Contemporary Mathematics, Volume: 506
2010; 302 pp; softcover
ISBN-13: 978-0-8218-4507-3
Expected publication date is February 14, 2010.
This volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008.
Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.
Graduate students and research mathematicians interested in affine Lie algebras and their generalizations.
B. Allison and G. Benkart -- Unitary Lie algebras and Lie tori of type
BC_{r}, rge3
V. Chari and D. Hernandez -- Beyond Kirillov-Reshetikhin modules
X. Chen and K.-B. Nam -- Root vectors and an integral PBW basis of composition
algebra of the valued graph A_2^{(2)}
B. Cox, V. Futorny, and K. C. Misra -- Imaginary Verma modules and Kashiwara
algebras for U_q(widehat{mathfrak{sl}(2)})
G. Fourier, M. Okado, and A. Schilling -- Perfectness of Kirillov-Reshetikhin crystals for nonexceptional types
Y. Pei, N. Hu, and M. Rosso -- Multiparameter quantum groups and quantum shuffles, (I)
J. Morita -- Tilings, Lie theory and combinatorics
E. Mukhin, V. Tarasov, and A. Varchenko -- The mathfrak{gl}_2 Bethe algebra
associated with a nilpotent element
M. Igarashi and T. Nakashima -- Affine geometric crystal of type D_4^{(3)}
K.-H. Neeb -- Unitary highest weight modules of locally affine Lie algebras
P. Senesi -- Finite-dimensional representation theory of loop algebras: A survey
Y. Yoshii -- Locally extended affine root systems
Graduate Studies in Mathematics, Volume: 110
2010; approx. 215 pp; hardcover
ISBN-13: 978-0-8218-4898-2
Expected publication date is March 25, 2010.
This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincare duality, is almost a triviality in this approach.
Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7-spheres.
This book is based on courses the author taught in Mainz and Heidelberg. Readers should be familiar with the basic notions of point-set topology and differential topology. The book can be used for a combined introduction to differential and algebraic topology, as well as for a quick presentation of (co)homology in a course about differential geometry.
Graduate students and research mathematicians interested in algebraic and differential topology.
A quick introduction to stratifolds
Smooth manifolds revisited
Stratifolds
Stratifolds with boundary: c-stratifolds
mathbb{Z}/2-homology
The Mayer-Vietoris sequence and homology groups of spheres
Brouwer's fixed point theorem, separation, invariance of dimension
Homology of some important spaces and the Euler characteristic
Integral homology and the mapping degree
A comparison theorem for homology theories and CW-complexes
Kunneth's theorem
Some lens spaces and quaternionic generalizations
Cohomology and Poincare duality
Induced maps and the cohomology axioms
Products in cohomology and the Kronecker pairing
The signature
The Euler class
Chern classes and Stiefel-Whitney classes
Pontrjagin classes and applications to bordism
Exotic 7-spheres
Relation to ordinary singular (co)homology
Appendix A: Constructions of stratifolds
Appendix B: The detailed proof of the Mayer-Vietoris sequence
Appendix C: The tensor product
Bibliography
Index
Mathematical Surveys and Monographs, Volume: 159
2010; approx. 454 pp; hardcover
ISBN-13: 978-0-8218-4924-8
Expected publication date is April 3, 2010.
The purpose of this book is to develop the foundations of potential theory
and rational dynamics on the Berkovich projective line over an arbitrary
complete, algebraically closed non-Archimedean field. In addition to providing
a concrete and "elementary" introduction to Berkovich analytic
spaces and to potential theory and rational iteration on the Berkovich
line, the book contains applications to arithmetic geometry and arithmetic
dynamics. A number of results in the book are new, and most have not previously
appeared in book form. Three appendices--on analysis, mathbb{R}-trees,
and Berkovich's general theory of analytic spaces--are included to make
the book as self-contained as possible.
The authors first give a detailed description of the topological structure
of the Berkovich projective line and then introduce the Hsia kernel, the
fundamental kernel for potential theory. Using the theory of metrized graphs,
they define a Laplacian operator on the Berkovich line and construct theories
of capacities, harmonic and subharmonic functions, and Green's functions,
all of which are strikingly similar to their classical complex counterparts.
After developing a theory of multiplicities for rational functions, they
give applications to non-Archimedean dynamics, including local and global
equidistribution theorems, fixed point theorems, and Berkovich space analogues
of many fundamental results from the classical Fatou-Julia theory of rational
iteration. They illustrate the theory with concrete examples and exposit
Rivera-Letelier's results concerning rational dynamics over the field of
p-adic complex numbers. They also establish Berkovich space versions of
arithmetic results such as the Fekete-Szego theorem and Bilu's equidistribution
theorem.
Graduate students and research mathematicians interested in number theory, algebraic geometry, and non-Archimedean dynamics.
The Berkovich unit disc
The Berkovich projective line
Metrized graphs
The Hsia kernel
The Laplacian on the Berkovich projective line
Capacity theory
Harmonic functions
Subharmonic functions
Multiplicities
Applications to the dynamics of rational maps
Some results from analysis and topology
mathbb{R}-trees and Gromov hyperbolicity
Brief overview of Berkovich's theory
Bibliography
Index
Contemporary Mathematics, Volume: 507
2010; 298 pp; softcover
ISBN-13: 978-0-8218-4803-6
Expected publication date is March 13, 2010.
This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday.
This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.
Graduate students and research mathematicians interested in orthogonal polynomials, approximation theory, and their applications.
F. Marcellan and A. Martinez-Finkelshtein -- Guillermo Lopez Lagomasino: mathematical life
B. de la Calle Ysern -- A walk through approximation theory
L. Baratchart and M. Yattselev -- Asymptotic uniqueness of best rational
approximants to complex Cauchy transforms in L^2 of the circle
L. Garza and F. Marcellan -- Quadrature rules on the unit circle. A survey.
A. Ibort, P. Linares, and J. G. Llavona -- On the multilinear trigonometric problem of moments
A. B. J. Kuijlaars -- Multiple orthogonal polynomial ensembles
E. Levin and D. S. Lubinsky -- Some equivalent formulations of universality limits in the bulk
A. Lopez Garcia -- Greedy energy points with external fields
A. Martinez-Finkelshtein and E. A. Rakhmanov -- On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials
E. B. Saff -- Remarks on relative asymptotics for general orthogonal polynomials
B. Simon -- Fine structure of the zeros of orthogonal polynomials: a progress report
H. Stahl -- A potential-theoretic problem connected with complex orthogonality
W. Van Assche -- Orthogonal polynomials and approximation theory: some open problems
Approx. 484 pages
Trim size 7 1/2 X 9 1/4 in
Copyright 2009
Hardcover
Expected Release Date: Jan 2010
Key Features
Integrates biological, statistical and computational concepts
Inclusion of R & SAS code
Provides coverage of complex statistical methods in context with applications in bioinformatics
Exercises and examples aid teaching and learning presented at the right level
Bayesian methods and the modern multiple testing principles in one convenient book
Designed for a one or two semester senior undergraduate or graduate bioinformatics course, Statistical Bioinformatics takes a broad view of the subject - not just gene expression and sequence analysis, but a careful balance of statistical theory in the context of bioinformatics applications. The inclusion of R and SAS code as well as the development of advanced methodology such as Bayesian and Markov models provides students with the important foundation needed to conduct bioinformatics.
Introduction
Genomics
Probability and Statistical Theory
Special Distributions, Properties and Applications
Statistical Inference and Applications
Nonparametric Statistics
Bayesian Statistics
Markov Chain, Monte Carlo
Analysis of Variance
Design of Experiments
Multiple Testing of Hypotheses