Bøger i Colloquium Publications serien

Focuses on the interplay among noncommutative geometry, physics, and number theory. This book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry.

Filling a big gap in the literature, this book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz.

Presents a self-contained development of the regularity theory for solutions of fully nonlinear elliptic equations. This book describes various techniques that are needed to extend the classical Schauder and Calderon-Zygmund regularity theories for linear elliptic equations to the fully nonlinear context.

Suitable for students and researchers in topology. this work provides the reader with an understanding of the physical properties of Euclidean 3-space - the space in which we presume we live.

Presents a study of problems related to the theory of infinite-dimensional dynamical systems. This work studies their properties for various non-autonomous equations of mathematical physics: the 2D and 3D Navier-Stokes systems, reaction-diffusion systems, dissipative wave equations, the complex Ginzburg-Landau equation, and others.

Presents a systematic and unified study of geometric nonlinear functional analysis. This book presents a study of uniformly continuous and Lipschitz functions between Banach spaces, which leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories.

Covers topics including the algebraic theory of non-linear differential equations and their symmetries, the local aspects of the theory of chiral algebras, and the formalism of chiral homology treating 'the space of conformal blocks' of the conformal field theory.

A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike.

A comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. A wide range of applications are included, both to traditional questions, and to areas pr

Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool.

Covers the author's principle of arithmetical paraphrases, which won him the Bocher Prize in 1924; this general principle served to unify and extend many isolated results in the theory of numbers. This book provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers.

Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. This book is Morse's own exposition of his ideas.

Presents a comprehensive study of the algebraic theory of quadratic forms, from classical theory to the developments, including results and proofs. Written from the viewpoint of algebraic geometry, this book includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible.

Part of ""Colloquium Series"", this book presents systematic treatment of orthogonal polynomials.

Features lattice theory and portrays its structure and indicates some of its most interesting applications.

Presents an exposition of the whole variety of topics related to quantum cohomology. In this monograph, the author's approach to quantum cohomology is based on the notion of the Frobenius manifold. It deals with this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry.