Contemporary Mathematics, Volume: 537
2011; 324 pp; softcover
ISBN-13: 978-0-8218-5239-2
Expected publication date is April 9, 2011.
This book contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3-8, 2009, in Sao Paulo, Brazil.
It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding Theory.
Graduate students and research mathematicians interested in group theory, associative and non-associative algebras, and coding theory.
R. Alfaro -- Linear codes over mathbb{F}_q[u]/(u^t)
M. M. S. Alves and E. Batista -- Globalization theorems for partial Hopf (co)actions, and some of their applications
N. Andruskiewitsch, F. Fantino, G. A. Garcia, and L. Vendramin -- On Nichols algebras associated to simple racks
I. Angiono and A. G. Iglesias -- Pointed Hopf algebras with standard braiding are generated in degree one
A. Berele and A. Regev -- Asymptotics of Young tableaux in the (k,ell)
hook
C. Boyallian and J. I. Liberati -- Classification of irreducible representations over finite simple Lie conformal superalgebras
C. Carvalho -- Pure gaps and bounds for the generalized Hamming weights of Goppa codes
F. N. Castro, L. A. Medina, and I. M. Rubio -- Exact divisibility of exponential sums over the binary field via the covering method
W. Cortes, V. Rodrigues, and A. Sant'Ana -- All hereditary torsion theories are higher differential
A. Davydov and A. Molev -- A categorical approach to classical and quantum Schur-Weyl duality
M. Dokuchaev -- Partial actions: A survey
V. O. Ferreira and L. S. I. Murakami -- On free associative algebras linearly graded by finite groups
V. Futorny, S. Ovsienko, and M. Saorin -- Gelfand-Tsetlin categories
A. Giambruno and E. Zelmanov -- On growth of codimensions of Jordan algebras
L. Gutierrez-Frez, J. Pantoja, and J. Soto-Andrade -- Geometric Weil representations
for star-analogues of SL(2,k)
K. Igusa -- Exceptional sequences, braid groups and clusters
F. Levstein and L. Saal -- Spherical distributions of some generalized Gelfand pairs attached to the Heisenberg group
C. A. Lopez-Andrade and H. Tapia-Recillas -- On the linearity and quasi-cyclicity of the Gray image of codes over a Galois ring
M. Lorenz -- Some applications of Frobenius algebras to Hopf algebras
J. Tirao -- The algebra of differential operators associated to a weight matrix: A first example
Contemporary Mathematics, Volume: 538
2011; approx. 484 pp; softcover
ISBN-13: 978-0-8218-4890-6
Expected publication date is April 10, 2011.
This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain.
The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.
This book is published in cooperation with Real Sociedad Matematica Espanola (RSME).
Graduate students and research mathematicians interested in algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularity theory.
A historical note
A. Libgober -- Development of the theory of Alexander invariants in algebraic geometry
Algebraic geometry and fundamental groups
P. Aluffi and M. Marcolli -- Feynman motives and deletion-contraction relations
M. Amram, R. Lehman, R. Shwartz, and M. Teicher -- Classification of fundamental groups of Galois covers of surfaces of small degree degenerating to nice plane arrangements
D. Arapura -- Homomorphisms between Kahler groups
E. A. Artal-Bartolo, J. I. Cogolludo-Agustin, and D. Matei -- Quasi-projectivity, Artin-Tits groups, and pencil maps
A. Degtyarev -- Topology of plane algebraic curves: The algebraic approach
L. Maxim and J. Schurmann -- Hirzebruch invariants of symmetric products
A. I. Suciu -- Fundamental groups, Alexander invariants, and cohomology jumping loci
Braids and knots
J. Gonzalez-Meneses -- On reduction curves and Garside properties of braids
L. H. Kauffman -- Topological quantum information, Khovanov homology and the Jones polynomial
L. Paris -- HOMFLYPT skein module of singular links
Hyperplane arrangements
N. Budur, A. Dimca, and M. Saito -- First Milnor cohomology of hyperplane arrangements
G. Gaiffi, F. Mori, and M. Salvetti -- Minimal CW-complexes for complements to line arrangements via discrete Morse theory
R. Randell -- The topology of hyperplane arrangements
Singularities
E. Artal-Bartolo, P. Cassou-Nogues, I. Luengo, and A. M. Melle-Hernandez
-- On nu-quasi-ordinary power series: Factorization, Newton trees and resultants
J. L. Cisneros-Molina, J. Seade, and J. Snoussi -- Milnor fibrations for real and complex singularities
J. F. de Bobadilla -- On homotopy types of complements of analytic sets and Milnor fibres
D. Kerner and A. Nemethi -- The Milnor fibre signature is not semi-continuous
A. Nemethi, W. D. Neumann, and A. Pichon -- Principal analytic link theory in homology sphere links
M. Oka -- On mixed Brieskorn variety
P. Popescu-Pampu -- Introduction to Jung's method of resolution of singularities
S. S.-T. Yau, L. Zhao, and H. Zuo -- Biggest sharp polynomial estimate of integral points in right-angled simplices
Graduate Studies in Mathematics, Volume: 123
2011; approx. 411 pp; hardcover
ISBN-13: 978-0-8218-5284-2
Expected publication date is May 28, 2011.
This book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form.
The first three chapters are on elementary distribution theory and Sobolev
spaces with many examples and applications to equations with constant coefficients.
The following chapters study the Cauchy problem for parabolic and hyperbolic
equations, boundary value problems for elliptic equations, heat trace asymptotics,
and scattering theory. The book also covers microlocal analysis, including
the theory of pseudodifferential and Fourier integral operators, and the
propagation of singularities for operators of real principal type. Among
the more advanced topics are the global theory of Fourier integral operators
and the geometric optics construction in the large, the Atiyah-Singer index
theorem in mathbb R^n, and the oblique derivative problem.
Graduate students and research mathematicians interested in partial differential equations.
Theory of distributions
Fourier transforms
Applications of distributions to partial differential equations
Second order elliptic equations in bounded domains
The scattering theory
Pseudodifferential operators
Elliptic boundary value problems and parametrices
Fourier integral operators
Index
Mathematical Surveys and Monographs, Volume: 171
2011; approx. 634 pp; hardcover
ISBN-13: 978-0-8218-5285-9
Expected publication date is May 29, 2011.
Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries).
The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes.
This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
Graduate students and research mathematicians interested in random matrix theory and its applications.
Introduction
Classical ensembles
Gaussian Ensembles: Semicircle law
Gaussian Ensembles: Central Limit Theorem for linear eigenvalue statistics
Gaussian Ensembles: Joint eigenvalue distribution and related results
Gaussian Unitary Ensemble
Gaussian Orthogonal Ensemble
Wishart and Laguerre Ensembles
Classical compact groups ensembles: Global regime
Classical compact groups ensembles: Local regime
Law of addition of random matrices
Matrix Models
Matrix Models: Global regime
Bulk universality for hermitian Matrix Models
Universality for special points of hermitian Matrix Models
Jacobi matrices and limiting laws for linear eigenvalue statistics
Universality for real symmetric Matrix Models
Unitary Matrix Models
Ensembles with independent and weakly dependent entries
Matrices with Gaussian correlated entries
Wigner Ensembles
Sample covariance and related matrices
Bibliography
Index
744 pages
Trim Size 7 3/4 X 9 7/16 in
Copyright 2011
9780123838742 Hardcover
Expected Release Date: Feb 2011
Key Features
Presents recent results in quantum computing, quantum information theory, and quantum error correcting codes.
Covers both classical and quantum information theory and error correcting codes.
The last chapter of the book covers physical implementation of quantum information processing devices.
Covers the mathematical formalism and the concepts in Quantum Mechanics critical for understanding the properties and the transformations of quantum information.
A new discipline, Quantum Information Science, has emerged in the last two decades of the twentieth century at the intersection of Physics, Mathematics, and Computer Science. Quantum Information Processing is an application of Quantum Information Science which covers the transformation, storage, and transmission of quantum information; it represents a revolutionary approach to information processing.
This book covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing.
Quantum information theory and quantum error correction build on the scope, concepts, methodology, and techniques developed in the context of their close relatives, classical information theory and classical error correcting codes.
Graduate students, advanced undergraduate students and professionals (postdocs, faculty, industry research staff) in computer science, electrical engineering, physics, applied physics, mathematics, and maybe chemistry.