Expected publication date is October 21, 2004
Description
This book contains recent and exciting developments on the
structure of moduli spaces, with an emphasis on the algebraic
structures that underlie this structure. Topics covered include
Hilbert schemes of points, moduli of instantons, coherent sheaves
and their derived categories, moduli of flat connections, Hodge
structures, and the topology of affine varieties.
Two beautiful series of lectures are a particularly fine feature
of the book. One is an introductory series by Manfred Lehn on the
topology and geometry of Hilbert schemes of points on surfaces,
and the other, by Hiraku Nakajima and Kota Yoshioka, explains
their recent work on the moduli space of instantons over {mathbb
R}^4.
The material is suitable for graduate students and researchers
interested in moduli spaces in algebraic geometry, topology, and
mathematical physics.
Contents
M. Lehn -- Lectures on Hilbert schemes
H. Nakajima and K. Yoshioka -- Lectures on instanton counting
C. Bartocci and M. Jardim -- Hyper-Kahler Nahm transforms
A. Braverman -- Instanton counting via affine Lie algebras. I.
Equivariant J-functions of (affine) flag manifolds and Whittaker
vectors
M. A. A. de Cataldo and L. Migliorini -- The Gysin map is
compatible with mixed Hodge structures
N.-K. Ho and L. C. Jeffrey -- Representations of fundamental
groups of nonorientable 2-manifolds
Y. Namikawa -- Mukai flops and derived categories. II
S. Hosono, B. H. Lian, K. Oguiso, and S.-T. Yau -- Fourier-Mukai
number of a K3 surface
J. Sawon -- Derived equivalence of holomorphic symplectic
manifolds
M. Roth and R. Vakil -- The affine stratification number and the
moduli space of curves
M. Verbitsky -- Coherent sheaves on generic compact tori
W.-P. Li, Z. Qin, and W. Wang -- The cohomology rings of Hilbert
schemes via Jack polynomials
Details:
Series: CRM Proceedings & Lecture Notes,Volume: 38
Publication Year: 2004
ISBN: 0-8218-3568-8
Paging: 258 pp.
Binding: Softcover
Expected publication date is November 13, 2004
Description
This book is devoted to the applications of probability theory to
the theory of nonlinear partial differential equations. More
precisely, it is shown that all positive solutions for a class of
nonlinear elliptic equations in a domain are described in terms
of their traces on the boundary of the domain. The main
probabilistic tool is the theory of superdiffusions, which
describes a random evolution of a cloud of particles. A
substantial enhancement of this theory is presented that will be
of interest to anyone who works on applications of probabilistic
methods to mathematical analysis.
The book is suitable for graduate students and research
mathematicians interested in probability theory and its
applications to differential equations.
Also of interest by this author is Diffusions, Superdiffusions
and Partial Differential Equations in the AMS series, Colloquium
Publications.
Contents
Introduction
Analytic approach
Probabilistic approach
mathbb{N}-measures
Moments and absolute continuity properties of superdiffusions
Poisson capacities
Basic inequality
Solutions w_Gamma are sigma-moderate
All solutions are sigma-moderate
Appendix A: An elementary property of the Brownian motion
Appendix B: Relations between Poisson and Bessel capacities
References
Subject index
Notation index
Details:
Series: University Lecture Series, Volume: 34
Publication Year: 2004
ISBN: 0-8218-3682-X
Paging: 120 pp.
Binding: Softcover
Expected publication date is December 24, 2004
Description
This volume offers an excellent selection of cutting-edge
articles about fractal geometry, covering the great breadth of
mathematics and related areas touched by this subject. Included
are rich survey articles and fine expository papers. The high-quality
contributions to the volume by well-known researchers--including
two articles by Mandelbrot--provide a solid cross-section of
recent research representing the richness and variety of
contemporary advances in and around fractal geometry.
In demonstrating the vitality and diversity of the field, this
book will motivate further investigation into the many open
problems and inspire future research directions. It is suitable
for graduate students and researchers interested in fractal
geometry and its applications.
This is a two-part volume. Part 1 covers analysis, number theory,
and dynamical systems; Part 2, multifractals, probability and
statistical mechanics, and applications.
Contents
M. L. Lapidus -- Fractal geometry and applications-An
introduction to this volume
J. Barral and S. Jaffard -- Cherche Livre... et plus si affinite/Looking
for a book...and more, if affinity
M. Berry -- Benefiting from fractals
M.-O. Coppens -- Benoit Mandelbrot, wizard of science
R. L. Devaney -- Mandelbrot's vision for mathematics
M. M. Dodson -- Benoit Mandelbrot and York
B. Duplantier -- Nul n'entre ici s'il n'est geometre/Let no one
ignorant of geometry enter here
M. L. Frame -- A decade of working with a maverick
M. Frantz -- Breakfast with Mandelbrot
J.-P. Kahane -- Old memories
D. B. Mumford -- My encounters with Benoit Mandelbrot
L. Nottale -- Fractal geometry and the foundations of physics
B. Sapoval -- Is randomness partially tamed by fractals?
J. E. Taylor -- On knowing Benoit Mandelbrot
Analysis
M. M. France -- Reflections, ripples and fractals
M. Frantz -- Lacunarity, Minkowski content, and self-similar sets
in mathbb{R}
F. Morgan -- Fractals and geometric measure theory: Friends and
foes
H. Furstenberg and Y. Katznelson -- Eigenmeasures,
equidistribution, and the multiplicity of beta-expansions
A. Kameyama -- Distances on topological self-similar sets
A. Teplyaev -- Energy and laplacian on the Sierpinski gasket
C. Sabot -- Electrical networks, symplectic reductions, and
application to the renormalization map of self-similar lattices
B. Solomyak -- Notes on Bernoulli convolutions
Number theory
T. Hilberdink -- Some connections between Bernoulli convolutions
and analytic number theory
S. Jaffard -- On Davenport expansions
M. M. Dodson and S. Kristensen -- Hausdorff dimension and
diophantine approximation
M. L. Lapidus and M. van Frankenhuijsen -- Fractality, self-similarity
and complex dimensions
Dynamical systems
B. Kahng -- The invariant fractals of symplectic piecewise affine
elliptic dynamics
S. Crovisier -- Almost sure rotation number of circle
endomorphisms
V. Baladi -- Kneading determinants and transfer operators in
higher dimensions
V. Afraimovich, L. Ramirez, and E. Ugalde -- The spectrum of
dimensions for Poincare recurrences for nonuniformly hyperbolic
geometric constructions
M. Comerford -- A survey of results in random iteration
D. Schleicher -- On fibers and local connectivity of Mandelbrot
and multibrot sets
Multifractals
J. Barral and B. B. Mandelbrot -- Introduction to infinite
products of independent random functions (Random multiplicative
multifractal measures, part I)
J. Barral and B. B. Mandelbrot -- Non-degeneracy, moments,
dimension, and multifractal analysis for random multiplicative
measures (Random multiplicative multifractal measures, part II)
J. Barral -- Techniques for the study of infinite products of
independent random functions (Random multiplicative multifractal
measures, part III)
S. P. Jaffard -- Wavelet techniques in multifractal analysis
J. L. Vehel and S. Seuret -- The 2-microlocal formalism
J. Peyriere -- A vectorial multifractal formalism
Probability and statistical mechanics
B. M. Hambly and T. Kumagai -- Heat kernel estimates for
symmetric random walks on a class of fractal graphs and stability
under rough isometries
Y. Xiao -- Random fractals and Markov processes
G. F. Lawler, O. Schramm, and W. Werner -- On the scaling limit
of planar self-avoiding walk
B. Duplantier -- Conformal fractal geometry & boundary
quantum gravity
Applications
A. Desolneux, B. Sapoval, and A. Baldassarri -- Self-organized
percolation power laws with and without fractal geometry in the
etching of random solids
M.-O. Coppens -- Nature inspired chemical engineering-Learning
from the fractal geometry of nature in sustainable chemical
engineering
F. K. Musgrave -- Fractal forgeries of nature
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Proceedings of Symposia in Pure Mathematics, Volume: 72
Publication Year: 2004
ISBN: 0-8218-3292-1
Paging: approximately 1110 pp.
Binding: Hardcover
Expected publication date is December 10, 2004
Description
This volume, honoring over forty years of Miklos Csorgo's work in
probability and statistics, reflects the state of current
research. It offers a comprehensive collection of surveys
introducing new results with complete proofs and expository
papers giving an historic overview.
Contributions were made by an international cast of experts. The
book covers the following topics: path properties of stochastic
processes, probability theory with applications, complete
convergence of renewal counting processes and bootstrap means,
weak convergence of random size sums, almost sure stability of
weighted maxima, procedures for detecting changes in statistical
models, statistical inference via conditional quantiles,
cumulative sums, multinomial samples, empirical processes,
applications to economics, and self-normalized partial sums
processes. The section, "Applications to Economics",
deals primarily with applications of stochastics to financial
time series models.
The book is suitable for graduate students and researchers
interested in probability theory, stochastic processes,
mathematical statistics, and applications of these mathematical/statistical
sciences.
Contents
Path properties of stochastic processes
E. Csaki, A. Foldes, and Z. Shi -- Our joint work with Miklos
Csorgo
D. Khoshnevisan -- Brownian sheet and quasi-sure analysis
G. Peccati and M. Yor -- Hardy's inequality in L^2([0,1]) and
principal values of Brownian local times
G. Peccati and M. Yor -- Four limit theorems for quadratic
functionals of Brownian motion and Brownian bridge
P. Revesz -- Tell me the values of a Wiener at integers, I tell
you its local time
Probability theory with applications
R. J. Bhansali, M. P. Holland, and P. S. Kokoszka -- Chaotic maps
with slowly decaying correlations and intermittency
Y. Davydov and V. Paulauskas -- Recent results on p-stable convex
compact sets with applications
Y. Davydov and R. Zitikis -- Convex rearrangements of random
elements
D. A. Dawson, L. G. Gorostiza, and A. Wakolbinger -- Hierarchical
random walks
K. A. Ross and Q.-M. Shao -- On Helgason's number and
Khintchine's inequality
Complete convergence of renewal counting processes and bootstrap
means
A. Gut and J. Steinebach -- Convergence rates and precise
asymptotics for renewal counting processes and some first passage
times
S. Csorgo -- On the complete convergence of bootstrap means
Weak convergence of random size sums, almost sure stability of
weighted maxima
I. Cwiklinska and Z. Rychlik -- Weak convergence of random sums
and maximum random sums under nonrandom norming
R. J. Tomkins -- Criteria for the almost sure stability of
weighted maxima of bounded i.i.d. random variables
Procedures for detecting changes in statistical models
M. Huskova -- Permutation principle and bootstrap in change point
analysis
E.-E. A. A. Aly -- Change point detection based on L-statistics
E. Atenafu and E. Gombay -- Sequential tests for change in the
parameters of nested random effects model
M. Orasch -- Using U-statistics based processes to detect
multiple change-points
Statistical inference via conditional quantiles, cumulative sums,
multinomial samples, and empirical processes
E. Parzen -- Statistical methods learning and conditional
quantiles
M. D. Burke -- Testing regression models: A strong martingale
approach
A. R. Dabrowski and H. Dehling -- Conditional distribution of the
H-coefficient in nonparametric unfolding models
K. Ghoudi and B. Remillard -- Empirical processes based on pseudo-observations
II: The multivariate case
Applications to economics
I. Berkes, L. Horvath, and P. Kokoszka -- Probabilistic and
statistical properties of GARCH processes
R. Kulperger -- Stochastic finance: Discrete time processes and
risk neutral pricing
D. L. McLeish -- Estimating the correlation of processes using
extreme values
H. Yu -- Analyzing residual processes of (G)ARCH time series
models
Self-normalized partial sums processes
M. Csorgo, B. Szyszkowicz, and Q. Wang -- On weighted
approximations and strong limit theorems for self-normalized
partial sums processes
Q. Wang -- On Darling-Erdos type theorems for self-normalized
sums
Details:
Series: Fields Institute Communications, Volume: 44
Publication Year: 2004
ISBN: 0-8218-3561-0
Paging: 530 pp.
Binding: Hardcover
Hardback - 244x162mm - ISBN:1-9039-9655-4 - 332 Pages - July 2004
A ‘stochastic’ process is a ‘random’ or ‘conjectural’ process, and this book is concerned with applied probability and statistics. Whilst maintaining the mathematical rigour this subject requires, it addresses topics of interest to engineers, such as problems in modelling, control, reliability maintenance, data analysis and engineering involvement with insurance.
The aim of this publication is to present important current tools used in the stochastic processes ? estimation, optimization and recursive logarithms ? in a form accessible to engineers (and that can also be applied to Matlab programs), and to gather together, in a unified presentation, many of the results in probability and statistics.
Amongst the themes covered in the chapters are mathematical expectation arising from increasing information patterns, the estimation of probability distribution, the treatment of distribution of real random phenomena (in engineering, economics, biology and medicine etc), and expectation maximization. The latter part of the book considers optimization algorithms, which can be used, for example, to help in the better utilization of resources, and stochastic approximation algorithms, which can provide prototype models in many practical applications.