenting the work of a broad range of
mathematicians and
physicists who use and study orbifolds, it
familiarizes readers
with the various points of view and types
of results the
researchers bring to the subject.
Contents
D. Abramovich, T. Graber, and A. Vistoli
-- Algebraic orbifold
quantum products
W. Chen and Y. Ruan -- Orbifold Gromov-Witten
theory
C. Dong, K. Liu, and X. Ma -- On orbifold
elliptic genus
T. Graber and E. Zaslow -- Open-string Gromov-Witten
invariants:
Calculations and a mirror "theorem"
T. J. Jarvis and T. Kimura -- Orbifold quantum
cohomology of the
classifying space of a finite group
R. M. Kaufmann -- Orbifold Frobenius algebras,
cobordisms and
monodromies
E. Lupercio and B. Uribe -- Loop groupoids,
Gerbes, and twisted
sectors on orbifolds
M. Marino and C. Vafa -- Framed knots at
large $N$
I. Moerdijk -- Orbifolds as groupoids: An
introduction
M. Poddar -- Orbifold cohomology group of
toric varieties
Z. Qin and W. Wang -- Hilbert schemes and
symmetric products: A
dictionary
Y. Ruan -- Stringy orbifolds
E. Sharpe -- Discrete torsion, quotient stacks,
and string
orbifolds
K. Wendland -- Orbifold constructions of
$K3$: A link between
conformal field theory and geometry
Details:
Series: Contemporary Mathematics, Volume:
310
Publication Year: 2003
ISBN: 0-8218-2990-4
Paging: approximately 368 pp.
Binding: Softcover
Expected publication date is December 7,
2002
Description
This volume derives from the second Iberoamerican
Congress on
Geometry, held in 2001 in Mexico at the Centro
de Investigacion
en Matematicas A.C., an internationally recognized
program of
research in pure mathematics. The conference
topics were chosen
with an eye toward the presentation of new
methods, recent
results, and the creation of more interconnections
between the
different research groups working in complex
manifolds and
hyperbolic geometry. This volume reflects
both the unity and the
diversity of these subjects.
Researchers around the globe have been working
on problems
concerning Riemann surfaces, as well as a
wide scope of other
issues: the theory of Teichmuller spaces,
theta functions,
algebraic geometry and classical function
theory.
Included here are discussions revolving around
questions of
geometry that are related in one way or another
to functions of a
complex variable. There are contributors
on Riemann surfaces,
hyperbolic geometry, Teichmuller spaces,
and quasiconformal maps.
Complex geometry has many applications--triangulations
of
surfaces, combinatorics, ordinary differential
equations, complex
dynamics, and the geometry of special curves
and jacobians, among
others. In this book, research mathematicians
in complex
geometry, hyperbolic geometry and Teichmuller
spaces will find a
selection of strong papers by international
experts.
Contents
A. M. Bonifant and M. Dabija -- Self-maps
of ${\mathbb P}^2$ with
invariant elliptic curves
J. F. Brock -- Pants decompositions and the
Weil-Petersson metric
A. Carocca, S. Recillas, and R. E. Rodriguez
-- Dihedral groups
acting on Jacobians
C. J. Earle -- Schwarz's lemma and Teichmuller
contraction
C. J. Earle, V. Markovic, and D. Saric --
Barycentric extension
and the Bers embedding for asymptotic Teichmuller
space
A. L. Epstein -- Symmetric rigidity for real
polynomials with
real critical points
H. M. Farkas and I. Kra -- On theta constant
identities and the
evaluation of trigonometric sums
A. Gamburd and E. Makover -- On the genus
of a random Riemann
surface
F. P. Gardiner, J. Hu, and N. Lakic -- Earthquake
curves
F. P. Gardiner and N. Lakic -- Efficient
smooth quasiconformal
mappings
T. M. Gendron -- The Ehrenpreis conjecture
and the moduli-rigidity
gap
J. Gilman and L. Keen -- Word sequences and
intersection numbers
L. Giraldo and X. Gomez-Mont -- A law of
conservation of number
for local Euler characteristics
G. Gonzalez-Diez and W. J. Harvey -- On families
of algebraic
curves with automorphisms
R. A. Hidalgo -- Real surfaces, Riemann matrices
and algebraic
curves
N. Lakic and S. Mitra -- Approximation by
meromorphic quadratic
differentials
B. Maskit -- On the topology of classical
Schottky space
R. Silhol -- Hyperbolic lego and algebraic
curves in genus 2 and
3
P. Susskind -- The Margulis region and continued
fractions
Details:
Series: Contemporary Mathematics, Volume:
311
Publication Year: 2002
ISBN: 0-8218-2957-2
Paging: 343 pp.
Binding: Softcover
Expected publication date is December 20,
2002
Description
This book presents nineteen refereed articles
written by
participants in the Singapore International
Symposium in Topology
and Geometry (SISTAG), held July 2-6, 2001,
at the National
University of Singapore. Beyond being a simple
snapshot of the
meeting in the form of a proceedings, it
serves as a
commemorative volume consisting of papers
selected to show the
diversity and depth of the mathematics presented
at SISTAG.
The book presents articles on low-dimensional
topology,
algebraic, differential and symplectic geometry,
and algebraic
topology. While papers reflect the focus
of the conference, many
documents written after SISTAG and included
in this volume
represent the latest thinking in the fields
of topology and
geometry. While representation from Pacific
Rim countries is
strong, the list of contributors is international
in scope and
includes many recognized experts.
This volume is of interest to graduate students
and
mathematicians working in the fields of algebraic
geometry,
differential geometry, geometric topology,
low-dimensional
topology, algebraic topology, symplectic
geometry and
mathematical physics.
Contents
A. G. Aleksandrov -- Moduli of logarithmic
connections along a
free divisor
S. Altinok, G. Brown, and M. Reid -- Fano
3-folds, K3 surfaces
and graded rings
I. Bokor -- A notion of connected sum for
certain $CW$-complexes
Y. S. Cho -- The cohomology ring of $S^2$-fibrations
C. M. Gordon -- Links and their complements
B. Hassett and Y. Tschinkel -- On the effective
cone and the
moduli space of pointed rational curves
J. A. Hillman -- On 4-dimensional mapping
tori
W. Jaco, D. Letscher, and J. H. Rubinstein
-- Algorithms for
essential surfaces in 3-manifolds
D. Joyce -- On counting special Lagrangian
homology 3-spheres
Y. Kamiya and K. Shimomura -- $E_*$-homology
spheres for a
connective spectrum $E$
B. H. Lian, K. Liu, and S.-T. Yau -- Some
applications of mirror
principle
R. Mazzeo and F. Pacard -- Bifurcating nodoids
M. McQuillan -- Formal formal schemes
Y.-G. Oh -- Holomorphic volume preserving
maps and special
Lagrangian submanifolds
S. Pan -- On a new curve evolution problem
in the plane
C. Shen and F. Wang -- Some applications
of the theory of
critical points
Y.-B. Shen -- On complete submanifolds with
parallel mean
curvature in $R^{n+p}$
Y. Yu and J. Zhou -- Semi-classical asymptotics
D.-Q. Zhang -- On endomorphisms of algebraic
surfaces
Details:
Series: Contemporary Mathematics, Volume:
314
Publication Year: 2003
ISBN: 0-8218-2820-7
Paging: 263 pp.
Binding: Softcover