Fields Institute Monographs, Volume: 28
2011; 291 pp; hardcover
ISBN-13: 978-0-8218-4271-3
Expected publication date is August 19, 2011.
Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics--linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms--and thus inherit some of the characteristics of both.
This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the "classical" fields--algebraically closed, real closed, finite, local and global. A detailed exposition of the background material needed is given in the first chapter.
It was A. Frohlich who first gave a systematic organization of this subject, in a series of papers beginning in 1969. His paper Orthogonal and symplectic representations of groups represents the culmination of his published work on orthogonal and symplectic representations. The author has included most of the work from that paper, extending it to include unitary representations, and also providing new approaches, such as the use of the equivariant Brauer-Wall group in describing the principal invariants of orthogonal representations and their interplay with each other.
Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians interested in orthogonal, symplectic and unitary representation of finite groups.
Background material
Isometry representations of finite groups
Hermitian forms over semisimple algebras
Equivariant Witt-Grothendieck and Witt groups
Representations over finite, local and global fields
Frohlich's invariant, Clifford algebras and the equivariant Brauer-Wall group
Bibliography
Glossary
Index
Contemporary Mathematics, Volume: 548
2011; 163 pp; softcover
ISBN-13: 978-0-8218-5289-7
Expected publication date is August 14, 2011.
This volume contains the proceedings of the NIMS Thematic Workshop on Mathematical and Statistical Methods for Imaging, which was held from August 10-13, 2010, at Inha University, Incheon, Korea.
The goal of this volume is to give the reader a deep and unified understanding of the field of imaging and of the analytical and statistical tools used in imaging. It offers a good overview of the current status of the field and of directions for further research. Challenging problems are addressed from analytical, numerical, and statistical perspectives. The articles are devoted to four main areas: analytical investigation of robustness; hypothesis testing and resolution analysis, particularly for anomaly detection; new efficient imaging techniques; and the effects of anisotropy, dissipation, or attenuation in imaging.
Graduate students and research mathematicians interested in mathematical and statistical aspects of image processing.
J. Garnier -- Use of random matrix theory for target detection, localization, and reconstruction
P. Garapon -- Resolution limits in source localization and small inclusion imaging
S. Gdoura and L. G. Bustos -- Transient wave imaging of anomalies: A numerical study
G. Bao, J. Lin, and F. Triki -- Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data
M. Lim and S. Yu -- Reconstruction of the shape of an inclusion from elastic moment tensors
J. C. Schotland -- Path integrals and optical tomography
K. Jeon and C.-O. Lee -- Denoising of B_2 data for conductivity reconstruction
in magnetic resonance electrical impedance tomography (MREIT)
D. G. Alfaro Vigo and K. Solna -- Time reversal for inclusion detection in one-dimensional randomly layered media
E. Bretin and A. Wahab -- Some anisotropic viscoelastic Green functions
H. Ammari, E. Bretin, J. Garnier, and A. Wahab -- Time reversal in attenuating acoustic media
University Lecture Series, Volume: 57
2011; approx. 199 pp; softcoverISBN-10: 0-8218-5331-7
ISBN-13: 978-0-8218-5331-3
Expected publication date is September 25, 2011.
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure often coming from geometry.
This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real. The book begins with an overview, giving background on real solutions to univariate polynomials and the geometry of sparse polynomial systems. The first half of the book concludes with fewnomial upper bounds and with lower bounds to sparse polynomial systems. The second half of the book begins by sampling some geometric problems for which all solutions can be real, before devoting the last five chapters to the Shapiro Conjecture, in which the relevant polynomial systems have only real solutions.
Graduate students and research mathematicians interested in real algebraic geometry.
Overview
Real solutions of univariate polynomials
Sparse polynomial systems
Toric degenerations and Kushnirenko's theorem
Fewnomial upper bounds
Fewnomial upper bounds from Gale dual polynomial systems
Lower bounds for sparse polynomial systems
Some lower bounds for systems of polynomials
Enumerative real algebraic geometry
The Shapiro Conjecture for Grassmannians
The Shapiro Conjecture for rational functions
Proof of the Shapiro Conjecture for Grassmannians
Beyond the Shapiro Conjecture for the Grassmannian
The Shapiro Conjecture beyond the Grassmannian
Bibliography
Index of notation
Index
Translations of Mathematical Monographs, Volume: 240
Iwanami Series in Modern Mathematics
2011; approx. 231 pp; softcover
ISBN-13: 978-0-8218-1355-3
Expected publication date is September 24, 2011.
This book, the second of three related volumes on number theory, is the
English translation of the original Japanese book. Here, the idea of class
field theory, a highlight in algebraic number theory, is first described
with many concrete examples. A detailed account of proofs is thoroughly
exposited in the final chapter. The authors also explain the local-global
method in number theory, including the use of ideles and adeles. Basic
properties of zeta and L-functions are established and used to prove the
prime number theorem and the Dirichlet theorem on prime numbers in arithmetic
progressions. With this book, the reader can enjoy the beauty of numbers
and obtain fundamental knowledge of modern number theory.
The translation of the first volume was published as Number Theory 1: Fermat's Dream, Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics), vol. 186, American Mathematical Society, 2000.
Graduate students and research mathematicians interested in number theory.
What is class field theory?
Local and global fields
zeta (II)
Class field theory (II)
Appendix B. Galois theory
Appendix C. Lights of places
Appendix. Answers to questions
Appendix. Answers to exercises
Index
*
Contemporary Mathematics, Volume: 549
2011; 163 pp; softcover
ISBN-13: 978-0-8218-6872-0
Expected publication date is September 3, 2011.
This volume represents the 2009 Jairo Charris Seminar in Symmetries of Differential and Difference Equations, which was held at the Universidad Sergio Arboleda in Bogota, Colombia.
The papers include topics such as Lie symmetries, equivalence transformations and differential invariants, group theoretical methods in linear equations, namely differential Galois theory and Stokes phenomenon, and the development of some geometrical methods in theoretical physics.
The reader will find new interesting results in symmetries of differential and difference equations, applications in classical and quantum mechanics, two fundamental problems of theoretical mechanics, the mathematical nature of time in Lagrangian mechanics and the preservation of the equations of motion by changes of frame, and discrete Hamiltonian systems arising in geometrical optics and analogous to those of finite quantum mechanics.
This book is published in cooperation with Instituto de Matematicas y sus Aplicaciones (IMA).
Graduate students and research mathematicians interested in using symmetries in various areas of analysis.
A. A. Monforte and J.-A. Weil -- A reduction method for higher order variational equations of Hamiltonian systems
N. H. Ibragimov -- A survey on integration of parabolic equations by reducing them to the heat equation
S. Jimenez -- Weil jets, Lie correspondences and applications
J. Mozo-Fernandez -- Some applications of summability: An illustrated survey
J. M. Diaz -- The structure of time and inertial forces in Lagrangian mechanics
P. J. Olver -- Differential invariant algebras
J. Sauloy -- The Stokes phenomenon for linear q-difference equations
K. B. Wolf -- Finite Hamiltonian systems on phase space
Pure and Applied Undergraduate Texts, Volume: 16
2011; approx. 308 pp; hardcover
ISBN-13: 978-0-8218-6901-7
Expected publication date is October 7, 2011.
The text covers a broad spectrum between basic and advanced complex variables on the one hand and between theoretical and applied or computational material on the other hand. With careful selection of the emphasis put on the various sections, examples, and exercises, the book can be used in a one- or two-semester course for undergraduate mathematics majors, a one-semester course for engineering or physics majors, or a one-semester course for first-year mathematics graduate students. It has been tested in all three settings at the University of Utah.
The exposition is clear, concise, and lively. There is a clean and modern approach to Cauchy's theorems and Taylor series expansions, with rigorous proofs but no long and tedious arguments. This is followed by the rich harvest of easy consequences of the existence of power series expansions.
Through the central portion of the text, there is a careful and extensive treatment of residue theory and its application to computation of integrals, conformal mapping and its applications to applied problems, analytic continuation, and the proofs of the Picard theorems.
Chapter 8 covers material on infinite products and zeroes of entire functions. This leads to the final chapter which is devoted to the Riemann zeta function, the Riemann Hypothesis, and a proof of the Prime Number Theorem.
Undergraduate and graduate students interested in complex analysis (one variable).
The complex numbers
Analytic functions
Power series expansions
The general Cauchy theorems
Residue theory
Conformal mappings
Analytic continuation and the Picard theorems
Infinite products
The gamma and zeta functions
Bibliography
Index
Graduate Studies in Mathematics, Volume: 126
2011; approx. 219 pp; hardcover
ISBN-13: 978-0-8218-6919-2
Expected publication date is October 14,
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Caratheodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Radamacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis.
There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text.
As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Graduate students interested in analysis, in particular, measure theory.
Measure theory
Related articles
Bibliography
Index