Contemporary Mathematics, Volume: 447
2007; 256 pp; softcover
ISBN-10: 0-8218-4241-2
ISBN-13: 978-0-8218-4241-6
Expected publication date is December 21, 2007.
This volume consists of refereed research articles written by some of the speakers at this international conference in honor of the sixty-fifth birthday of Jean-Michel Combes. The topics span modern mathematical physics with contributions on state-of-the-art results in the theory of random operators, including localization for random Schrodinger operators with general probability measures, random magnetic Schrodinger operators, and interacting multiparticle operators with random potentials; transport properties of Schrodinger operators and classical Hamiltonian systems; equilibrium and nonequilibrium properties of open quantum systems; semiclassical methods for multiparticle systems and long-time evolution of wave packets; modeling of nanostructures; properties of eigenfunctions for first-order systems and solutions to the Ginzburg-Landau system; effective Hamiltonians for quantum resonances; quantum graphs, including scattering theory and trace formulas; random matrix theory; and quantum information theory. Graduate students and researchers will benefit from the accessibility of these articles and their current bibliographies.
Readership
Graduate students and research mathematicians interested in mathematical physics and statistical mechanics.
Table of Contents
W. H. Aschbacher -- On the emptiness formation probability in quasi-free states
V. Chulaevsky -- Wegner-Stollmann type estimates for some quantum lattice systems
M. Combescure -- The mutually unbiased bases revisited
H. D. Cornean, T. G. Pedersen, and B. Ricaud -- Pertubative vs. variational methods in the study of carbon nanotubes
S. De Bievre, P. Lafitte, and P. E. Parris -- Normal transport at positive temperatures in classical Hamiltonian open systems
P. Exner and J. Lipovsky -- Equivalence of resolvent and scattering resonances on quantum graphs
S. Fournais and B. Helffer -- Optimal uniform elliptic estimates for the Ginzburg-Landau system
F. Germinet and A. Klein -- Localization for a continuum Cantor-Anderson Hamiltonian
F. Germinet and S. Tcheremchantsev -- Generalized fractal dimensions on the negative axis for non compactly supported measures
F. Ghribi, P. D. Hislop, and F. Klopp -- Localization for Schrodinger operators with random vector potentials
G. A. Hagedorn and A. Joye -- Vibrational levels associated with hydrogen bonds and semiclassical Hamiltonian normal forms
V. Jaksic and C.-A. Pillet -- On the strict positivity of entropy production
A. Jensen and G. Nenciu -- Uniqueness results for transient dynamics of quantum systems
V. Kostrykin, J. Potthoff, and R. Schrader -- Heat kernels on metric graphs and a trace formula
J. L. Lebowitz, A. Lytova, and L. Pastur -- On a random matrix model of quantum relaxation
D. Robert -- Revivals of wave packets and Bohr-Sommerfeld quantization rules
L. E. Thomas and Y. Wang -- On a linear stochastic wave equation modeling heat flow
D. R. Yafaev -- Exponential decay of eigenfunctions of first order systems
Contemporary Mathematics, Volume: 448
2007; 270 pp; softcover
ISBN-10: 0-8218-4094-0
ISBN-13: 978-0-8218-4094-8
Expected publication date is December 30, 2007.
This volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.
Readership
Graduate students and research mathematicians interested in communitative algebra and algebraic geometry.
Table of Contents
M. Bertolini, G. M. Besana, and C. Turrini -- Instability of projective reconstruction from 1-view near critical configurations in higher dimensions
K. A. Chandler -- Examples and counterexamples on the conjectured Hilbert function of multiple points
C. Ciuperca, W. Heinzer, J. Ratliff, and D. Rush -- Projectively full ideals in Noetherian rings, a survey
K. Dalili and W. V. Vasconcelos -- Cohomological degrees and the HomAB conjecture
J. A. Eagon -- A minimal generating set for the first syzygies of a monomial ideal
E. Gorla -- Lifting the determinantal property
H. T. Ha and A. Van Tuyl -- Resolutions of square-free monomial ideals via facet ideals: A survey
M. Hochster -- Some finiteness properties of Lyubeznik's mathcal{F}-modules
C. Huneke, J. Migliore, U. Nagel, and B. Ulrich -- Minimal homogeneous liaison and Licci ideals
J. O. Kleppe and R. M. Miro-Roig -- Unobstructedness and dimension of families of codimension 3 ACM algebras
A. Lanteri and H. Maeda -- Ample vector bundles with sections vanishing on submanifolds of sectional genus three
Y. Lu, D. J. Bates, A. J. Sommese, and C. W. Wampler -- Finding all real points of a complex curve
R. M. Miro-Roig -- On the multiplicity conjecture
J. M. Rojas -- Efficiently detecting torsion points and subtori
A. K. Singh and S. Spiroff -- Divisor class groups of graded hypersurfaces
K. E. Smith and H. M. Thompson -- Irrelevent exceptional divisors for curves on a smooth surface
M. A. van Opstall and R. Veliche -- Variation of hyperplane sections
C. Yuen -- Jet schemes of determinantal varieties
2008; approx. 549 pp; hardcover
ISBN-10: 0-8218-4222-6
ISBN-13: 978-0-8218-4222-5
Expected publication date is February 1, 2008.
Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line.
In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular flow on the associated moduli space of fractal membranes. Conjecturally, under the action of the modular flow, the spacetime geometries become increasingly symmetric and crystal-like, hence, arithmetic. Correspondingly, the zeros of the associated zeta functions eventually condense onto the critical line, towards which they are attracted, thereby explaining why the Riemann Hypothesis must be true.
Written with a diverse audience in mind, this unique book is suitable for graduate students, experts and nonexperts alike, with an interest in number theory, analysis, dynamical systems, arithmetic, fractal or noncommutative geometry, and mathematical or theoretical physics.
Readership
Graduate students and research mathematicians interested in number theory, noncommutative geometry, and physics.
Table of Contents
Introduction
String theory on a circle and T-duality: Analogy with the Riemann zeta function
Fractal strings and fractal membranes
Noncommutative models of fractal strings: Fractal membranes and beyond
Towards an `arithmetic site': Moduli spaces of fractal strings and membranes
Vertex algebras
The Weil conjectures and the Riemann hypothesis
The Poisson summation formula, with applications
Generalized primes and Beurling zeta functions
The Selberg class of zeta functions
The noncommutative space of Penrose tilings and quasicrystals
Bibliography
Conventions
Index of symbols
Subject index
Author index
2008; 371 pp; hardcover
ISBN-10: 0-8218-4441-5
ISBN-13: 978-0-8218-4441-0
Expected publication date is January 17, 2008.
Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle.
Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings.
Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform.
The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.
Readership
Undergraduate students interested in linear algebra; applications of linear algebra.
Table of Contents
The decoupling principle
Vector spaces and bases
Linear transformations and operators
An introduction to eigenvalues
Some crucial applications
Inner products
Adjoints, Hermitian operators, and unitary operators
The wave equation
Continuous spectra and the Dirac delta function
Fourier transforms
Green's functions
Matrix operations
Solutions to selected exercises
Index
2007; 163 pp; hardcover
ISBN-10: 0-8218-4428-8
ISBN-13: 978-0-8218-4428-1
Expected publication date is January 10, 2008.
Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.
The first edition was published with the title Notes on Complex Function Theory.
Readership
Undergraduate and graduate students interested in complex analysis.
Reviews
From a review of the previous edition ...
"The exposition is clear, rigorous, and friendly."
-- Zentralblatt MATH
Table of Contents
Complex numbers
Complex differentiation
Linear-fractional transformations
Elementary functions
Power series
Complex integration
Core versions of Cauchy's theorem, and consequences
Laurent series and isolated singularities
Cauchy's theorem
Further development of basic complex function theory
Appendix 1: Sufficient condition for differentiability
Appendix 2: Two instances of the chain rule
Appendix 3: Groups, and linear-fractional transformations
Appendix 4: Differentiation under the integral sign
References
Index