Contemporary Mathematics, Volume: 533
2011; 307 pp; softcover
ISBN-13: 978-0-8218-4812-8
Expected publication date is February 12, 2011.
This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.
Graduate students and research mathematicians interested in set theory and its modern applications.
Contemporary Mathematics, Volume: 534
2011; 168 pp; softcover
ISBN-13: 978-0-8218-4905-7
Expected publication date is February 11, 2011.
This volume contains survey papers on the theory of operator algebras based on lectures given at the "Lluis Santalo" Summer School of the Real Sociedad Matematica Espanola, held in July 2008 at the Universidad Internacional Menendez Pelayo, in Santander (Spain).
Topics in this volume cover current fundamental aspects of the theory of operator algebras, which have important applications such as:
K-Theory, the Cuntz semigroup, and Classification for C^*-algebras
Modular Theory for von Neumann algebras and applications to Quantum Field Theory
Amenability, Hyperbolic Groups, and Operator Algebras.
The theory of operator algebras, introduced in the thirties by J. von Neumann and F. J. Murray, was developed in close relationship with fundamental aspects of functional analysis, ergodic theory, harmonic analysis, and quantum physics. More recently, this field has shown many other fruitful interrelations with several areas of mathematics and mathematical physics.
Graduate students and research mathematicians interested in operator algebras, C^*-algebras, and K-theory.
P. Ara, F. Perera, and A. S. Toms -- K-theory for operator algebras. Classification of C*-algebras
F. Lledo -- Modular theory by example
D. Guido -- Modular theory for the von Neumann algebras of local quantum physics
N. P. Brown -- The symbiosis of C*- and W*-algebras
P. Ara, F. Lledo, and F. Perera -- Appendix: Basic definitions and results for operator algebras
Student Mathematical Library, Volume: 58
2011; 193 pp; softcover
ISBN-13: 978-0-8218-5242-2
Expected publication date is March 19, 2011.
Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion.
Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and L-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5,
The theories of elliptic curves, modular forms, and L-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.
Undergraduate and graduate students interested in number theory and L-functions.
Introduction
Elliptic curves
Modular curves
Modular forms
L-functions
PARI/GP and Sage
Complex analysis
Projective space
The p-adic numbers
Parametrization of torsion structures
Bibliography
Index
Graduate Studies in Mathematics, Volume: 120
2011; approx. 297 pp; hardcover
ISBN-13: 978-0-8218-5255-2
Expected publication date is March 11, 2011.
This is a textbook for an introductory graduate course on partial differential equations. Han focuses on linear equations of first and second order. An important feature of his treatment is that the majority of the techniques are applicable more generally. In particular, Han emphasizes a priori estimates throughout the text, even for those equations that can be solved explicitly. Such estimates are indispensable tools for proving the existence and uniqueness of solutions to PDEs, being especially important for nonlinear equations. The estimates are also crucial to establishing properties of the solutions, such as the continuous dependence on parameters.
Han's book is suitable for students interested in the mathematical theory of partial differential equations, either as an overview of the subject or as an introduction leading to further study.
Advanced undergraduate and graduate students interested in PDEs.
First-order differential equations
An overview of second-order PDEs
Laplace equations
Heat equations
Wave equations
First-order differential systems
Epilogue
Bibliography
Index
Contemporary Mathematics, Volume: 535
2011; 213 pp; softcover
ISBN-13: 978-0-8218-4948-4
Expected publication date is March 12, 2011.
This volume contains the proceedings of the conference on Spectral Theory and Geometric Analysis, held at Northeastern University, Boston, MA, from July 29-August 2, 2009, which honored Mikhail Shubin on his 65th birthday.
The papers in this volume cover important topics in spectral theory and geometric analysis such as resolutions of smooth group actions, spectral asymptotics, solutions of the Ginzburg-Landau equation, scattering theory, Riemann surfaces of infinite genus, tropical mathematics and geometric methods in the analysis of flows in porous media, and artificial black holes.
Graduate students and research mathematicians interested in spectral theory and geometry analysis.
P. Albin and R. Melrose -- Resolution of smooth group actions
E. Aulisa, A. Ibragimov, and M. Toda -- Geometric methods in the analysis of non-linear flows in porous media
G. Eskin -- Artificial black holes
B. Helffer and Y. A. Kordyukov -- Semiclassical spectral asymptotics for a two-dimensional magnetic Schrodinger operator: The case of discrete wells
R. O. Hryniv, Y. V. Mykytyuk, and P. A. Perry -- Sobolev mapping properties of the scattering transform for the Schrodinger equation
V. Ivrii -- Local spectral asymptotics for 2d-Schrodinger operators with strong magnetic field near the boundary
T. Kappeler, P. Lohrman, and P. Topalov -- On normalized differentials on families of curves of infinite genus
A. Larrain-Hubach, S. Rosenberg, S. Scott, and F. Torres-Ardila -- Characteristic classes and zeroth order pseudodifferential operators
G. L. Litvinov -- Tropical mathematics, idempotent analysis, classical mechanics and geometry
J. J. Perez -- A transversal Fredholm property for the \overline{\partial}-Neumann problem on G-bundles
T. Tzaneteas and I. M. Sigal -- Abrikosov lattice solutions of the Ginzburg-Landau equations