Description
This volume describes for the first time
in monograph form
important applications in numerical methods
of linear algebra.
The author presents new material and extended
results from recent
papers in a very readable style.
The main goal of the book is to study the
behavior of the
resolvent of a matrix under the perturbation
by low rank matrices.
Whereas the eigenvalues (the poles of the
resolvent) and the
pseudospectra (the sets where the resolvent
takes large values)
can move dramatically under such perturbations,
the growth of the
resolvent as a matrix-valued meromorphic
function remains
essentially unchanged. This has practical
implications to the
analysis of iterative solvers for large systems
of linear
algebraic equations.
First, the book introduces the basics of
value distribution
theory of meromorphic scalar functions. It
then introduces a new
nonlinear tool for linear algebra, the total
logarithmic size of
a matrix, which allows for a nontrivial generalization
of Rolf
Nevanlinna's characteristic function from
the scalar theory to
matrix- and operator-valued functions. In
particular, the theory
of perturbations by low rank matrices becomes
possible. As an
example, if the spectrum of a normal matrix
collapses under a low
rank perturbation, there is always a compensation
in terms of the
loss of orthogonality of the eigenvectors.
This qualitative
phenomenon is made quantitative by using
the new tool.
Applications are given to rational approximation,
to the Kreiss
matrix theorem, and to convergence of Krylov
solvers.
The book is intended for researchers in mathematics
in general
and especially for those working in numerical
linear algebra.
Much of the book is understandable if the
reader has a good
background in linear algebra and a first
course in complex
analysis.
Details:
Series: Fields Institute Monographs, Volume:
18
Publication Year: 2003
ISBN: 0-8218-3247-6
Paging: 136 pp.
Binding: Hardcover
Expected publication date is April 27, 2003
Description
This volume presents the proceedings of the
international
conference on Combinatorial and Geometric
Representation Theory.
In the field of representation theory, a
wide variety of
mathematical ideas are providing new insights,
giving powerful
methods for understanding the theory, and
presenting various
applications to other branches of mathematics.
Over the past two
decades, there have been remarkable developments.
This book
explains the strong connections between combinatorics,
geometry,
and representation theory. It is suitable
for graduate students
and researchers interested in representation
theory.
Contents
H. H. Andersen -- Twisted Verma modules and
their quantized
analogues
S. Ariki -- On tameness of the Hecke algebras
of type B
G. Benkart and D. Moon -- Tensor product
representations of
Temperley-Lieb algebras and their centralizer
algebras
J. F. Carlson, Z. Lin, D. K. Nakano, and
B. J. Parshall -- The
restricted nullcone
W. J. Haboush -- Projective embeddings of
varieties of special
lattices
G. James -- Representations of general linear
groups
S.-J. Kang and J.-H. Kwon -- Fock space representations
for the quantum affine algebra U_q(C_2^{(1)})
M. Kashiwara -- Realizations of crystals
H. Nakajima -- t-analogs of q-characters
of quantum affine algebras of type A_n, D_n
A. Ram -- Skew shape representations are
irreducible
Details:
Series: Contemporary Mathematics, Volume:
325
Publication Year: 2003
ISBN: 0-8218-3212-3
Paging: 189 pp.
Binding: Softcover
A publication of the Theta Foundation.
Expected publication date is May 30, 2003
Description
This volume contains the proceedings of the
International
Conference on Operator Theory and Banach
Algebras. Over 70
participants from the world over attended.
The book contains 14
selected refereed papers; three are written
in English and the
rest in French. Half are survey papers referring
to different
domains; the remaining papers contain original
results with
complete proofs.
The main topics covered are the spectral
theory of operators on a
Banach space, classes of topological algebras
with applications
to physics, different classes of operators
on Hilbert and Banach
space, problems in Banach algebras, Lie algebras
of operators,
interaction between complex analysis and
operator theory, and
semigroups of operators.
All papers have been revised to account for
recent developments.
Overall, they present an accurate overview
of the domains
considered.
Contents
P. Aiena and M. Gonzalez -- Improjective
operators which are not
inessential
M. Akkar, R. A. Hassani, and A. Blali --
C-semi-groupes (alpha-integres affilies a
des algebres d'operateurs
B. Aupetit, E. Makai, M. Mbekhta, and J.
Zemanek -- The connected
components of the idempotents in the Calkin
algebra and their
liftings
F. Bagarello -- Quantum models and locally
convex ast-algebras
M. Cabrera and A. A. Mohammed -- Algebra
of quotients with
bounded evaluation of a normed prime algebra
G. Cassier -- Autour de quelques interactions
recentes entre
l'analyse complexe et la theorie des operateurs
R. E. Curto and W. Y. Lee -- Subnormality
and k-hyponormality
K. B. Laursen -- (delta)ecomposa(beta)ility
L. W. Marcoux -- A survey of (U+K)-orbits
A. Micali -- Sur les algebres de Banach-Bernstein
M. M. Neumann -- Intertwining restrictions
and quotients of
decomposable operators
A. R. Sourour -- The Lie structure of certain
algebras of
operators
C. Trapani -- CQ^ast-algebras of operators:
density properties
F.-H. Vasilescu -- Extensions of unbounded
symmetric
multioperators
Details:
Publisher: Theta Foundation
Publication Year: 2003
ISBN: 973-85432-1-5
Paging: 166 pp.
Binding: Softcover
Expected publication date is July 5, 2003
From a review of the French edition:
"A collective monograph dedicated to
the new and profound
relations between various theories previously
considered as
unrelated ... A specific feature of the book,
which distinguishes
it from many other monographs and textbooks
on the same subjects,
is its nature of a `guide for the non-specialist'
... it also
contains full proofs of some results difficult
to find elsewhere
... Examples are studied in great detail
... Recommended as a
first reading for a non-specialist who wants
to get acquainted
with the subject but who does not want to
get lost in its many
intricacies and ramifications."
-- Mathematical Reviews
Description
This is a collection of articles that grew
out of a workshop
organized to discuss deep links among various
topics that were
previously considered unrelated. Rather than
a typical workshop,
this gathering was unique as it was structured
more like a course
for advanced graduate students and research
mathematicians.
In the book, the authors present applications
of moduli spaces of
Riemann surfaces in theoretical physics and
number theory and on
Grothendieck's dessins d'enfants and their
generalizations.
Chapter 1 gives an introduction to Teichmuller
space that is more
concise than the popular textbooks, yet contains
full proofs of
many useful results which are often difficult
to find in the
literature. This chapter also contains an
introduction to moduli
spaces of curves, with a detailed description
of the genus zero
case, and in particular of the part at infinity.
Chapter 2 takes
up the subject of the genus zero moduli spaces
and gives a
complete description of their fundamental
groupoids, based at
tangential base points neighboring the part
at infinity; the
description relies on an identification of
the structure of these
groupoids with that of certain canonical
subgroupoids of a free
braided tensor category. It concludes with
a study of the
canonical Galois action on the fundamental
groupoids, computed
using Grothendieck-Teichmuller theory. Finally,
Chapter 3 studies
strict ribbon categories, which are closely
related to braided
tensor categories: Here they are used to
construct invariants of
3-manifolds which in turn give rise to quantum
field theories.
The material is suitable for advanced graduate
students and
researchers interested in algebra, algebraic
geometry, number
theory, and geometry and topology.
Contents
X. Buff, J. Fehrenbach, and P. Lochak --
Elements of the geometry
of moduli spaces of curves
L. Schneps -- Fundamental groupoids of genus
zero moduli spaces
and braided tensor categories
P. Vogel -- Witten-Reshetikhin-Turaev invariants
and quantum
field theories
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: SMF/AMS Texts and Monographs, Volume:
9
Publication Year: 2003
ISBN: 0-8218-3167-4
Paging: 131 pp.
Binding: Softcover
Expected publication date is June 7, 2003
Description
The AMS now makes available this succinct
and quite elegant
research monograph written by Fields Medalist
and eminent
researcher, Laurent Lafforgue. The material
is an outgrowth of
Lafforgue's lectures and seminar at the Centre
de Recherches
Mathematiques (University of Montreal, PQ,
Canada) where he held
the 2001-2002 Aisenstadt Chair.
In the book, he addresses an important recurrent
theme of modern
mathematics: the various compactifications
of moduli spaces,
which have a large number of applications.
This book treats the
case of thin Schubert varieties, which are
natural subvarieties
of Grassmannians. He was led to these questions
by a particular
case linked to his work on the Langlands
program. In this
monograph, he develops the theory in a more
systematic way, which
exhibits strong similarities with the case
of moduli of stable
curves.
Prerequisites are minimal and include basic
algebraic geometry,
and standard facts about Grassmann varieties,
their Plucker
embeddings, and toric varieties. The book
is suitable for
advanced graduate students and research mathematicians
interested
in the classification of moduli spaces.
Contents
Cellules de Schubert minces et espaces de
configurations de
matroides
Compactifications: Pavages de convexes entiers
et recollement des
cellules de Schubert minces
Etude de quelques familles simples de compactifications
Le fibre equivariant universel sur la variete
torique des
facettes des pavages
Variations de varietes projectives rationneles
avec structures
logarithmiques
References bibliographiques
Details:
Series: CRM Monograph Series, Volume: 19
Publication Year: 2003
ISBN: 0-8218-3358-8
Paging: 170 pp.
Binding: Hardcover