Böcker i Mathematical Surveys and Monographs-serien

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.

Presents an introduction to the conformally invariant processes that appear as scaling limits. This book covers such topics as stochastic integration, and complex Brownian motion and measures derived from Brownian motion. It is suitable for those interested in random processes and their applications in theoretical physics.

Explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations.

Presents an approach to algebraic geometry of curves that is treated as the theory of algebraic functions on the curve. This book discusses such topics as the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, and extensions of the fields of functions (covering theory) and of the fields of constants.

The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation. This book describes the theory of rings in which both maximal and minimal conditions hold for ideals.

Studies nonlocal bifurcations that occur on the boundary of the domain of Morse-Smale systems in the space of all dynamical systems. This work presents the foundations of normal forms and hyperbolic theories from the very first stages. The proofs are preceded by heuristic descriptions of the ideas.

Aims to treat a theory of elliptic boundary value problems in domains without singularities and in domains with conical or cuspidal points. This work focuses on fundamental results of the theory: estimates for solutions in different function spaces, regularity assertions and asymptotic formulas for the solutions near singular points.

Provides a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Much of the content has never before appeared in book form.

Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. This book intends to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation.

The Teichmuller space $T(X)$ is the space of marked conformal structures on a given quasi conformal surface $X$. This book uses quasi conformal mapping to give a unified and up-to-date treatment of $T(X)$. It offers a treatment of deformations of complex structures on infinite Riemann surfaces.

Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.

Summarizes the literature about the ring structure of the mod 2 cohomology of sporadic simple groups. This book offers background material on the relevant constructions from algebraic topology, and on local geometries from group theory.

Gives a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors have also attempted to give the appropriate references so that the reader may further pursue the statements and proofs of the various results.

Presents a comprehensive exposition of the modern theory of valued and ordered fields. This title presents the classical aspects of such fields: their arithmetic, topology, and Galois theory. It emphasizes the close connections and interplay between valuations and orderings, and to a large extent, studies them in a unified manner.

The theory of partitions, founded by Euler, has led in a natural way to the idea of basic hypergeometric series, also known as Eulerian series. These series were first studied systematically by Heine, but many early results are attributed to Euler, Gauss, and Jacobi. This book provides a simple approach to basic hypergeometric series.

An exposition of what is known about the fundamental groups of compact Kahler manifolds. It collects together various results obtained over the years which aim to characterise those infinite groups which can arise as fundamental groups of compact Kahler manifolds. Most of these results are negative ones, saying which groups do not arise.

Presents a framework for relating the homotopy theory of manifolds to the algebraic theory of quadratic forms, unifying previous results. This work offers a surgery obstruction theory for manifolds with arbitrary fundamental group, including the exact sequence for the set of manifold structures within a homotopy type, and many computations.

Describes the structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. This book presents an analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C^*$-algebras are based.

Includes an extensive treatment of Hurwitz polynomials and other topics. This title features material on infrapolynomials, abstract polynomials, and matrix methods.

Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. This book presents a treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces H{p}.

Around 1980, G Mason announced the classification of a certain subclass of a class of finite simple groups known as 'quasithin groups'. The classification of the finite simple groups depends upon a proof that there are no unexpected groups in this subclass. This book offers a proof of a theorem classifying a larger class of groups.

Around 1980, G Mason announced the classification of a certain subclass of a class of finite simple groups known as 'quasithin groups'. The classification of the finite simple groups depends upon a proof that there are no unexpected groups in this subclass. This book offers a proof of a theorem classifying a larger class of groups.

Over the years, the theory of Bergman spaces has undergone a remarkable metamorphosis. The subject of Bergman spaces is a masterful blend of complex function theory with functional analysis and operator theory. This book is suitable for those who have studied basic complex function theory, measure theory, and functional analysis.