Expected publication date is December 23, 2005
Description
Mathematics provides a language in which to formulate the laws
that govern nature. It is a language proven to be both powerful
and effective. In the quest for a deeper understanding of the
fundamental laws of physics, one is led to theories that are
increasingly difficult to put to the test.
In recent years, many novel questions have emerged in
mathematical physics, particularly in quantum field theory.
Indeed, several areas of mathematics have lately become
increasingly influential in physics and, in turn, have become
influenced by developments in physics. Over the last two decades,
interactions between mathematicians and physicists have increased
enormously and have resulted in a fruitful cross-fertilization of
the two communities.
This volume contains the plenary talks from the international
symposium on Noncommutative Geometry and Representation Theory in
Mathematical Physics held at Karlstad University (Sweden) as a
satellite conference to the Fourth European Congress of
Mathematics.
The scope of the volume is large and its content is relevant to
various scientific communities interested in noncommutative
geometry and representation theory. It offers a comprehensive
view of the state of affairs for these two branches of
mathematical physics. The book is suitable for graduate students
and researchers interested in mathematical physics.
Contents
N. Bazunova -- Construction of graded differential algebra with
ternary differential
C. Blohmann -- Calculation of the universal Drinfeld twist for
quantum su(2)
M. Cederwall -- Thoughts on membranes, matrices and non-commutativity
C. Chryssomalakos and E. Okon -- Stable quantum relativistic
kinematics
T. Ekedahl -- Kac-Moody algebras and the cde-triangle
A. Davydov -- Cohomology of crossed algebras
L. D. Faddeev -- Discretized Virasoro algebra
G. Felder and A. Varchenko -- Multiplication formulae for the
elliptic gamma function
G. Fiore -- New approach to Hermitian q-differential operators on mathbb{R}^N_q
J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert -- Picard
groups in rational conformal field theory
A. Gerasimov, S. Kharchev, D. Lebedev, and S. Oblezin -- On a
class of representations of quantum groups
M. Gorelik and V. Serganova -- Shapovalov forms for Poisson Lie
superalgebras
T. J. Hodges and M. Yakimov -- Triangular Poisson structures on
Lie groups and symplectic reduction
Y.-Z. Huang -- Vertex operator algebras, fusion rules and modular
transformations
L. Kadison -- Depth two and the Galois coring
N. Kamiya -- Examples of Peirce decomposition of generalized
Jordan triple system of second order--Balanced cases
I. Kantor and G. Shpiz -- Graded representations of graded Lie
algebras and generalized representations of Jordan algebras
E. Karolinsky, A. Stolin, and V. Tarasov -- Dynamical Yang-Baxter
equation and quantization of certain Poisson brackets
R. Kashaev and N. Reshetikhin -- Braiding for quantum gl_2 at roots of
unity
C. Korff -- Solving Baxter's TQ-equation via representation
theory
P. P. Kulish -- Noncommutative geometry and quantum field theory
E. Langmann -- Conformal field theory and the solution of the (quantum)
elliptic Calogero-Sutherland system
D. Larsson and S. D. Silvestrov -- Quasi-Lie algebras
O. A. Laudal -- Time-space and space-times
J. Lukierski and V. D. Lyakhovsky -- Two-parameter extension of the kappa-Poincare quantum deformation
V. E. Nazaikinskii, A. Y. Savin, B.-W. Schulze, and B. Y. Sternin
-- The index problem on manifolds with edges
D. Proskurin, Y. Savchuk, and L. Turowska -- On C^*-algebras generated
by some deformations of CAR relations
O. K. Sheinman -- Krichever-Novikov algebras and their
representations
S. D. Sinel'shchikov and L. Vaksman -- Quantum groups and bounded
symmetric domains
D. Sternheimer -- Quantization is deformation
K. Szlachanyi -- Monoidal Morita equivalence
V. N. Tolstoy -- Fortieth anniversary of extremal projector
method for Lie symmetries
Details:
Series: Contemporary Mathematics, Volume: 391
Publication Year: 2005
ISBN: 0-8218-3718-4
Paging: 384 pp.
Binding: Softcover
Expected publication date is December 29, 2005
Description
The University of Virginia (Charlottesville) hosted an
international conference on Infinite-dimensional Aspects of
Representation Theory and Applications. This volume contains
papers resulting from the mini-courses and talks given at the
meeting.
Beyond the techniques and ideas related to representation theory,
the book demonstrates connections to number theory, algebraic
geometry, and mathematical physics. Specific topics covered
include Hecke algebras, quantum groups, infinite-dimensional Lie
algebras, quivers, modular representations, and Gromov-Witten
invariants.
The book is suitable for graduate students and researchers
interested in representation theory.
Contents
S. Ariki -- Modular representation theory of Hecke algebras, a
survey
V. Chari and J. Greenstein -- An application of free Lie algebras
to polynomial current algebras and their representation theory
N. Jacon -- Canonical basic sets for Hecke algebras
M. Lau -- On universal central extensions of mathfrak{sl}_n(A)
H. Li -- Pseudoderivations, pseudoautomorphisms and simple
current modules for vertex algebras
W.-P. Li, Z. Qin, and W. Wang -- Hilbert scheme intersection
numbers, Hurwitz numbers, and Gromov-Witten invariants
K. C. Misra -- On Demazure crystals for U_q(D^{(3)}_4)
E. Mukhin and A. Varchenko -- Populations of solutions of the XXX Bethe
equations associated to Kac-Moody algebras
R. Rouquier -- Representations of rational Cherednik algebras
A. Savage -- A geometric construction of crystal graphs using
quiver varieties: Extension to the non-simply laced case
Details:
Series: Contemporary Mathematics, Volume: 392
Publication Year: 2005
ISBN: 0-8218-3701-X
Paging: 154 pp.
Binding: Softcover
Expected publication date is January 21, 2006
Description
The modern theory of automorphic forms, embodied in what has come
to be known as the Langlands program, is an extraordinary
unifying force in mathematics. It proposes fundamental relations
that tie arithmetic information from number theory and algebraic
geometry with analytic information from harmonic analysis and
group representations. These "reciprocity laws",
conjectured by Langlands, are still largely unproved. However,
their capacity to unite large areas of mathematics insures that
they will be a central area of study for years to come.
The goal of this volume is to provide an entry point into this
exciting and challenging field. It is directed, on the one hand,
at graduate students and professional mathematicians who would
like to work in the area. The longer articles in particular
represent an attempt to enable a reader to master some of the
more difficult techniques. On the other hand, the book will also
be useful to mathematicians who would like simply to understand
something of the subject. They will be able to consult the
expository portions of the various articles.
The volume is centered around the trace formula and Shimura
varieties. These areas are at the heart of the subject, but they
have been especially difficult to learn because of a lack of
expository material. The volume aims to rectify the problem. It
is based on the courses given at the 2003 Clay Mathematics
Institute Summer School. However, many of the articles have been
expanded into comprehensive introductions, either to the trace
formula or the theory of Shimura varieties, or to some aspect of
the interplay and application of the two areas.
This book is suitable for independent study.
Contents
J. Arthur -- An introduction to the trace formula
J. S. Milne -- Introduction to Shimura varieties
F. Murnaghan -- Linear algebraic groups
R. E. Kottwitz -- Harmonic analysis on reductive p-adic groups and Lie
algebras
S. DeBacker -- Homogeneity for reductive p-adic groups: An introduction
M. Goresky -- Compactifications and cohomology of modular
varieties
T. J. Haines -- Introduction to Shimura varieties with bad
reduction of parahoric type
T. C. Hales -- A statement of the fundamental lemma
P. Sarnak -- Notes on the generalized Ramanujan conjectures
List of participants
Details:
Series: Clay Mathematics Proceedings, Volume: 4
Publication Year: 2005
ISBN: 0-8218-3844-X
Paging: approximately 704 pp.
Binding: Softcover
Expected publication date is January 12, 2006
From a review of the German edition:
"The book covers all the topics which could be necessary
later for learning higher level differential geometry. The
material is very carefully sorted and easy-to-read."
-- Mathematical Reviews
Description
Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I!!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas.
With just the basic tools from multivariable calculus, plus a
little knowledge of linear algebra, it is possible to begin a
much richer and rewarding study of differential geometry, which
is what is presented in this book. It starts with an introduction
to the classical differential geometry of curves and surfaces in
Euclidean space, then leads to an introduction to the Riemannian
geometry of more general manifolds, including a look at Einstein
spaces. An important bridge from the low-dimensional theory to
the general case is provided by a chapter on the intrinsic
geometry of surfaces.
The first half of the book, covering the geometry of curves and
surfaces, would be suitable for a one-semester undergraduate
course. The local and global theories of curves and surfaces are
presented, including detailed discussions of surfaces of
rotation, ruled surfaces, and minimal surfaces.
The second half of the book, which could be used for a more
advanced course, begins with an introduction to differentiable
manifolds, Riemannian structures, and the curvature tensor. Two
special topics are treated in detail: spaces of constant
curvature and Einstein spaces.
The main goal of the book is to get started in a fairly
elementary way, then to guide the reader toward more
sophisticated concepts and more advanced topics. There are many
examples and exercises to help along the way. Numerous figures
help the reader visualize key concepts and examples, especially
in lower dimensions. For the second edition, a number of errors
were corrected and some text and a number of figures have been
added.
Contents
Notations and prerequisites from analysis
Curves in I!!R^n
The local theory of surfaces
The intrinsic geometry of surfaces
Riemannian manifolds
The curvature tensor
Spaces of constant curvature
Einstein spaces
Bibliography
List of notation
Index
Details:
Series: Student Mathematical Library, Volume: 16
Publication Year: 2006
ISBN: 0-8218-3988-8
Paging: approximately 376 pp.
Binding: Softcover
Expected publication date is January 7, 2006
Description
This volume presents topics addressed at the working group
meeting and workshop on Computer-generated Conjectures from Graph
Theoretic and Chemical Databases held at Rutgers University (Piscataway,
NJ). The events brought together theoreticians and practitioners
working in graph theory and chemistry to share ideas and to set
an agenda for future developments in the use of computers for
generating scientific conjectures.
Articles included in the volume were written by developers of
some of the most important programs used around the world today.
The disciplines represented include theoretical and applied
computer science, statistics, discrete and non-discrete
mathematics, chemistry, and information science.
The book is suitable for researchers and students interested in
the use of computers in graph theory.
Contents
J. W. Berry -- Considerations for future designers of general
purpose graph software
E. Breimer, M. Goldberg, D. Hollinger, and D. Lim -- Discovering
optimization algorithms through automated learning
G. Brinkmann, O. Delgado-Friedrichs, and U. von Nathusius --
Numbers of faces and boundary encodings of patches
D. Cvetkovic and S. Simic -- Graph theoretical results obtained
by the support of the expert system "graph"-An extended
survey
E. DeLaVina -- Graffiti.pc: A variant of graffiti
E. DeLaVina -- Some history of the development of graffiti
E. DeLaVina, S. Fajtlowicz, and W. Waller -- On some conjectures
of Griggs and graffiti
S. Fajtlowicz -- On the representation and characterization of fullerene
C_{60}
J. E. Graver -- The structure of fullerene signatures
J. E. Graver -- Catalog of all fullerenes with ten or more
symmetries
P. Hansen -- How far is, should and could be conjecture-making in
graph theory an automated process?
P. Hansen, M. Aouchiche, G. Caporossi, H. Melot, and D.
Stevanovic -- What forms do interesting conjectures have in graph
theory?
P. Hansen and H. Melot -- Variable neighborhood search for
extremal graphs. 9. Bounding the irregularity of a graph
S. M. Husband, C. P. Husband, N. Dean, and J. M. Tour --
Mathematics for the nanocell approach to molecular electronics
R. J. Kingan and S. R. Kingan -- A software system for matroids
C. E. Larson -- A survey of research in automated mathematical
conjecture-making
R. Laue, T. Gruner, M. Meringer, and A. Kerber -- Constrained
generation of molecular graphs
W. Myrvold, T. Prsa, and N. Walker -- A dynamic programming
approach for timing and designing clique algorithms
R. D. Pepper -- On new didactics of mathematics: Learning graph
theory via graffiti
T. Pisanski, M. Boben, and A. Zitnik -- Interactive conjecturing
with Vega
D. Stevanovic and G. Caporossi -- On the (1,2)-spectral spread of fullerenes
Details:
Series: DIMACS: Series in Discrete Mathematics and Theoretical
Computer Science, Volume: 69
Publication Year: 2005
ISBN: 0-8218-3761-3
Paging: approximately 384 pp.
Binding: Hardcover
Expected publication date is January 14, 2006
Description
This volume serves as an introduction to the Kodaira-Spencer
theory of deformations of complex structures. Based on notes
taken by James Morrow from lectures given by Kunihiko Kodaira at
Stanford University in 1965-1966, the book gives the original
proof of the Kodaira embedding theorem, showing that the
restricted class of Kahler manifolds called Hodge manifolds is
algebraic. Included are the semicontinuity theorems and the local
completeness theorem of Kuranishi.
Readers are assumed to know some algebraic topology. Complete
references are given for the results that are used from elliptic
partial differential equations. The book is suitable for graduate
students and researchers interested in abstract complex manifolds.
Contents
Definitions and examples of complex manifolds
Sheaves and cohomology
Geometry of complex manifolds
Applications of elliptic partial differential equations to
deformations
Bibliography
Index
Errata
Details:
Series: AMS Chelsea Publishing
Publication Year: 1971
ISBN: 0-8218-4055-X
Paging: 194 pp.
Binding: Hardcover