Mathematical Surveys and Monographs, Volume: 160
2010; 237 pp; hardcover
ISBN-13: 978-0-8218-4894-4
Expected publication date is February 13, 2010.
The subject of this book is the study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces. These are equipped with canonical topological actions that give rise to the usual concepts of conjugacy of actions and cohomology of cocycles. Structural properties of discrete groups such as amenability, Kazhdan's property (T) and the Haagerup Approximation Property play a significant role in this theory as they have important connections to the global structure of these spaces. One of the main topics discussed in this book is the analysis of the complexity of the classification problems of conjugacy and orbit equivalence of actions, as well as of cohomology of cocycles. This involves ideas from topological dynamics, descriptive set theory, harmonic analysis, and the theory of unitary group representations. Also included is a study of properties of the automorphism group of a standard probability space and some of its important subgroups, such as the full and automorphism groups of measure preserving equivalence relations and connections with the theory of costs.
The book contains nine appendices that present necessary background material in functional analysis, measure theory, and group representations, thus making the book accessible to a wider audience.
Graduate students and research mathematicians interested in ergodic theory and descriptive set theory.
Mathematical Surveys and Monographs, Volume: 161
2010; approx. 202 pp; hardcover
ISBN-13: 978-0-8218-4968-2
Expected publication date is April 10, 2010.
The purpose of this book is to present a Morse theoretic study of a very
general class of homogeneous operators that includes the p-Laplacian as
a special case. The p-Laplacian operator is a quasilinear differential
operator that arises in many applications such as non-Newtonian fluid flows
and turbulent filtration in porous media. Infinite dimensional Morse theory
has been used extensively to study semilinear problems, but only rarely
to study the p-Laplacian.
The standard tools of Morse theory for computing critical groups, such
as the Morse lemma, the shifting theorem, and various linking and local
linking theorems based on eigenspaces, do not apply to quasilinear problems
where the Euler functional is not defined on a Hilbert space or is not
C^2 or where there are no eigenspaces to work with. Moreover, a complete
description of the spectrum of a quasilinear operator is generally not
available, and the standard sequence of eigenvalues based on the genus
is not useful for obtaining nontrivial critical groups or for constructing
linking sets and local linkings. However, one of the main points of this
book is that the lack of a complete list of eigenvalues is not an insurmountable
obstacle to applying critical point theory.
Working with a new sequence of eigenvalues that uses the cohomological index, the authors systematically develop alternative tools such as nonlinear linking and local splitting theories in order to effectively apply Morse theory to quasilinear problems. They obtain nontrivial critical groups in nonlinear eigenvalue problems and use the stability and piercing properties of the cohomological index to construct new linking sets and local splittings that are readily applicable here.
Research mathematicians interested in nonlinear partial differential equations.
Morse theory and variational problems
Abstract formulation and examples
Background material
Critical point theory
p-Linear eigenvalue problems
Existence theory
Monotonicity and uniqueness
Nontrivial solutions and multiplicity
Jumping nonlinearities and the Dancer-Fu?ik spectrum
Indefinite eigenvalue problems
Anisotropic systems
Bibliography
Contemporary Mathematics, Volume: 510
2010; 329 pp; softcover
ISBN-13: 978-0-8218-4732-9
Expected publication date is April 11, 2010.
The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic geometry, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields of mathematics, such as algebraic geometry, dynamical systems, topology, geometric group theory, mathematical physics, and number theory. Recent years have seen a flowering of this legacy with a large number of people entering the subject.
This current volume contains articles on a wide variety of subjects that are central to this legacy. These include papers in Kleinian groups, classical Riemann surface theory, translation surfaces, algebraic geometry and dynamics. The majority of the papers present new research, but there are survey articles as well.
Graduate students and research mathematicians interested in hyperbolic geometry, Teichmuller theory, and discrete groups.
J. Belk and S. Koch -- Iterated monodromy for a two-dimensional map
J. Bowman -- Orientation-reversing involutions of the genus 3 Arnoux-Yoccoz surface and related surfaces
E. Bujalance and F.-J. Cirre -- A family of Riemann surfaces with orientation reversing automorhisms
L. Arenas-Carmona and A. M. Rojas -- Unramified prime covers of hyperelliptic
curves and pairs of p-gonal curves
A. Carocca, H. Lange, R. E. Rodriguez, and A. M. Rojas -- Prym and Prym-Tyurin varieties: A group-theoretical construction
V. Charette, T. A. Drumm, and W. Goldman -- Stretching three-holed spheres and the Margulis invariant
B. Farb and H. Masur -- Teichmuller geometry of moduli space, II: \mathcal{M}(S)
seen from far away
D. Gabai, R. Meyerhoff, and P. Milley -- Mom technology and hyperbolic 3-manifolds
U. Hamenstadt -- Dynamical properties of the Weil-Petersson metric
J. H. Hubbard and R. L. Miller -- Equidistribution of horocyclic flows on complete hyperbolic surfaces of finite area
L. Ji and S. A. Wolpert -- A cofinite universal space for proper actions for mapping class groups
M. Kapovich -- On sequences of finitely generated discrete groups
R. P. Kent IV and C. J. Leininger -- A fake Schottky group in mod(S)
D. D. Long and A. W. Reid -- Eigenvalues of hyperbolic elements in Kleinian groups
V. Malik -- Primitive words and self-intersections of curves on surfaces generated by the Gilman-Maskit discreteness algorithm
K. Matsuzaki -- Symmetric groups that are not the symmetric conjugates of Fuchsian groups
K. Ohshika and H. Miyachi -- Uniform models for the closure of the Riley slice
G. Mondello -- Poisson structures on the Teichmuller space of hyperbolic surfaces with conical points
Colloquium Publications, Volume: 57
2010; approx. 529 pp; hardcover
ISBN-13: 978-0-8218-4970-5
Expected publication date is May 15, 2010.
This monograph represents the state of the art both in respect of coverage of the general methods and in respect of the actual applications to interesting problems.
A unique feature of this monograph is how the authors take great pains to explain the fundamental ideas behind the proofs and to show how to approach a question in a correct fashion. So, this book is not just another monograph useful for consultation; rather, it is a teaching instrument of great value both for the specialist and the beginner in the field.
The authors must be congratulated for this exceptional monograph, the first of its kind for depth of content as well as for the effort made to explain the `why' and not limiting themselves to the `how to'. This is a true masterpiece that will prove to be indispensable to the serious researcher for many years to come.
--Enrico Bombieri, Institute for Advanced Study
This is a truly comprehensive account of sieves and their applications, by two of the world's greatest authorities. Beginners will find a thorough introduction to the subject, with plenty of helpful motivation. The more practised reader will appreciate the authors' insights into some of the more mysterious parts of the theory, as well as the wealth of new examples. No analytic number theorist should be without this volume, but it will not have a place on my bookshelves--it will be permanently on my desk!
--Roger Heath-Brown, University of Oxford,Fellow of Royal Society
This is a comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. Included is a wide range of applications, both to traditional questions such as those concerning primes, and to areas previously unexplored by sieve methods, such as elliptic curves, points on cubic surfaces and quantum ergodicity. New proofs are given also of some of the central theorems of analytic number theory; these proofs emphasize and take advantage of the applicability of sieve ideas.
The book contains numerous comments which provide the reader with insight into the workings of the subject, both as to what the sieve can do and what it cannot do. The authors reveal recent developements by which the parity barrier can be breached, exposing golden nuggets of the subject, previously inaccessible. The variety in the topics covered and in the levels of difficulty encountered makes this a work of value to novices and experts alike, both as an educational tool and a basic reference.
Graduate students and research mathematicians interested in number theory.
Sieve questions
Elementary considerations on arithmetic functions
Bombieri's sieve
Sieve of Eratosthenes-Legendre
Sieve principles and terminology
Brun's sieve--The big bang
Selberg's sieve--Kvadrater er positiv
Sieving by many residue classes
The large sieve
Molecular structure of sieve weights
The beta-sieve
The linear sieve
Applications to linear sequences
The semi-linear sieve
Applications--Choice but not prime
Asymptotic sieve and the parity principle
Combinatorial identities
Asymptotic sieve for primes
Equidistribution of quadratic roots
Capturing Gaussian primes
Primes represented by polynomials
Level of distribution of arithmetic sequences
Primes in short intervals
The least prime in an arithmetic progression
Almost-prime sieve
Mean-values of arithmetic functions
Differential-difference equations
Bibliography
Index
Description
Ross's classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries.
Professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.
Preface
Introduction to Probability Theory;
Random Variables
Conditional Probability and Conditional Expectation
Markov Chains
The Exponential Distribution and the Poisson Process
Continuous-Time Markov Chains
Renewal Theory and Its Applications
Queueing Theory
Reliability Theory
Brownian Motion and Stationary Processes
Simulation
Appendix: Solutions to Starred Exercises
Index
Bibliographic details
Hardbound, 800 pages, publication date: DEC-2009
ISBN-13: 978-0-12-375686-2