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Noncommutative differential geometry is a new approach to classical
geometry. It was originally used by Fields Medalist A. Connes in
the theory of foliations, where it led to striking extensions of
Atiyah-Singer index theory. It also may be applicable to hitherto
unsolved geometric phenomena and physical experiments. However,
noncommutative differential geometry was not well understood even
among mathematicians. Therefore, an international symposium on
commutative differential geometry and its applications to physics
was held in Japan, in July 1999. Topics covered included:
deformation problems, Poisson groupoids, operad theory,
quantization problems, and D-branes. The meeting was attended by
both mathematicians and physicists, which resulted in interesting
discussions. This volume contains the refereed proceedings of this
symposium. Providing a state of the art overview of research in
these topics, this book is suitable as a source book for a seminar
in noncommutative geometry and physics.
This volume contains papers presented at the meeting Deformation
Theory, Symplectic Geometry and Applications, held in Ascona, June
17-21, 1996. The contents touch upon many frontier domains of
modern mathematics, mathematical physics and theoretical physics
and include authoritative, state-of-the-art contributions by
leading scientists. New and important developments in the fields of
symplectic geometry, deformation quantization, noncommutative
geometry (NCG) and Lie theory are presented. Among the subjects
treated are: quantization of general Poisson manifolds; new
deformations needed for the quantization of Nambu mechanics;
quantization of intersection cardinalities; quantum shuffles; new
types of quantum groups and applications; quantum cohomology;
strong homotopy Lie algebras; finite- and infinite-dimensional Lie
groups; and 2D field theories and applications of NCG to gravity
coupled with the standard model. Audience: This book will be of
interest to researchers and post-graduate students of mathematical
physics, global analysis, analysis on manifolds, topological
groups, nonassociative rings and algebras, and Lie algebras.
This book contains the proceedings of a meeting that brought
together friends and colleagues of Guy Rideau at the Universite
Denis Diderot (Paris, France) in January 1995. It contains original
results as well as review papers covering important domains of
mathematical physics, such as modern statistical mechanics, field
theory, and quantum groups. The emphasis is on geometrical
approaches. Several papers are devoted to the study of symmetry
groups, including applications to nonlinear differential equations,
and deformation of structures, in particular
deformation-quantization and quantum groups. The richness of the
field of mathematical physics is demonstrated with topics ranging
from pure mathematics to up-to-date applications such as imaging
and neuronal models. Audience: Researchers in mathematical physics.
"
These two volumes constitute the Proceedings of the Conference
Moshe Flato, 1999'. Their spectrum is wide but the various areas
covered are, in fact, strongly interwoven by a common denominator,
the unique personality and creativity of the scientist in whose
honor the Conference was held, and the far-reaching vision that
underlies his scientific activity. With these two volumes, the
reader will be able to take stock of the present state of the art
in a number of subjects at the frontier of current research in
mathematics, mathematical physics, and physics. Volume I is
prefaced by reminiscences of and tributes to Flato's life and work.
It also includes a section on the applications of sciences to
insurance and finance, an area which was of interest to Flato
before it became fashionable. The bulk of both volumes is on
physical mathematics, where the reader will find these ingredients
in various combinations, fundamental mathematical developments
based on them, and challenging interpretations of physical
phenomena. Audience: These volumes will be of interest to
researchers and graduate students in a variety of domains, ranging
from abstract mathematics to theoretical physics and other
applications. Some parts will be accessible to proficient
undergraduate students, and even to persons with a minimum of
scientific knowledge but enough curiosity.
These two volumes constitute the Proceedings of the Conference
Moshe Flato, 1999'. Their spectrum is wide but the various areas
covered are, in fact, strongly interwoven by a common denominator,
the unique personality and creativity of the scientist in whose
honor the Conference was held, and the far-reaching vision that
underlies his scientific activity. With these two volumes, the
reader will be able to take stock of the present state of the art
in a number of subjects at the frontier of current research in
mathematics, mathematical physics, and physics. Volume I is
prefaced by reminiscences of and tributes to Flato's life and work.
It also includes a section on the applications of sciences to
insurance and finance, an area which was of interest to Flato
before it became fashionable. The bulk of both volumes is on
physical mathematics, where the reader will find these ingredients
in various combinations, fundamental mathematical developments
based on them, and challenging interpretations of physical
phenomena. Audience: These volumes will be of interest to
researchers and graduate students in a variety of domains, ranging
from abstract mathematics to theoretical physics and other
applications. Some parts will be accessible to proficient
undergraduate students, and even to persons with a minimum of
scientific knowledge but enough curiosity."
Noncommutative differential geometry is a new approach to classical
geometry. It was originally used by Fields Medalist A. Connes in
the theory of foliations, where it led to striking extensions of
Atiyah-Singer index theory. It also may be applicable to hitherto
unsolved geometric phenomena and physical experiments.
However, noncommutative differential geometry was not well
understood even among mathematicians. Therefore, an international
symposium on commutative differential geometry and its applications
to physics was held in Japan, in July 1999. Topics covered
included: deformation problems, Poisson groupoids, operad theory,
quantization problems, and D-branes. The meeting was attended by
both mathematicians and physicists, which resulted in interesting
discussions. This volume contains the refereed proceedings of this
symposium.
Providing a state of the art overview of research in these topics,
this book is suitable as a source book for a seminar in
noncommutative geometry and physics.
These two volumes constitute the Proceedings of the ConfA(c)rence
MoshA(c) Flato, 1999'. Their spectrum is wide but the various areas
covered are, in fact, strongly interwoven by a common denominator,
the unique personality and creativity of the scientist in whose
honor the Conference was held, and the far-reaching vision that
underlies his scientific activity. With these two volumes, the
reader will be able to take stock of the present state of the art
in a number of subjects at the frontier of current research in
mathematics, mathematical physics, and physics. Volume I is
prefaced by reminiscences of and tributes to Flato's life and work.
It also includes a section on the applications of sciences to
insurance and finance, an area which was of interest to Flato
before it became fashionable. The bulk of both volumes is on
physical mathematics, where the reader will find these ingredients
in various combinations, fundamental mathematical developments
based on them, and challenging interpretations of physical
phenomena. Audience: These volumes will be of interest to
researchers and graduate students in a variety of domains, ranging
from abstract mathematics to theoretical physics and other
applications. Some parts will be accessible to proficient
undergraduate students, and even to persons with a minimum of
scientific knowledge but enough curiosity.
These two volumes constitute the Proceedings of the ConfA(c)rence
MoshA(c) Flato, 1999'. Their spectrum is wide but the various areas
covered are, in fact, strongly interwoven by a common denominator,
the unique personality and creativity of the scientist in whose
honor the Conference was held, and the far-reaching vision that
underlies his scientific activity. With these two volumes, the
reader will be able to take stock of the present state of the art
in a number of subjects at the frontier of current research in
mathematics, mathematical physics, and physics. Volume I is
prefaced by reminiscences of and tributes to Flato's life and work.
It also includes a section on the applications of sciences to
insurance and finance, an area which was of interest to Flato
before it became fashionable. The bulk of both volumes is on
physical mathematics, where the reader will find these ingredients
in various combinations, fundamental mathematical developments
based on them, and challenging interpretations of physical
phenomena. Audience: These volumes will be of interest to
researchers and graduate students in a variety of domains, ranging
from abstract mathematics to theoretical physics and other
applications. Some parts will be accessible to proficient
undergraduate students, and even to persons with a minimum of
scientific knowledge but enough curiosity.
This volume contains papers presented at the meeting Deformation
Theory, Symplectic Geometry and Applications, held in Ascona, June
17-21, 1996. The contents touch upon many frontier domains of
modern mathematics, mathematical physics and theoretical physics
and include authoritative, state-of-the-art contributions by
leading scientists. New and important developments in the fields of
symplectic geometry, deformation quantization, noncommutative
geometry (NCG) and Lie theory are presented. Among the subjects
treated are: quantization of general Poisson manifolds; new
deformations needed for the quantization of Nambu mechanics;
quantization of intersection cardinalities; quantum shuffles; new
types of quantum groups and applications; quantum cohomology;
strong homotopy Lie algebras; finite- and infinite-dimensional Lie
groups; and 2D field theories and applications of NCG to gravity
coupled with the standard model. Audience: This book will be of
interest to researchers and post-graduate students of mathematical
physics, global analysis, analysis on manifolds, topological
groups, nonassociative rings and algebras, and Lie algebras.
This book contains the proceedings of a meeting that brought
together friends and colleagues of Guy Rideau at the Universite
Denis Diderot (Paris, France) in January 1995. It contains original
results as well as review papers covering important domains of
mathematical physics, such as modern statistical mechanics, field
theory, and quantum groups. The emphasis is on geometrical
approaches. Several papers are devoted to the study of symmetry
groups, including applications to nonlinear differential equations,
and deformation of structures, in particular
deformation-quantization and quantum groups. The richness of the
field of mathematical physics is demonstrated with topics ranging
from pure mathematics to up-to-date applications such as imaging
and neuronal models. Audience: Researchers in mathematical physics.
"
Poisson geometry lies at the cusp of noncommutative algebra and
differential geometry, with natural and important links to
classical physics and quantum mechanics. This book presents an
introduction to the subject from a small group of leading
researchers, and the result is a volume accessible to graduate
students or experts from other fields. The contributions are:
Poisson Geometry and Morita Equivalence by Bursztyn and Weinstein;
Formality and Star Products by Cattaneo; Lie Groupoids, Sheaves and
Cohomology by Moerdijk and Mrcun; Geometric Methods in
Representation Theory by Schmid; Deformation Theory: A Powerful
Tool in Physics Modelling by Sternheimer.
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