SMF/AMS Texts and Monographs, Volume: 13
2006; 105 pp; softcover
ISBN-10: 0-8218-3166-6
ISBN-13: 978-0-8218-3166-3
Expected publication date is November 5, 2006.
The correspondence between Einstein metrics and their conformal
boundaries has recently been the focus of great interest. This is
particularly so in view of the relation with the physical theory
of the AdS/CFT correspondence.
In this book, this correspondence is seen in the wider context of
asymptotically symmetric Einstein metrics, that is Einstein
metrics whose curvature is asymptotic to that of a rank one
symmetric space. There is an emphasis on the correspondence
between Einstein metrics and geometric structures on their
boundary at infinity: conformal structures, CR structures, and
quaternionic contact structures introduced and studied in the
book.
Two new constructions of such Einstein metrics are given, using
two different kinds of techniques:
analytic methods to construct complete Einstein metrics, with a
unified treatment of all rank one symmetric spaces, relying on
harmonic analysis;
algebraic methods (twistor theory) to construct local solutions
of the Einstein equation near the boundary.
Titles in this series are copublished with Societe Mathematique
de France. SMF members are entitled to AMS member discounts.
Readership
Graduate students and research mathematicians interested in
differential geometry, global analysis, and Einstein metrics.
Table of Contents
Introduction
Einstein deformations of hyperbolic metrics
Quaternionic contact structures
Quaternionic-Kahler metrics
Bibliography
Graduate Studies in Mathematics, Volume: 71
2006; 633 pp; hardcover
ISBN-10: 0-8218-3929-2
ISBN-13: 978-0-8218-3929-4
Expected publication date is December 7, 2006.
The book presents the basics of Riemannian geometry in its modern
form as geometry of differentiable manifolds and the most
important structures on them. The authors' approach is that the
source of all constructions in Riemannian geometry is a manifold
that allows one to compute scalar products of tangent vectors.
With this approach, the authors show that Riemannian geometry has
a great influence to several fundamental areas of modern
mathematics and its applications. In particular,
・Geometry is a bridge between pure mathematics and natural
sciences, first of all physics. Fundamental laws of nature are
formulated as relations between geometric fields describing
various physical quantities.
・The study of global properties of geometric objects leads to
the far-reaching development of topology, including topology and
geometry of fiber bundles.
・Geometric theory of Hamiltonian systems, which describe many
physical phenomena, led to the development of symplectic and Poisson
geometry. Field theory and the multidimensional calculus of
variations, presented in the book, unify mathematics with
theoretical physics.
・Geometry of complex and algebraic manifolds unifies Riemannian
geometry with modern complex analysis, as well as with algebra
and number theory.
Prerequisites for using the book include several basic
undergraduate courses, such as advanced calculus, linear algebra,
ordinary differential equations, and elements of topology.
Readership
Graduate students and research mathematicians interested in
modern geometry and its applications.
Table of Contents
Contemporary Mathematics, Volume: 414
2006; 417 pp; softcover
ISBN-10: 0-8218-3923-3
ISBN-13: 978-0-8218-3923-2
This book offers a presentation of some new trends in operator
theory and operator algebras, with a view to their applications.
It consists of separate papers written by some of the leading
practitioners in the field. The content is put together by the
three editors in a way that should help students and working
mathematicians in other parts of the mathematical sciences gain
insight into an important part of modern mathematics and its
applications.
While different specialist authors are outlining new results in
this book, the presentations have been made user friendly with
the aid of tutorial material. In fact, each paper contains three
things: a friendly introduction with motivation, tutorial
material, and new research. The authors have strived to make
their results relevant to the rest of mathematics. A list of
topics discussed in the book includes wavelets, frames and their
applications, quantum dynamics, multivariable operator theory, C^*-algebras,
and von Neumann algebras. Some longer papers present recent
advances on particular, long-standing problems such as extensions
and dilations, the Kadison-Singer conjecture, and diagonals of
self-adjoint operators.
Readership
Graduate students and research mathematicians interested in
theory of operators and operator algebras.
Contemporary Mathematics,Volume: 415
2006; 307 pp; softcover
ISBN-10: 0-8218-3765-6
ISBN-13: 978-0-8218-3765-8
This volume is a collection of articles dedicated to quantum
graphs, a newly emerging interdisciplinary field related to
various areas of mathematics and physics. The reader can find a
broad overview of the theory of quantum graphs. The articles
present methods coming from different areas of mathematics:
number theory, combinatorics, mathematical physics, differential
equations, spectral theory, global analysis, and theory of
fractals. They also address various important applications, such
as Anderson localization, electrical networks, quantum chaos,
mesoscopic physics, superconductivity, optics, and biological
modeling.
Readership
Graduate students and research mathematicians interested in
quantum graphs and application to number theory, mathematical
physics, and other areas.
Table of Contents
M. Aizenman, R. Sims, and S. Warzel -- Fluctuation-based proof of
the stability of ac spectra of random operators on tree graphs
M. Baker and X. Faber -- Metrized graphs, Laplacian operators,
and electrical networks
G. Berkolaiko -- Form factor expansion for large graphs: A
diagrammatic approach
J. Bolte and J. Harrison -- The spectral form factor for quantum
graphs with spin-orbit coupling
R. Carlson -- Linear network models related to blood flow
K. Chen, S. Molchanov, and B. Vainberg -- Localization on Avron-Exner-last
graphs: I. Local perturbations
F. Chung and R. M. Richardson -- Weighted Laplacians and the
sigma function of a graph
P. Exner and O. Turek -- Approximations of permutation-symmetric
vertex couplings in quantum graphs
D. Fontaine, T. Smith, and A. Teplyaev -- Resistance of random
Sierpinski gaskets
M. Freidlin and M. Weber -- Small diffusion asymptotics for exit
problems on graphs
L. Friedlander -- Determinant of the Schrodinger operator on a
metric graph
S. A. Fulling -- Local spectral density and vacuum energy near a
quantum graph vertex
M. D. Horton, H. M. Stark, and A. A. Terras -- What are zeta
functions of graphs and what are they good for?
J. P. Keating -- Fluctuation statistics for quantum star graphs
V. Kostrykin and R. Schrader -- Laplacians on metric graphs:
Eigenvalues, resolvents and semigroups
S. Molchanov and B. Vainberg -- Transition from a network of thin
fibers to the quantum graph: An explicitly solvable model
B.-S. Ong -- On the limiting absorption principle and spectra of
quantum graphs
J. Rubinstein -- Quantum mechanics, superconductivity and fluid
flow in narrow networks
H. Schanz -- A relation between the bond scattering matrix and
the spectral counting function for quantum graphs
U. Smilansky and M. Solomyak -- The quantum graph as a limit of a
network of physical wires
B. Winn -- On the trace formula for quantum star graphs
Proceedings of Symposia in Pure Mathematics, Volume: 75
2006; approx. 306 pp; hardcover
ISBN-10: 0-8218-3963-2
ISBN-13: 978-0-8218-3963-8
Expected publication date is December 21, 2006.
Multiple Dirichlet series are Dirichlet series in several complex
variables. A multiple Dirichlet series is said to be perfect if
it satisfies a finite group of functional equations and has
meromorphic continuation everywhere. The earliest examples came
from Mellin transforms of metaplectic Eisenstein series and have
been intensively studied over the last twenty years. More
recently, many other examples have been discovered and it appears
that all the classical theorems on moments of L-functions as well
as the conjectures (such as those predicted by random matrix
theory) can now be obtained via the theory of multiple Dirichlet
series. Furthermore, new results, not obtainable by other
methods, are just coming to light. This volume offers an account
of some of the major research to date and the opportunities for
the future. It includes an exposition of the main results in the
theory of multiple Dirichlet series, and papers on moments of
zeta- and L-functions, on new examples of multiple Dirichlet
series, and on developments in the allied fields of automorphic
forms and analytic number theory.
Readership
Graduate students and research mathematicians interested in
number theory, especially automorphic forms and connections to
analytic number theory.
Table of Contents
Multiple Dirichlet series and their applications
G. Chinta, S. Friedberg, and J. Hoffstein -- Multiple Dirichlet
series and automorphic forms
Q. Zhang -- Applications of multiple Dirichlet series in mean
values of L-functions
A. Diaconu and D. Goldfeld -- Second moments of quadratic Hecke L-series
and multiple Dirichlet series I
B. Brubaker, D. Bump, G. Chinta, S. Friedberg, and J. Hoffstein
-- Weyl group multiple Dirichlet series I
B. Brubaker and D. Bump -- Residues of Weyl group multiple
Dirichlet series associated to widetilde{mathrm{GL}}_{n+1}
M. R. Murty and K. Sinha -- Multiple Hurwitz zeta functions
R. Masri -- Multiple zeta values over global function fields
A. Deitmar -- Generalised Selberg zeta functions and a
conjectural Lefschetz formula
Automorphic forms and analytic number theory
Y. Choie and N. Diamantis -- Rankin-Cohen brackets on higher
order modular forms
D. Ginzburg -- Eulerian integrals for GL_n
M. N. Huxley -- Is the Hlawka zeta function a respectable object?
A. Ivic -- On sums of integrals of powers of the zeta-function in
short intervals
M. Jutila and Y. Motohashi -- Uniform bounds for Rankin-Selberg L-functions
Y. Motohashi -- Mean values of zeta-functions via representation
theory
C. J. Mozzochi -- On the pair correlation of the Eigenvalues of
the hyperbolic Laplacian for PSL(2,mathbb{Z})backslash H II
Z. Rudnick and K. Soundararajan -- Lower bounds for moments of L-functions:
Symplectic and orthogonal examples
Graduate Studies in Mathematics, Volume: 78
2006; 518 pp; hardcover
ISBN-10: 0-8218-3813-X
ISBN-13: 978-0-8218-3813-6
Expected publication date is January 11, 2007.
Linear algebra permeates mathematics, perhaps more so than any
other single subject. It plays an essential role in pure and
applied mathematics, statistics, computer science, and many
aspects of physics and engineering. This book conveys in a user-friendly
way the basic and advanced techniques of linear algebra from the
point of view of a working analyst. The techniques are
illustrated by a wide sample of applications and examples that
are chosen to highlight the tools of the trade. In short, this is
material that the author wishes he had been taught as a graduate
student.
Roughly the first third of the book covers the basic material of
a first course in linear algebra. The remaining chapters are
devoted to applications drawn from vector calculus, numerical
analysis, control theory, complex analysis, convexity and
functional analysis. In particular, fixed point theorems,
extremal problems, matrix equations, zero location and eigenvalue
location problems, and matrices with nonnegative entries are
discussed. Appendices on useful facts from analysis and
supplementary information from complex function theory are also
provided for the convenience of the reader.
The book is suitable as a text or supplementary reference for a
variety of courses on linear algebra and its applications, as
well as for self-study.
Readership
Undergraduates and first-year graduates interested in linear
algebra and applications.
Table of Contents
Vector spaces
Gaussian elimination
Additional applications of Gaussian elimination
Eigenvalues and eigenvectors
Determinants
Calculating Jordan forms
Normed linear spaces
Inner product spaces and orthogonality
Symmetric, Hermitian and normal matrices
Singular values and related inequalities
Pseudoinverses
Triangular factorization and positive definite matrices
Difference equations and differential equations
Vector valued functions
The implicit function theorem
Extremal problems
Matrix valued holomorphic functions
Matrix equations
Realization theory
Eigenvalue location problems
Zero location problems
Convexity
Matrices with nonnegative entries
Some facts from analysis
More complex variables
Bibliography
Index
Contemporary Mathematics,Volume: 416
2006; 284 pp; softcover
ISBN-10: 0-8218-3456-8
ISBN-13: 978-0-8218-3456-5
Expected publication date is December 1, 2006.
This volume deals systematically with connections between
algebraic number theory and low-dimensional topology. Of
particular note are various inspiring interactions between number
theory and low-dimensional topology discussed in most papers in
this volume. For example, quite interesting are the use of
arithmetic methods in knot theory and the use of topological
methods in Galois theory. Also, expository papers in both number
theory and topology included in the volume can help a wide group
of readers to understand both fields as well as the interesting
analogies and relations that bring them together.
Readership
Graduate students and research mathematicians interested in low-dimensional
topology, number theory, and relations between them.
Table of Contents
M. M. Asaeda, J. H. Przytycki, and A. S. Sikora --
Categorification of the skein module of tangles
A. Besser and H. Furusho -- The double shuffle relations for p-adic
multiple zeta values
N. Boston -- Galois p-groups unramified at p--A survey
K. Fuluta -- On capitulation theorems for infinite groups
H. Furusho -- Multiple zeta values and Grothendieck-Teichmuller
groups
S. Garoufalidis and J. S. Geronimo -- Asymptotics of q-difference
equations
W. M. Goldman -- The mapping class group acts reducibly on SU(n)-character
varieties
J. Hillman, D. Matei, and M. Morishita -- Pro-p link groups and p-homology
groups
H. Murakami -- A quantum introduction to knot theory
K. Murasugi -- Classical knot invariants and elementary number
theory
H. Nakamura and H. Tsunogai -- Harmonic and equianharmonic
equations in the Grothendieck-Teichmuller group, II
L. Rozansky -- On p-adic properties of the Witten-Reshetikhin-Turaev
invariant
Y. Shimizu -- Seiberg-Witten integrable systems and periods of
rational elliptic surfaces
Y. Taguchi -- On the finiteness of various representations
H. Tsunogai -- Some new-type equations in the Grothendieck-Teichmuller
group arising from geometry of mathcal{M}_{0,5}