Masayoshi Miyanishi, Osaka University, Toyonaka, Japan
Open Algebraic Surfaces
Description
Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful
Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods
to study the geometry and topology of open algebraic surfaces.
The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in
particular to the study of affine surfaces. Prerequisite to understanding the text is a basic background in algebraic geometry. This volume is a continuation of the work presented in the author's previous publication, Algebraic Geometry, Volume 136 in the AMS series, Translations of
Mathematical Monographs.
Contents
Complete algebraic surfaces
Open algebraic surfaces
Affine algebraic surfaces
Bibliography
Index
Details:
Publisher: American Mathematical Society
Series: CRM Monograph Series, Volume: 12
Publication Year: 2000
ISBN: 0-8218-0504-5
Paging: 259 pp.
Binding: Hardcover
Edited by: Michael Baake, Universitat Tubingen, Germany,
Robert V. Moody, University of Alberta, Edmonton, AB, CanadaDirections in Mathematical Quasicrystals
Description
This volume includes twelve solicited articles which survey the current state of knowledge and some of the open questions on the mathematics of aperiodic order. A number of the articles deal with the sophisticated mathematical ideas that are being developed from physical motivations.
Many prominent mathematical aspects of the subject are presented, including the geometry of aperiodic point sets and their diffractive properties, self-affine tilings, the role of $C^*$-algebras in tiling theory, and the interconnections between symmetry and aperiodic point sets. Also discussed are the question of pure point diffraction of general model sets, the arithmetic of shelling icosahedral quasicrystals, and the study of self-similar measures on model sets.
From the physical perspective, articles reflect approaches to the mathematics of quasicrystal growth and the Wulff shape, recent results on the spectral nature of aperiodic Schr?dinger operators with implications to transport theory, the characterization of spectra through gap-labeling, and the mathematics of planar dimer models.
A selective bibliography with comments is also provided to assist the reader in getting an overview of the field. The book will serve as a comprehensive guide and an inspiration to those interested in learning more about this intriguing subject.
Contents
M. Baake and R. V. Moody -- Self-similar measures for quasicrystals
G. Bernuau and M. Duneau -- Fourier analysis of deformed model sets
J. C. Lagarias -- Mathematical quasicrystals and the problem of diffraction
P. A. B. Pleasants -- Designer quasicrystals: Cut-and-project sets with pre-assigned properties
M. Schlottmann -- Generalized model sets and dynamical systems
A. Weiss -- On shelling icosahedral quasicrystals
J. Kellendonk and I. F. Putnam -- Tilings, $C*$-algebras, and $K$-theory
J. Bellissard, D. J. L. Herrmann, and M. Zarrouati -- Hulls of aperiodic solids and gap labeling theorems
K. B?r?czky, Jr., U. Schnell, and J. M. Wills -- Quasicrystals, parametric density, and Wulff-shape
D. Damanik -- Gordon-type arguments in the spectral theory of one-dimensional quasi-crystals
R. Kenyon -- The planar dimer model with boundary: A survey
A. Vince -- Digit tiling of euclidean space
M. Baake and U. Grimm -- A guide to quasicrystal literature
Index
Details:
Publisher: American Mathematical Society
Series: CRM Monograph Series, Volume: 13
Publication Year: 2000
ISBN: 0-8218-2629-8
Paging: 379 pp.
Binding: Hardcover
Edited by: J. Harnad, /G. Sabidussi, /P. Winternitz,
Centre de Recherches Mathematiques, Universite de Montreal, PQ, CanadaIntegrable Systems: From Classical to Quantum
Description
This volume presents the papers based upon lectures given at the 1999 Seminaire de Mathemathiques Superieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in surprisingly different directions.
Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number
of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror
symmetry, quantum cohomology, etc.
This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.
Contents
J. Balog, L. Feh?r, and L. Palla -- On the chiral WZNW phase space, exchange r-matrices and Poisson-Lie groupoids
J. Harnad -- Loop groups, $R$-matrices and separation of variables
J. C. Hurtubise -- The geometry of generalised Hitchin systems
V. E. Korepin -- Determinant representation for form factors
D. A. Korotkin -- Isomonodromic deformations in genus zero and one: Algebro-geometric solutions and Schlesinger transformations
J.-M. Maillet -- Quantum inverse scattering problem and correlation functions of integrable models
W. Miller, Jr. -- Multiseparability and superintegrability for classical and quantum systems
T. Miwa -- Integrability and symmetry of the XXZ model
N. Reshetikhin -- Characteristic systems on Poisson Lie groups and their quantization
S. N. M. Ruijsenaars -- Special functions associated with Calogero-Moser type quantum systems
E. K. Sklyanin -- B?cklund transformations and Baster's $Q$-operator
C. A. Tracy and H. Widom -- Universality of the distribution functions of random matrix theory
Details:
Publisher: American Mathematical Society
Series: CRM Proceedings & Lecture Notes, Volume: 26
Publication Year: 2000
ISBN: 0-8218-2093-1
Paging: 264 pp.
Binding: Softcover
Edited by: Fritz Gesztesy, University of Missouri, Columbia, MO, et al
Stochastic Processes, Physics and Geometry:
New Interplays. I: A Volume in Honor of Sergio Albeverio
Description
This volume and Stochastic Processes, Physics and Geometry: New Interplays. II present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of
Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry.
The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems,
quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas.
Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary
connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional
contributed papers.
Details:
Publisher: American Mathematical Society
Series: Conference Proceedings, Canadian Mathematical Society, Volume: 28
Publication Year: 2000
ISBN: 0-8218-1959-3
Paging: 333 pp.
Binding: Softcover
Edited by: Fritz Gesztesy, University of Missouri, Columbia, MO, et al.
Stochastic Processes, Physics and Geometry:
New Interplays. II: A Volume in Honor of Sergio Albeverio
Description
This volume and Stochastic Processes, Physics and Geometry: New Interplays. I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical
physics, and geometry.
The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas.
Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers.
Details:
Publisher: American Mathematical Society
Series: Conference Proceedings, Canadian Mathematical Society, Volume: 29
Publication Year: 2000
ISBN: 0-8218-1960-7
Paging: approximately 664 pp.
Binding: Softcover
Edited by: Caroline Grant Melles, U.S. Naval Academy, Annapolis, MD,
and Ruth I. Michler, University of North Texas, Denton, TXSingularities in Algebraic and Analytic Geometry
Description
This volume contains the proceedings of an AMS special session held at the 1999 Joint Mathematics Meetings in San Antonio. The participants were an international group of researchers studying singularities from algebraic and analytic viewpoints. The contributed papers contain original results as well as some expository and historical material. This volume is dedicated to Oscar Zariski, on the one hundredth anniversary of his birth.
Topics include the role of valuation theory in algebraic geometry with recent applications to the structure of morphisms; algorithmic approaches to resolution of equisingular surface singularities and locally toric varieties; weak subintegral closures of ideals an Rees valuations; constructions of universal weakly subintegral extensions of rings; direct-sum decompositions of finitely generated modules; construction and examples of resolution graphs of surface singularities; Jacobians of
meromorphic curves; investigation of spectral numbers of curve singularities using Puiseux pairs; Grner basis calculations of Hochschild homology for hypersurfaces with isolated singularities; and the theory of characteristic classes of singular spaces--a brief history with conjectures and open problems.
Contents
S. S. Abhyankar and A. Assi -- Factoring the Jacobian
M. A. Vitulli -- Weak normalization and weak subintegral closure
L. G. Roberts -- Integral dependence and weak subintegrality
R. Wiegand -- Singularities and direct-sum decompositions
S. D. Cutkosky -- Valuations in algebra and geometry
C. Ban and L. J. McEwan -- Simultaneous resolution of equisingular quasi-ordinary singularities
C. G. Melles and P. Milman -- Single-step combinatorial resolution via coherent sheaves of ideals
A. Nemethi -- Resolution graphs of some surface singularities, I. (Cyclic coverings)
A. Nemethi and Szilard -- Resolution graphs of some surface singularities, II. (Generalized Iomdin series)
L. J. McEwan -- Inequalities for spectral distributions of curve singularities
R. I. Michler -- Isolated singularities with large Hochschild homology
J.-P. Brasselet -- Milnor classes via polar varieties
Details:
Publisher: American Mathematical Society
Series: Contemporary Mathematics, Volume: 266
Publication Year: 2000
ISBN: 0-8218-2005-2
Paging: 187 pp.
Binding: Softcover