This proceedings volume widely surveys new problems, methods
and techniques in mathematical physics. The 22 original papers
featured are of great interest to various areas of applied
mathematics. They are presented in honour of Professor Salvatore
Rionero 70th birthday.
Contents:
A Time Dependent Inverse Problem in Photon Transport (A Belleni-Morante)
New Applications of a Versatile Liapunov Functional (J N Flavin)
Thermodynamic Limit for Spin Glasses (S Graffi)
Stabilizing Effects in Fluid Dynamics Problems (G Mulone)
An Alternative Kinematics for Multilattices (M Pitteri)
On Contact Powers and Null Lagrangian Fluxes (P P Guidugli &
G V Caffarelli)
Control Aspects in Gas Dynamics (P Renno)
A Functional Framework for Applied Continuum Mechanics (G Romano
& M Diaco)
Exchange of Stabilities in Porous Media and Penetrative
Convection Effects (B Straughan)
Effects of Adaptation on Competition among Species (D Lacitignola
& C Tebaldi)
and other papers
Readership: Graduate students, academics and researchers in
mathematical physics.
276pp Pub. date: Jan 2005
ISBN 981-256-077-7
This volume collects research papers in quantum probability
and related fields and reflects the recent developments in
quantum probability ranging from the foundations to its
applications.
This volume collects research papers in quantum probability and
related fields and reflects the recent developments in quantum
probability ranging from the foundations to its applications.
Contents:
Probability Measures in Terms of Creation, Annihilation and
Neutral Operators (L Accardi et al.)
Generating Function Method for Orthogonal Polynomials and
Jacobi?Szego Parameters (N Asai et al.)
Multiquantum Markov Semigroups, Interacting Branching Processes
and Nonlinear Kinetic Equations. Finite Dimensional Case (V P
Belavkin & C R Williams)
A Note on Vacuum-Adapted Semimartingales and Monotone
Independence (A C R Belton)
Regular Quantum Stochastic Cocycles have Exponential Product
Systems (B V R Bhat & J M Lindsay)
Quantum Mechanics on the Circle Through Hopf q-Deformations of
the Kinematical Algebra with Possible Applications to Levy
Processes (V K Dobrev et al.)
On Algebraic and Quantum Random Walks (D Ellinas)
Dual Representations for the Schrodinger Algebra (P Feinsilver
& R Schott)
A Limit Theorem for Conditionally Independent Beam Splittings (K
H Fichtner et al.)
On Quantum Logical Gates on a General Fock Space (W Freudenberg
et al.)
On an Argument of David Deutsch (R Gill)
The Method of Double Product Integrals in Quantisation of Lie
Bialgebras (R L Hudson)
Asymptotics of Large Truncated Haar Unitary Matrices (J L Reffy)
Three Ways to Representations of BA(E) (M Skeide)
On Topological Entropy of Quotients and Extensions (J Zacharias)
and other papers
Readership: Researchers in the fields of probability,
mathematical physics and functional analysis.
548pp Pub. date: Jan 2005
ISBN 981-256-147-1
Over the last decade the physics of black holes has been
revolutionized by developments that grew out of Jacob Bekensteinfs
realization that black holes have entropy. Stephen Hawking raised
profound issues concerning the loss of information in black hole
evaporation and the consistency of quantum mechanics in a world
with gravity. For two decades these questions puzzled theoretical
physicists and eventually led to a revolution in the way we think
about space, time, matter and information. This revolution has
culminated in a remarkable principle called gThe Holographic
Principleh, which is now a major focus of attention in
gravitational research, quantum field theory and elementary
particle physics. Leonard Susskind, one of the co-inventors of
the Holographic Principle as well as one of the founders of
String theory, develops and explains these concepts.
Contents:
Black Holes and Quantum Mechanics:
The Schwarzschild Black Hole
Scalar Wave Equation in a Schwarzschild Background
Quantum Fields in Rindler Space
Entropy of the Free Quantum Field in Rindler Space
Thermodynamics of Black Holes
Charged Black Holes
The Stretched Horizon
The Laws of Nature
The Puzzle of Information Conservation in Black Hole Environments
Horizons and the UV/IR Connection
Entropy Bounds and Holography:
Entropy Bounds
The Holographic Principle and Anti de Sitter Space
Black Holes in a Box
Black Holes and Strings:
Strings
Entropy of Strings and Black Holes
Readership: Graduate students, researchers and theoretical
physicists.
200pp Pub. date: Dec 2004
ISBN 981-256-083-1
ISBN 981-256-131-5(pbk)
This volume marks the twentieth anniversary of the Bialowieza
series of meetings on Differential Geometric Methods in Physics;
the anniversary meeting was held during July 1?7, 2001. The
Bialowieza meetings, held every year during the first week of
July, have now grown into an annual pilgrimage for an
international group of physicists and mathematicians. The topics
discussed at the meetings, while within the broad area of
differential geometric methods in physics, have focused around
quantization, coherent states, infinite dimensional systems,
symplectic geometry, spectral theory and harmonic analysis. The
present volume brings together a set of specially invited papers
from leading experts in the various fields, who have contributed
to these meetings and whose work represents a cross-section of
the topics discussed. Consequently, rather than a proceedings
volume, this book embodies the spirit of the Bialowieza workshops
and reflects their scientific tenor, as a tribute to the
completion of two decades of a shared scientific experience.
This book will be of interest to researchers and graduate
students working in the area of differential geometric methods in
physics, as it gives interesting glimpses into the present state
of the art from different points of view.
Contents:
Aspects of Quantization:
Diffeomorphism Groups and Quantum Configurations (G A Goldin)
Functorial Quantization and the Guillemin?Sternberg Conjecture (N
P Landsman)
Coherent State Method in Geometric Quantization (A Odzijewicz)
The Group of Volume Preserving Diffeomorphisms and the Lie
Algebra of Unimodular Vector Fields: Survey of Some Classical and
Not-So-Classical Results (C Roger)
Symplectic and Poisson Geometry:
Moduli Space of Germs of Symplectic Connections of Ricci Type (M
Cahen)
Banach Lie?Poisson Spaces (A Odzijewicz & T S Ratiu)
Other Mathematical Methods:
Spectra of Operators Associated with Dynamical Systems: From
Ergodicity to the Duality Principle (A B Antonevich et al.)
An Ergodic Arnold?Liouville Theorem for Locally Symmetric Spaces
(J Hilgert)
The Renormalization Fixed Point as a Mathematical Object (R P
Langlands)
A Cohomological Description of Abelian Bundles and Gerbes (R
Picken)
On a Quantum Group of Unitary Operators: The Quantum az + b Group
(W Pusz & S L Woronowicz)
Readership: Physicists and mathematicians in the area of
differential geometric methods in physics.
276pp Pub. date: Jan 2005
ISBN 981-256-146-3
Series: Progress in Mathematics, Vol. 41
2005, X, 166 p., Softcover
ISBN: 0-8176-4369-9
About this textbook
Some remarkable connections between commutative algebra and
combinatorics have been discovered in recent years. This book
provides an overview of two of the main topics in this area. The
first concerns the solutions of linear equations in nonnegative
integers. Applications are given to the enumeration of integer
stochastic matrices (or magic squares), the volume of polytopes,
combinatorial reciprocity theorems, and related results. The
second topic deals with the face ring of a simplicial complex,
and includes a proof of the Upper Bound Conjecture for Spheres.
An introductory chapter giving background information in algebra,
combinatorics and topology broadens access to this material for
non-specialists.
New to this edition is a chapter surveying more recent work
related to face rings, focusing on applications to f-vectors.
Table of contents
Contents.- Preface to the Second Edition.- Preface to the First
Edition.- Notation.- Background: Combinatorics.- Commutative
algebra and homological algebra.- Topology.- Chapter I:
Nonnegative Integral Solutions to Linear Equations: Integer
stochastic matrices (magic squares).- Graded algebras and modules.-
Elementary aspects of N-solutions to linear equations.- Integer
stochastic matrices again.- Dimension, depth, and Cohen-Macaulay
modules.- Local cohomology.- Local cohomology of the modules M
phi,alpha.- Reciprocity.- Reciprocity for integer stochastic
matrices.- Rational points in integer polytopes.- Free
resolutions.- Duality and canonical modules.- A final look at
linear equations.- Chapter II: The Face Ring of a Simplicial
Complex: Elementary properties of the face ring.- f-vectors and h-vectors
of complexes and multicomplexes.- Cohen-Macaulay complexes and
the Upper Bound Conjecture.- Homological properties of face rings.-
Gorenstein face rings.- Gorenstein Hilbert Functions.- Canonical
modules of face rings.- Buchsbaum complexes.- Chapter III:
Further Aspects of Face Rings: Simplicial polytopes, toric
varieties, and the g-theorem.- Shellable simplicial complexes.-
Matroid complexes, level complexes, and doubly Cohen-Macaulay
complexes.- Balances complexes, order complexes, and flag
complexes.- Splines.- Algebras with straightening law and
simplical posets.- Relative simplical complexes.- Group actions.-
Subcomplexes.- Subdivisions.- Problems on Simplicial Complexes
and their Face Rings.- Bibliography.- Index.
Seminaires et Congres 8 (2004), xx+430 pages
Resume :
La theorie des systemes differentiels geometriques est l'etude
des Modules coherents sur l'Anneau des operateurs differentiels
sur une variete analytique ou algebrique. Elle intervient dans de
nombreuses branches des mathematiques: geometrie algebrique,
arithmetique, groupes et algebres de Lie, topologie algebrique
des singularites... Ce livre est le resultat de la redaction de
plusieurs cours donnes lors d'une ecole du C.I.M.P.A. en
septembre 1996. Il veut offrir au lecteur, par la prise en compte
des elements les plus recents de la theorie, une synthese des
nombreux articles de recherche sur ce sujet. Ainsi, la plupart
des cours ont ete ecrits pour etre lus par des etudiants
commencant la recherche mathematique.
Mots clefs :
-module, bases de Grobner, complexe de de Rham, connexions
meromorphes regulieres, cycle caracteristique, cycles
evanescents, dualite, dualite de Grothendieck-Verdier,
filtration, V-filtration, foncteur image inverse, indice,
irregularite, faisceau d'irregularite, modules holonomes, modules
specialisables, monodromie, operateur differentiel d'ordre
infini, pentes, positivite, regularite, critere fondamental de la
regularite, reseau canonique, theoreme de comparaison, theoreme
de division
Abstract:
Elements of the theory of geometric differential systems
The theory of geometric differential systems consists in the
study of coherent Modules on the Ring of differential operators
on a complex analytic or algebraic manifold. It is used in
various branches of mathematics: algebraic geometry, arithmetics,
Lie groups and Lie algebras, algebraic topology of singularities...
This book contains the texts of lectures given at a C.I.M.P.A.
summer school in september 1996. It offers a complete survey of
the theory, taking into account the most recent advances. Most of
the lectures are aimed at young researchers.
Key words:
-module, canonical lattice, characteristic cycle, comparison
theorem, de Rham complex, division theorem, duality, filtration,
V-filtration, Grobner basis, Grothendieck-Verdier duality,
holonomic modules, index, infinite order differential operator,
inverse image functor, irregularity, irregularity sheaf,
monodromy, positivity, regularity, fundamental criterion of
regularity, regular meromorphic connections, slopes,
specializable modules, vanishing cycles
ISBN : 2-85629-151-1