Expected publication date is June 11, 2003
Description
This monograph is the first to deal with
graph representation as
a field of study. It is written from both
a mathematical and
computer science perspective. Synthesizing
the two traditions
opens a number of interesting new research
areas. Some individual
classes of graphs are important, but are
not adequately covered
in any current text. This book gives a much
more current view of
important algorithmic developments in intersection
graph classes
than is currently available and includes
a large number of new
open problems.
It deals with the questions that arise from
storing a graph in a
computer. Different classes of graphs admit
different forms of
computer representations, and focusing on
the representations
gives a new perspective on a number of problems.
For a variety of
classes of graphs, the book considers such
questions as existence
of good representations, algorithms for finding
representations,
questions of characterizations in terms of
representation, and
how the representation affects the complexity
of optimization
problems. General models of efficient computer
representations
are also considered.
The book is designed to be used both as a
text for a graduate
course on topics related to graph representation
and as a
monograph for anyone interested in research
in the field of graph
representation. The material is of interest
both to those
focusing purely on graph theory and to those
working in the area
of graph algorithms.
Contents
Explanatory remarks
Introduction
Implicit representation
Intersection and containment representations
Real numbers in graph representations
Classes which use global information
Visibility graphs
Intersection of graph classes
Graph classes defined by forbidden subgraphs
Chordal bipartite graphs
Matrices
Decomposition
Elimination schemes
Recognition algorithms
Robust algorithms for optimization problems
Characterization and construction
Applications
Glossary
Survey of results on graph classes
Bibliography
Index
Details:
Series: Fields Institute Monographs, Volume:
19
Publication Year: 2003
ISBN: 0-8218-2815-0
Paging: 342 pp.
Binding: Hardcover
Expected publication date is June 8, 2003
Description
In this book, the authors geometrically construct
Riemann
surfaces of infinite genus by pasting together
plane domains and
handles. To achieve a meaningful generalization
of the classical
theory of Riemann surfaces to the case of
infinite genus, one
must impose restrictions on the asymptotic
behavior of the
Riemann surface. In the construction carried
out here, these
restrictions are formulated in terms of the
sizes and locations
of the handles and in terms of the gluing
maps.
The approach used has two main attractions.
The first is that
much of the classical theory of Riemann surfaces,
including the
Torelli theorem, can be generalized to this
class. The second is
that solutions of Kadomcev-Petviashvilli
equations can be
expressed in terms of theta functions associated
with Riemann
surfaces of infinite genus constructed in
the book. Both of these
are developed here. The authors also present
in detail a number
of important examples of Riemann surfaces
of infinite genus (hyperelliptic
surfaces of infinite genus, heat surfaces
and Fermi surfaces).
The book is suitable for graduate students
and research
mathematicians interested in analysis and
integrable systems.
Contents
$L^2$-cohomology, exhaustions with finite
charge and theta series
The Torelli Theorem
Examples
The Kadomcev-Petviashvilli equation
Bibliography
Details:
Series: CRM Monograph Series, Volume: 20
Publication Year: 2003
ISBN: 0-8218-3357-X
Paging: 296 pp.
Binding: Hardcover
Expected publication date is July 16, 2003
Description
"We explore widely in the valley of
ordinary
representations, and we take the reader over
the mountain pass
leading to the valley of modular representations,
to a point from
which (s)he can survey this valley, but we
do not attempt to
widely explore it. We hope the reader will
be sufficiently
fascinated by the scenery to further explore
both valleys on his/her
own."
--from the Preface
Representation theory plays important roles
in geometry, algebra,
analysis, and mathematical physics. In particular,
representation
theory has been one of the great tools in
the study and
classification of finite groups. There are
some beautiful results
that come from representation theory: Frobenius's
Theorem,
Burnside's Theorem, Artin's Theorem, Brauer's
Theorem--all of
which are covered in this textbook. Some
seem uninspiring at
first, but prove to be quite useful. Others
are clearly deep from
the outset. And when a group (finite or otherwise)
acts on
something else (as a set of symmetries, for
example), one ends up
with a natural representation of the group.
This book is an introduction to the representation
theory of
finite groups from an algebraic point of
view, regarding
representations as modules over the group
algebra. The approach
is to develop the requisite algebra in reasonable
generality and
then to specialize it to the case of group
representations.
Methods and results particular to group representations,
such as
characters and induced representations, are
developed in depth.
Arithmetic comes into play when considering
the field of
definition of a representation, especially
for subfields of the
complex numbers. The book has an extensive
development of the
semisimple case, where the characteristic
of the field is zero or
is prime to the order of the group, and builds
the foundations of
the modular case, where the characteristic
of the field divides
the order of the group.
The book assumes only the material of a standard
graduate course
in algebra. It is suitable as a text for
a year-long graduate
course. The subject is of interest to students
of algebra, number
theory and algebraic geometry. The systematic
treatment presented
here makes the book also valuable as a reference.
Contents
Introduction
Semisimple rings and modules
Semisimple group representations
Induced representations and applications
Introduction to modular representations
General rings and modules
Modular group representations
Some useful results
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics,
Volume: 59
Publication Year: 2003
ISBN: 0-8218-3222-0
Paging: approximately 232 pp.
Binding: Hardcover
Iwanami Series in Modern Mathematics
Expected publication date is July 31, 2003
Description
Algebraic geometry plays an important role
in several branches of
science and technology. This is the third
of three volumes by
Kenji Ueno on scheme theory, the most natural
form of algebraic
geometry. This, in addition to Algebraic
Geometry 1 and Algebraic
Geometry 2, makes an excellent textbook for
a second course in
algebraic geometry.
In this volume, the author goes beyond introductory
notions and
presents the theory of schemes and sheaves
with the goal of
studying the properties necessary for the
full development of
modern algebraic geometry. The main topics
discussed in the book
include dimension theory, flat and proper
morphisms, regular
schemes, smooth morphisms, completion, and
Zariski's main theorem.
Ueno also presents the theory of algebraic
curves and their
Jacobians, and the relation between algebraic
and analytic
geometry, including Kodaira's Vanishing Theorem.
The book contains numerous exercises and
problems with solutions.
It is suitable for a graduate course on algebraic
geometry or for
independent study.
Contents
Fundamental properties of scheme theory
Algebraic curves and Jacobi varieties
Algebraic geometry and analytic geometry
Overview and references
Solutions to problems
Solutions to exercises
Index
Details:
Series: Translations of Mathematical Monographs,Volume:
218
Publication Year: 2003
ISBN: 0-8218-1358-7
Paging: approximately 240 pp.
Binding: Softcover
Expected publication date is May 11, 2003
Description
This volume contains 13 papers from the conference
on "Hilbert
Schemes, Vector Bundles and Their Interplay
with Representation
Theory". The papers are written by leading
mathematicians in
algebraic geometry and representation theory
and present the
latest developments in the field.
Among other contributions, the volume includes
several very
impressive and elegant theorems in representation
theory by R.
Friedman and J. W. Morgan, convolution on
homology groups of
moduli spaces of sheaves on K3 surfaces by
H. Nakajima, and
computation of the $S^1$ fixed points in
Quot-schemes and mirror
principle computations for Grassmanians by
S.-T. Yau, et al.
The book is of interest to graduate students
and researchers in
algebraic geometry, representation theory,
topology and their
applications to high energy physics.
Contents
R. Friedman and J. W. Morgan -- Minuscule
representations,
invariant polynomials, and spectral covers
S. Hosono, B. H. Lian, K. Oguiso, and S.-T.
Yau -- Fourier-Mukai
partners of a K3 surface of Picard number
one
J. Li -- Moduli spaces associated to a singular
variety and the
moduli of bundles over universal curves
H. Nakajima -- Convolution on homology groups
of moduli spaces of
sheaves on K3 surfaces
W.-P. Li, Z. Qin, and Q. Zhang -- Curves
in the Hilbert schemes
of points on surfaces
X. Wu -- Limiting linear subspaces on non-reduced
schemes
B. P. Purnaprajna -- Geometry of canonical
covers of varieties of
minimal degree with applications to Calabi-Yau
threefolds
W. Wang -- Universal rings arising in geometry
and group theory
D. Burns, Y. Hu, and T. Luo -- HyperKahler
manifolds and
birational transformations in dimension 4
N. M. Kumar, C. Peterson, and A. P. Rao --
Standard vector bundle
deformations on ${\mathbb P}^n$
B. H. Lian, C.-H. Liu, K. Liu, and S.-T.
Yau -- The $S^1$ fixed
points in Quot-schemes and mirror principle
computations
W. Li -- The semi-infinity of Floer (co)homologies
R. Friedman and J. W. Morgan -- Automorphism
sheaves, spectral
covers, and the Kostant and Steinberg sections
Details:
Series: Contemporary Mathematics,Volume:
322
Publication Year: 2003
ISBN: 0-8218-3264-6
Paging: approximately 256 pp.
Binding: Softcover