Proceedings of Symposia in Pure Mathematics, Volume: 89
2015; approx. 337 pp; hardcover
ISBN-13: 978-1-4704-1112-1
Expected publication date is April 30, 2015.
This volume contains the proceedings of the semester long special program on Hyperbolic Dynamics, Large Deviations and Fluctuations, which was held from January-June 2013, at the Center Interfacultaire Bernoulli, Ecole Polytechnique Federale de Lausanne, Switzerland.
The broad theme of the program was the long term behavior of dynamical systems and their statistical behavior. During the last 50 years, the statistical properties of dynamical systems of many different types have been the subject of extensive study in statistical mechanics and thermodynamics, ergodic and probability theories, and some areas of mathematical physics. The results of this study have had a profound effect on many different areas in mathematics, physics, engineering and biology.
The papers in this volume cover topics in large deviations and thermodynamics formalism and limit theorems for dynamic systems.
The material presented is primarily directed at researchers and graduate students in the very broad area of dynamical systems and ergodic theory, but will also be of interest to researchers in related areas such as statistical physics, spectral theory and some aspects of number theory and geometry.
Graduate students and research mathematicians interested in dynamical systems, ergodic theory, statistical mechanics, and mathematical physics.
D. Dolgopyat, Y. Pesin, M. Pollicott, and L. Stoyanov -- Hyperbolic dynamics, fluctuations and large deviations
Large deviations and thermodynamical formalism
J. Buzzi -- The almost Borel structure of diffeomorphisms with some hyperbolicity
Y. Kifer -- Lectures on large deviations in probability and dynamical systems
O. M. Sarig -- Thermodynamic formalism for countable Markov shifts
Limit theorems for dynamical systems
G. Forni -- Limit theorems for horocycle flows
S. Gouezel -- Limit theorems in dynamical systems using the spectral method
J. Marklof -- Kinetic limits of dynamical systems
Additional topics
D. Dolgopyat and B. Fayad -- Limit theorems for toral translations
Y. Guivarc'h -- Spectral gap properties and limit theorems for some random walks and dynamical systems
J. De Simoi and C. Liverani -- The martingale approach after Varadhan and Dolgopyat
CBMS Regional Conference Series in Mathematics, Number: 121
2015; 216 pp; softcover
ISBN-13: 978-1-4704-2017-8
Expected publication date is April 16, 2015.
The Uncertainty Principle in Harmonic Analysis (UP) is a classical, yet rapidly developing, area of modern mathematics. Its first significant results and open problems date back to the work of Norbert Wiener, Andrei Kolmogorov, Mark Krein and Arne Beurling. At present, it encompasses a large part of mathematics, from Fourier analysis, frames and completeness problems for various systems of functions to spectral problems for differential operators and canonical systems.
These notes are devoted to the so-called Toeplitz approach to UP which recently brought solutions to some of the long-standing problems posed by the classics. After a short overview of the general area of UP the discussion turns to the outline of the new approach and its results. Among those are solutions to Beurling's Gap Problem in Fourier analysis, the Type Problem on completeness of exponential systems, a problem by Polya and Levinson on sampling sets for entire functions, Bernstein's problem on uniform polynomial approximation, problems on asymptotics of Fourier integrals and a Toeplitz version of the Beurling-Malliavin theory. One of the main goals of the book is to present new directions for future research opened by the new approach to the experts and young analysts.
Graduate students and research mathematicians interested in harmonic and complex analysis and special problems.
Contemporary Mathematics, Volume: 633
2015; 123 pp; softcover
ISBN-13: 978-0-8218-9859-8
Expected publication date is April 2, 2015.
This volume contains the proceedings of the AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, held January 9-10, 2013 in San Diego, CA and the AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, held April 6-7, 2013 at Boston College, Chestnut Hill, MA.
Over the past few years the field of group-based cryptography has attracted attention from both group theorists and cryptographers. The new techniques inspired by algorithmic problems in non-commutative group theory and their complexity have offered promising ideas for developing new cryptographic protocols. The papers in this volume cover algorithmic group theory and applications to cryptography.
Graduate students and research mathematicians interested in group theory and crytography.
Contemporary Mathematics, Volume: 634
2015; 265 pp; softcover
ISBN-13: 978-1-4704-1032-2
Expected publication date is April 2, 2015.
This volume contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1-4, 2013, at the Universite d'Artois, Lens, France. It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping algebras, and Leavitt path algebras.
Material from the course "Foundations of Algebraic Coding Theory", given by Steven Dougherty, is included and provides the reader with the history and background of coding theory as well as the interplay between coding theory and algebra. In module theory, many new results related to (almost) injective modules, injective hulls and automorphism-invariant modules are presented. Broad generalizations of classical projective covers are studied and category theory is used to describe the structure of some modules. In some papers related to more classical ring theory such as quasi duo rings or clean elements, new points of view on classical conjectures and standard open problems are given. Descriptions of codes over local commutative Frobenius rings are discussed, and a list of open problems in coding theory is presented within their context.
Graduate students and research mathematicians interested in noncommutative rings and coding theory.
Graduate Studies in Mathematics, Volume: 164
2015; approx. 307 pp; hardcover
ISBN-13: 978-1-4704-2196-0
Expected publication date is May 28, 2015.
Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemeredi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.
Graduate students and research mathematicians interested in graph theory, geometric group theory, and arithmetic combinatorics.
Expansion in Cayley graphs
Expander graphs: Basic theory
Expansion in Cayley graphs, and Kazhdan's property (T)
Quasirandom groups
The Balog-Szemeredi-Gowers lemma, and the Bourgain-Gamburd expansion machine
Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality
Non-concentration in subgroups
Sieving and expanders
Related articles
Cayley graphs the algebra of groups
The Lang-Weil bound
The spectral theorem and its converses for unbounded self-adjoint operators
Notes on Lie algebras
Notes on groups of Lie type
Bibliography
Index