Graduate Studies in Mathematics, Volume: 19
2010; 749 pp; hardcover
ISBN-13: 978-0-8218-4974-3
Expected publication date is April 2, 2010.
This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including
a new chapter on nonlinear wave equations,
more than 80 new exercises,
several new sections,
a significantly expanded bibliography
Introduction
Representation formulas for solutions
Four important linear partial differential equations
Nonlinear first-order PDE
Other ways to represent solutions
Theory for linear partial differential equations
Sobolev spaces
Second-order elliptic equations
Linear evolution equations
Theory for nonlinear partial differential equations
The calculus of variations
Nonvariational techniques
Hamilton-Jacobi equations
Systems of conservation laws
Nonlinear wave equations
Appendices
Bibliography
Index
Mathematical Surveys and Monographs, Volume: 162
2010; 605 pp; hardcover
ISBN-13: 978-0-8218-4983-5
Expected publication date is April 30, 2010.
Elliptic Boundary Value Problems in Domains with Point Singularities - V A Kozlov, V G Maz'ya and J Rossmann
Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations - V A Kozlov, V G Maz'ya and J Rossmann
This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives.
The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points.
The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.
Graduate students and research mathematicians interested in elliptic PDEs.
Introduction
The Dirichlet problem for strongly elliptic systems in polyhedral domains
Prerequisites on elliptic boundary value problems in domains with conical points
The Dirichlet problem for strongly elliptic systems in a dihedron
The Dirichlet problem for strongly elliptic systems in a cone with edges
The Dirichlet problem in a bounded domain of polyhedral type
The Miranda-Agmon maximum principle
Neumann and mixed boundary value problems for second order systems in polyhedral domains
Boundary value problems for second order systems in a dihedron
Boundary value problems for second order systems in a polyhedral cone
Boundary value problems for second order systems in a bounded polyhedral domain
Mixed boundary value problems for stationary Stokes and Navier-Stokes systems in polyhedral domains
Boundary value problem for the Stokes system in a dihedron
Mixed boundary value problems for the Stokes system in a polyhedral cone
Mixed boundary value problems for the Stokes and Navier-Stokes systems in a bounded domain of polyhedral type
Historical remarks
Bibliography
Index
List of symbols
Contemporary Mathematics, Volume: 511
2010; 200 pp; softcover
ISBN-13: 978-0-8218-4805-0
Expected publication date is May 8, 2010.
This volume consists of contributions by researchers who were invited to the Harlaxton Conference on Computational Group Theory and Cohomology, held in August of 2008, and to the AMS Special Session on Computational Group Theory, held in October 2008.
This volume showcases examples of how Computational Group Theory can be applied to a wide range of theoretical aspects of group theory. Among the problems studied in this book are classification of p-groups, covers of Lie groups, resolutions of Bieberbach groups, and the study of the lower central series of free groups. This volume also includes expository articles on the probabilistic zeta function of a group and on enumerating subgroups of symmetric groups.
Researchers and graduate students working in all areas of Group Theory will find many examples of how Computational Group Theory helps at various stages of the research process, from developing conjectures through the verification stage. These examples will suggest to the mathematician ways to incorporate Computational Group Theory into their own research endeavors.
Graduate students and research mathematicians interested in group theory and computation.
B. Benesh -- The probabilistic Zeta function
B. Eick and T. Rossmann -- Periodicities for graphs of p-groups beyond coclass
G. Ellis, H. Mohammadzadeh, and H. Tavallaee -- Computing covers of Lie algebras
D. F. Holt -- Enumerating subgroups of the symmetric group
D. A. Jackson, A. M. Gaglione, and D. Spellman -- Weight five basic commutators as relators
P. Moravec and R. F. Morse -- Basic commutators as relations: a computational perspective
L.-C. Kappe and G. Mendoza -- Groups of minimal order which are not n-power closed
L.-C. Kappe and J. L. Redden -- On the covering number of small alternating groups
A. Magidin and R. F. Morse -- Certain homological functors of 2-generator p-groups of class 2
M. Roder -- Geometric algorithms for resolutions for Bieberbach groups
F. Russo -- Nonabelian tensor product of soluble minimax groups
J. Schmidt -- Finite groups have short rewriting systems
Contemporary Mathematics, Volume: 512
2010; 177 pp; softcover
ISBN-13: 978-0-8218-4892-0
Expected publication date is May 9, 2010.
The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Symplectic Topology and Measure Preserving Dynamical Systems held in Snowbird, Utah in July 2007.
The aim of the conference was to bring together specialists of symplectic topology and of measure preserving dynamics to try to connect these two subjects. One of the motivating conjectures at the interface of these two fields is the question of whether the group of area preserving homeomorphisms of the 2-disc is or is not simple. For diffeomorphisms it was known that the kernel of the Calabi invariant is a normal proper subgroup, so the group of area preserving diffeomorphisms is not simple. Most articles are related to understanding these and related questions in the framework of modern symplectic topology.
Graduate students and research mathematicians interested in symplectic topology and dynamical systems.
A. Banyaga -- A Hofer-like metric on the group of symplectic diffeomorphisms
M. Entov and L. Polterovich -- C^0-rigidity of Poisson brackets
F. Le Roux -- Six questions, a proposition and two pictures on Hofer distance for Hamiltonian diffeomorphisms on surfaces
J. N. Mather -- Order structure on action minimizing orbits
D. McDuff -- Loops in the Hamiltonian group: A survey
Y.-G. Oh -- The group of Hamiltonian homeomorphisms and continuous Hamiltonian flows
Mathematical Surveys and Monographs, Volume: 163
2010; approx. 525 pp; hardcover
ISBN-13: 978-0-8218-4661-2
Expected publication date is June 11, 2010.
The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects.
The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of kappa-solutions including the kappa-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other.
The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.
Graduate students and research mathematicians interested in geometric analysis, Ricci flow, Perelman's work on Poincare.
Entropy, mu-invariant, and finite time singularities
Geometric tools and point picking methods
Geometric properties of kappa-solutions
Compactness of the space of kappa-solutions
Perelman's pseudolocality theorem
Tools used in proof of pseudolocality
Heat kernel for static metrics
Heat kernel for evolving metrics
Estimates of the heat equation for evolving metrics
Bounds for the heat kernel for evolving metrics
Elementary aspects of metric geometry
Convex functions on Riemannian manifolds
Asymptotic cones and Sharafutdinov retraction
Solutions to selected exercises
Bibliography
Index
Graduate Studies in Mathematics, Volume: 114
2010; approx. 1015 pp; hardcover
ISBN-13: 978-0-8218-4741-1
Expected publication date is August 26, 2010.
This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free).
The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Grobner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn-Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra.
Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic K-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization.
Graduate students interested in algebra.
Groups I
Commutative rings I
Fields
Groups II
Commutative rings II
Rings
Representation theory
Advanced linear algebra
Homology
Commutative rings III
Bibliography
Index