Contemporary Mathematics,Volume: 461
2008; 265 pp; softcover
ISBN-13: 978-0-8218-4309-3
Expected publication date is August 1, 2008.
This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.
Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorial design theory.
Graduate students and research mathematicians interested in finite fields and applications.
D. J. Bernstein and T. Lange -- Analysis and optimization of elliptic-curve single-scalar multiplication
S. Boztas -- On influences of Boolean variables and their computation
N. Brandstatter and A. Winterhof -- Subsequences of Sidelnikov sequences
R. P. Brent and P. Zimmermann -- A multi-level blocking distinct-degree factorization algorithm
M. Car -- New bounds on some parameters in the Waring problem for polynomials over a finite field
M. Cipu and S. D. Cohen -- Dickson polynomial permutations
V. Deolalikar -- Ring theoretic study of linear codes using additive polynomials
G. Effinger -- Toward a complete twin primes theorem for polynomials over finite fields
E. El-Mahassni and I. E. Shparlinski -- On the distribution of the elliptic curve power generator
A. Enge -- Discrete logarithms in curves over finite fields
A. Garcia and H. Stichtenoth -- Some remarks on the Hasse-Arf theorem
D. Gomez and A. Winterhof -- Character sums for sequences of iterations of Dickson polynomials
J. Jedwab -- What can be used instead of a Barker sequence?
A. M. Johnston -- Order dividing extension fields and the root computation problem
P. Langevin, G. Leander, and G. McGuire -- Kasami bent functions are not equivalent to their duals
E. Orozco -- Reduced linear modular systems
N. Pinnawala and A. Rao -- Cocyclic Butson Hadamard matrices and codes over $\mathbb{Z}_n$ via the trace map
I. M. Rubio, G. L. Mullen, C. Corrada, and F. N. Castro -- Dickson permutation polynomials that decompose in cycles of the same length
V. K. Murty and K. W. Shum -- Equidistribution of roots of $L$-function of Gold exponential sum
H. Tapia-Recillas -- The simplex code over Galois rings
J. A. Thas -- Finite fields and Galois geometries
Contemporary Mathematics,Volume: 462
2008; 143 pp; softcover
ISBN-13: 978-0-8218-4147-1
Expected publication date is August 2, 2008.
This volume represents the proceedings of the conference on Topics in Deformation Quantization and Non-Commutative Structures held in Mexico City in September 2005. It contains survey papers and original contributions by various experts in the fields of deformation quantization and non-commutative derived algebraic geometry in the interface between mathematics and physics.
It also contains an article based on the XI Memorial Lectures given by M. Kontsevich, which were delivered as part of the conference.
This is an excellent introductory volume for readers interested in learning about quantization as deformation, Hopf algebras, and Hodge structures in the framework of non-commutative algebraic geometry.
Readership
Graduate students and research mathematicians interested in non-commutative algebraic geometry, deformation quantization and operator algebras.
Table of Contents
M. Kontsevich -- XI Solomon Lefschetz memorial lecture series: Hodge structures in non-commutative geometry (Notes by Ernesto Lupercio)
C. Blohmann, X. Tang, and A. Weinstein -- Hopfish structure and modules over irrational rotation algebras
D. Sternheimer -- Deformations and quantizations, an introductory overview
S. Formanski and M. Przanowski -- SDYM and heavenly equations in deformation quantization
O. Obregon, C. Ramirez, and M. Sabido -- On a possible construction of noncommutative topological invariants
D. Rojas-Sandoval and C. Villegas-Blas -- On coherent states for spaces of holomorphic functions related to the hydrogen atom problem in dimensions $n=2,3,5$
M. Rosenbaum, J. D. Vergara, and L. R. Juarez -- Noncommutativity from canonical and noncanonical structures
N. Vasilevski -- Commutative algebras of Toeplitz operators and Berezin quantization
2008; approx. 409 pp; hardcover
ISBN-13: 978-0-8218-4506-6
Expected publication date is September 21, 2008.
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space.
The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the proofs at the end of the chapter or skip them altogether. This style also caters to the expert who needs a handbook and prefers formulations not overshadowed by proofs. Most of the proofs are simple and easy to discover.
The book can be useful and enjoyable for readers with quite different backgrounds and interests. The text is structured in such a way that it is easy to determine what to expect from each piece and how to use it. There is core material, which makes up a relatively small part of the book. The core material is interspersed with examples, illustrative and training problems, and relevant discussions.
The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathematics. With almost no prerequisites (except real numbers), the book can serve as a text for a course on general and beginning algebraic topology.
Undergraduate and graduate students interested in topology.
General topology
Structures and spaces
Continuity
Topological properties
Topological constructions
Topological algebra
Elements of algebraic topology
Fundamental group
Covering spaces and calculation of fundamental groups
Fundamental group and maps
Cellular techniques
Hints, comments, advices, solutions, and answers
Bibliography
Index
Mathematical Surveys and Monographs, Volume: 148
2008; approx. 317 pp; hardcover
ISBN-13: 978-0-8218-4431-1
Expected publication date is September 4, 2008.
In the fifteen years since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several quite different approaches have been used to understand this phenomenon. This book is an account of those approaches, which involve such varied objects and domains as combinatorial group theory, self-distributive algebra, finite combinatorics, automata, low-dimensional topology, mapping class groups, and hyperbolic geometry. The remarkable point is that all these approaches lead to the same ordering, making the latter rather canonical.
We have attempted to make the ideas in this volume accessible and interesting to students and seasoned professionals alike. Although the text touches upon many different areas, we only assume that the reader has some basic background in group theory and topology, and we include detailed introductions wherever they may be needed, so as to make the book as self-contained as possible.
The present volume follows the book, Why are braids orderable?, written by the same authors and published in 2002 by the Societe Mathematique de France. The current text contains a considerable amount of new material, including ideas that were unknown in 2002. In addition, much of the original text has been completely rewritten, with a view to making it more readable and up-to-date.
Graduate students and research mathematicians interested in braid, group theory, low-dimensional topology.
From a review of the previous edition:
"...this is a timely and very carefully written book describing important, interesting and beautiful results in this new area of research concerning braid groups. It will no doubt create much interest and inspire many more insights into these order structures."
-- Stephen P. Humphries for Mathematical Reviews
Introduction
Braid groups
A linear ordering of braids
Applications of the braid ordering
Self-distributivity
Handle reduction
Connection with the Garside structure
Alternating decompositions
Dual braid monoids
Automorphisms of a free group
Curve diagrams
Relaxation algorithms
Triangulations
Hyperbolic geometry
The space of all braid orderings
Bi-ordering the pure braid groups
Open questions and extensions
Bibliography
Index
Key definitions
Index of notation