Description
Shimura curves are a far-reaching generalization of the classical
modular curves. They lie at the crossroads of many areas,
including complex analysis, hyperbolic geometry, algebraic
geometry, algebra, and arithmetic. This monograph presents
Shimura curves from a theoretical and algorithmic perspective.
The main topics are Shimura curves defined over the rational
number field, the construction of their fundamental domains, and
the determination of their complex multiplication points. The
study of complex multiplication points in Shimura curves leads to
the study of families of binary quadratic forms with algebraic
coefficients and to their classification by arithmetic Fuchsian
groups. In this regard, the authors develop a theory full of new
possibilities that parallels Gauss' theory on the classification
of binary quadratic forms with integral coefficients by the
action of the modular group.
This is one of the few available books explaining the theory of
Shimura curves at the graduate student level. Each topic covered
in the book begins with a theoretical discussion followed by
carefully worked-out examples, preparing the way for further
research.
Contents
Quaternion algebras and quaternion orders
Introduction to Shimura curves
Quaternion algebras and quadratic forms
Embeddings and quadratic forms
Hyperbolic fundamental domains for Shimura curves
Complex multiplication points in Shimura curves
The Poincare package
Tables
Further contributions to the study of Shimura curves
Applications of Shimura curves
Bibliography
Index
Details:
Series: CRM Monograph Series, Volume: 22
Publication Year: 2004
ISBN: 0-8218-3359-6
Paging: 196 pp.
Binding: Hardcover
Description
The book consists of two sets of lecture notes devoted to
slightly different methods of analysis of concurrent and
probabilistic computational systems.
The first set of lectures develops a calculus of streams (a
generalization of the set of natural numbers) based on the
coinduction principle coming from the theory of coalgebras. It is
now well understood that the interplay between algebra (for
describing structure) and coalgebra (for describing dynamics) is
crucial for understanding concurrent systems. There is a striking
analogy between streams and formula calculus reminiscent of those
appearing in quantum calculus. These lecture notes will appeal to
anyone working in concurrency theory but also to algebraists and
logicians.
The other set of lecture notes focuses on methods for
automatically verifying probabilistic systems using techniques of
model checking. The unique aspect of these lectures is the
coverage of both theory and practice. The authors have been
responsible for one of the most successful experimental systems
for probabilistic model checking. These lecture notes are of
interest to software engineers, real-time programmers,
researchers in machine learning and numerical analysts who may
well be interested to see how standard numerical techniques are
used in a novel context.
Both sets of lectures are expository and suitable for graduate
courses in theoretical computer science and for research
mathematicians interested in design and analysis of concurrent
and probabilistic computational systems.
Contents
On streams and coinduction
Preface
Acknowledgments
Streams and coinduction
Stream calculus
Analytical differential equations
Coinductive counting
Component connectors
Key differential equations
Bibliography
Modelling and verification of probabilistic systems
Preface
Introduction
Discrete-time Markov chains
Markov decision processes
Continuous-time Markov chains
Probabilistic timed automata
Implementation
Measure theory and probability
Iterative solution methods
Bibliography
Details:
Series: CRM Monograph Series, Volume: 23
Publication Year: 2004
ISBN: 0-8218-3571-8
Paging: 215 pp.
Binding: Hardcover
Description
This volume includes the proceedings of a workshop on Invariant
Theory held at Queen's University (Ontario). The workshop was
part of the theme year held under the auspices of the Centre de
recherches mathematiques (CRM) in Montreal. The gathering brought
together two communities of researchers: those working in
characteristic 0 and those working in positive characteristic.
The book contains three types of papers: survey articles
providing introductions to computational invariant theory,
modular invariant theory of finite groups, and the invariant
theory of Lie groups; expository works recounting recent research
in these three areas and beyond; and open problems of current
interest.
The book is suitable for graduate students and researchers
working in invariant theory.
Contents
G. Bousquet and L. Moser-Jauslin -- A local study of embeddings
of complexity one
H. Derksen -- Constructive invariant theory
H. Derksen and G. Kemper -- On global degree bounds for
invariants
P. Fleischmann -- On invariant theory of finite groups
A. G. Helminck -- Combinatorics related to orbit closures of
symmetric subgroups in flag varieties
F. Hivert and N. M. Thiery -- Deformation of symmetric functions
and the rational Steenrod algebra
W. van der Kallen -- Cohomology with Grosshans graded
coefficients
D. B. Karagueuzian and P. Symonds -- The module structure of a
group action on a polynomial ring: examples, generalizations, and
applications
N. E. Kechagias -- An invariant theoretic description of the
primitive elements of the mod-p cohomology of a finite loop space
which are annihilated by Steenrod operations
F. Knop -- On Noether's and Weyl's bound in positive
characteristic
M. D. Neusel -- Comparing the depths of rings of invariants
V. L. Popov -- Moment polytopes of nilpotent orbit closures;
dimension and isomorphism of simple modules; and variations on
the theme of J. Chipalkatti
Z. Reichstein -- Compressions of group actions
L. G. Rybnikov -- Commutativity of weakly commutative Riemannian
homogeneous spaces
G. W. Schwarz -- Group actions and quotients for compact Lie
groups and algebraic groups
J. Segal -- Notes on invariant rings of divided powers
R. J. Shank -- Classical covariants and modular invariants
A. V. Smirnov -- Classification of nearly closed orbits for the
action of semisimple complex linear groups on the projective
spaces
N. M. Thiery and S. Thomasse -- Convex cones and SAGBI bases of
permutation invariants
D. L. Wehlau -- Some problems in invariant theory
R. M. W. Wood -- The Peterson conjecture for algebras of
invariants
O. Yakimova -- Weakly symmetric and weakly commutative spaces
Details:
Series: CRM Proceedings & Lecture Notes, Volume: 35
Publication Year: 2004
ISBN: 0-8218-3244-1
Paging: 287 pp.
Binding: Softcover
Description
As part of its series of Emphasis Years in Mathematics,
Northwestern University hosted an International Conference on
Algebraic Topology. The purpose of the conference was to develop
new connections between homotopy theory and other areas of
mathematics.
This proceedings volume grew out of that event. Topics discussed
include algebraic geometry, cohomology of groups, algebraic K-theory,
and mathbb{A}^1 homotopy theory. Among the contributors to the
volume were Alejandro Adem, Ralph L. Cohen, Jean-Louis Loday, and
many others.
The book is suitable for graduate students and research
mathematicians interested in homotopy theory and its relationship
to other areas of mathematics.
Contents
A. Adem -- Constructing and deconstructing group actions
M. Behrens and S. Pemmaraju -- On the existence of the self map
v_2^9 on the Smith-Toda complex V(1) at the prime 3
C. Broto, R. Levi, and B. Oliver -- The theory of p-local groups:
a survey
R. L. Cohen and A. Stacey -- Fourier decompositions of loop
bundles
D. Dugger and D. C. Isaksen -- Weak equivalences of simplicial
presheaves
B. Fresse -- Koszul duality of operads and homology of partitions
posets
W. Gajda -- On K_{ast}(mathbb{Z}) and classical conjectures in
the arithmetic of cyclotomic fields
G. Gutman -- Finite group actions in elliptic cohomology
L. Hesselholt -- Topological Hochschild homology and the de Rham-Witt
complex for mathbb{Z}_{(p)}-algebras
M. Hovey -- Homotopy theory of comodules over a Hopf algebroid
J. F. Jardine -- Bousfield's E_{2} model theory for simplicial
objects
Y. Kamiya and K. Shimomura -- A relation between the Picard group
of the E(n)-local homotopy category and E(n)-based Adams spectral
sequence
A. Libman -- Homotopy limits of monad algebras
J.-L. Loday and M. Ronco -- Trialgebras and families of polytopes
M. A. Mandell -- Equivariant symmetric spectra
B. Richter and A. Robinson -- Gamma homology of group algebras
and of polynomial algebras
L. Scull -- Formality and S^1-equivariant algebraic models
B. Shipley -- A convenient model category for commutative ring
spectra
P. Symonds -- The Tate-Farrell cohomology of the Morava
stabilizer group S_{p-1} with coefficients in E_{p-1}
J. M. Turner -- Characterizing simplicial commutative algebras
with vanishing Andre-Quillen homology
Details:
Series: Contemporary Mathematics,Volume: 346
Publication Year: 2004
ISBN: 0-8218-3285-9
Paging: 507 pp.
Binding: Softcover
Description
This volume grew out of a workshop on spectral theory of
differential operators and inverse problems held at the Research
Institute for Mathematical Sciences (Kyoto University). The
gathering of nearly 100 participants at the conference suggests
the increasing interest in this field of research.
The focus of the book is on spectral theory for differential
operators and related inverse problems. It includes selected
topics from the following areas: electromagnetism, elasticity,
the Schrodinger equation, differential geometry, and numerical
analysis. The material is suitable for graduate students and
researchers interested in inverse problems and their applications.
Contents
V. G. Romanov and M. Yamamoto -- On the determination of wave
speed and potential in a hyperbolic equation by two measurements
Y. Kurylev, M. Lassas, and E. Somersalo -- Focusing waves in
electromagnetic inverse problems
H. Ammari and H. Kang -- Reconstruction of conductivity
inhomogeneities of small diameter via boundary measurements
S. Kim and M. Yamamoto -- Unique determination of inhomogeneity
in a stationary isotropic Lame system with variable coefficients
M. Ikehata -- Mittag-Leffler's function and extracting from
Cauchy data
G. Eskin and J. Ralston -- On the inverse boundary value problem
for linear isotropic elasticity and Cauchy-Riemann systems
M. Ikehata and G. Nakamura -- Pointwise reconstruction of the
jump at the boundaries of inclusions
S.-i. Nakagiri and J. Ha -- Constant parameters identification
problems of coupled sine-Gordon equations
D. Chelkak, P. Kargaev, and E. Korotyaev -- Inverse problem for
harmonic oscillator perturbed by potential
A. Melin -- Some transforms in potential scattering in odd
dimension
G. Uhlmann and A. Vasy -- Inverse problems in N-body scattering
A. Katsuda -- Asymptotics of heat kernels on nilpotent coverings
and related topics
R. Kuwabara -- Eigenvalues associated with a periodic orbit of
the magnetic flow
H. Isozaki -- Inverse problems and hyperbolic manifolds
T. Takiguchi -- Reconstruction of measurable plane sets from
their orthogonal projections
K. Iijima, K. Shirota, and K. Onishi -- A numerical computation
for inverse boundary value problems by using the adjoint method
H. Urakawa -- The Dirichlet eigenvalue problem, the finite
element method and graph theory
J. Cheng, Y. C. Hon, and Y. B. Wang -- A numerical method for the
discontinuous solutions of Abel integral equations
Details:
Series: Contemporary Mathematics,Volume: 348
Publication Year: 2004
ISBN: 0-8218-3421-5
Paging: 243 pp.
Binding: Softcover