Fabec Raymond Louisiana State University
Fundamentals of Infinite Dimensional Representation
Theory
Pitman Monographs and Surveys in Pure and
Applied Mathematics,vol.114
Description
Infinite dimensional representation theory
blossomed in the
latter half of the twentieth century, developing
in part with
quantum mechanics and
becoming one of the mainstays of modern mathematics.
Fundamentals
of Infinite Dimensional Representation Theory
provides an
accessible account of
the topics in analytic group representation
theory and operator
algebras from which much of the subject has
evolved. It presents
new and old results in
a coherent and natural manner and studies
a number of tools
useful in various areas of this diversely
applied subject.
From Borel spaces and selection theorems
to Mackey's theory of
induction, measures on homogeneous spaces,
and the theory of left
Hilbert algebras,
the author's self-contained treatment allows
readers to choose
from a wide variety of topics and pursue
them independently
according to their needs.
Beyond serving as both a general reference
and as a text for
those requiring a background in group-operator
algebra
representation theory, for careful
readers, this monograph helps reveal not
only the subject's
utility, but also its inherent beauty.
Audience
Graduate students and researchers in representation
theory,
harmonic analysis, and operator algebras;
Mathematicians and
theoretical physicists
interested in representation theory
Contents
Borel Spaces and Selection Theorems
Preliminaries of C* Algebras
Type One von Neumann Algebras
Groups and Group Actions
Induced Actions and Representations
Dual Topologies
Left Hilbert Algebras
The Fourier-Stieltjes Algebra
Fundamentals of Infinite Dimensional Representation
Theory
Catalog Number: C2123, ISBN: 1584882123,
No of pages: 448
Publication Date: 06/28/00
Vincent Maillot, Ecole Normale Superieure, Paris, France
Geometrie d'Arakelov des VarietesToriques
et Fibresen Droites Integrables
Description
The author's aim in this paper is twofold.
First, he extends the
Gillet-Soul・arithmetic intersection theory
so that it
encompasses integrable line bundles. In so
doing, he
uses as an essential tool a product theory
for positive currents
developed by Bedford-Taylor and Demailly.
Secondly, he applies
this construction to smooth projective
toric varieties. In this framework, he proves,
among other
things, that canonical heights of hypersurfaces
are related to
their Mahler measure. As a consequence of
the
results, the author proves an arithmetic
analogue of the
Bernstein-Kushnirenko theorem. Text is in
French.
Contents
Introduction
Varietestoriques sur $/mathrm{Spec} /mathbb{Z}$
Varietestoriques complexes
Produits de courants
Groupes de Chow arithmetiques generalises
Courants de Chern canoniques sur les varietestoriques
Geometrie d'Arakelov des varietestoriques
Un theorie de Bernstein-Koushnirenko arithmetique
Bibliographie
Index des notations
Details:
Series: Memoires de la Societe Mathematique
de France,
Number: 80
Publication Year: 2000
ISBN: 2-85629-088-4
Paging: 129 pp.
Binding: Softcover
A publication of the Societe Mathematique de France.
Seminaire Bourbaki, Volume 1998/99, Exposes850-864
Description
Following the format of the seminar, one
finds here fifteen
survey lectures on the following topics of
current interest: the
theory of Lie groups and algebras, algebraic geometry, p-adic arithmetical algebraic geometry,
combinatorial geometry, differential geometry,
partial differential equations, probabilities,
celestial mechanics, and
quantum computing. Four articles are in English,
the rest are in
French.
Contents
Novembre 1998
J.-Y. Chemin -- Explosion geometerique pour
certaines equations
d'ondes non lineaires [d'opres Serge Alinhac]
P. Colmez -- Fonctions L p-adiques
J.-P. Demailly -- Metehodes $L^2$ et resultats
effectifs en
geometerie algebrique
T. Komorowski -- Brownian motion in a Poisson
obstacle field
S. Marmi -- Chaotic behaviour in the solar
system [following J.
Laskar]
Mars 1999
M. Boileau -- Uniformisation en dimension
trois
N. Burq -- Formules de trace, resonances
et quasi-modes [d'apres
Sjtrand-Zworski, Stefanov-Vodev et al.]
H. Carayol -- Preuve de la conjecture de
Langlands locale pour
$GL_n$: Travaux de Harris-Taylor et Henniart
O. Mathieu -- Classification des algebres
de Lie simples
M. Talagrand -- Verres de spin et optimisation
combinatoire
Juin 1999
C. Breuil -- Integration sur les varietees$p$-adiques
[d'apres
Coleman, Colmez]
R. Bryant -- Recent advances in the theory
of holonomy
Y. I. Manin -- Classical computing, quantum
computing, and Shor's
factoring algorithm
J. Oesterl・-- Densit・maximale des empilements
de spheres en
dimension 3 [d'apres T. C. Hales et S. P.
Ferguson]
J.-P. Serre -- Sous-groupes finis des groupes
de Lie
Details:
Series: Asterisque,
Number: 266
Publication Year: 2000
ISBN: 2-85629-090-6
Paging: 483 pp.
Binding: Softcover
Rapha Cerf, Universite Paris Sud, Orsay, France
Large Deviations for Three Dimensional Supercritical
Percolation
Description
In this volume, the author considers Bernoulli
bond percolation
on the three dimensional cubic lattice in
the supercritical
regime. He proves a large deviation principle
for
the rescaled configuration. From that, a
picture of the Wulff
crystal of the model emerges.
Contents
Introduction
The large deviation principles
Sketch of the proofs
The model
Surface tension
The surface energy of a Caccioppoli set
Coarse graining
The central lemma
Proof of the LDP for a single cluster
Collections of sets
The surface energy of a Caccioppoli partition
Proof of the LDP for the whole configuration
Appendix
References
Details:
Series: Asterisque,
Number: 267
Publication Year: 2000
ISBN: 2-85629-091-4
Paging: 177 pp.
Binding: Softcover
Richard M. Weiner
(Univ. of Marburg, Germany and Laboratoire
de Physique Theoretique, Orsay, Univ. Paris-Sud,
France)
Introduction to Bose-Einstein Correlations
and Subatomic Interferometry
ISBN: 0-471-96922-2
Hardcover
Pages: 232
Published: Mar 2000
Copyright: 2000
Bose-Einstein and interferometry bridge particle
physics and
quantum physics and are currently an area
of strong interest in
high-energy
physics. This work demonstrates how and why
the phenomena can be
used to determine the size and lifetime of
particle sources.
Subject: Physics / Solid State Physics /
Condensed Matter
Contents
The Foundations.
Hadron Interferometry.
Currents.
Sources.
Applications to Ultrarelativistic Nucleus-Nucleus
Collisions.
Correlations and Multiplicity Distributions.
Photons Versus Hadrons: Outlook.
Index.