This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, ge…
The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and…
This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, top…
Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fie…
This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The aut…
Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects togeth…
Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how…
In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construc…
The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev-Suslin theorem, a culmination of work initiated by Braue…
Incorporated in this 2003 volume are the first two books in Mukai's series on moduli theory. The notion of a moduli space is central to geometry. However, its influence is not confined there; for example, the theory of moduli spaces is a crucial ing…
This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives…
This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and provides many illustrations of applications of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective…
The theme of this work, the logarithmic integral, lies athwart much of twentieth-century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and compl…
Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is cl…
A revised and updated version of the first edition.
This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues like Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theo…
Many fundamental processes in analysis are best understood by studying and comparing the summability of series in various modes of convergence. This text provides the beginning graduate student, one with basic knowledge of real and functional analys…
In this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding com…
Cohomology of Drinfeld Modular Varieties provides an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over numb…
From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebr…
In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle-Mass…
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional c…
This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, co…
This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abe…
This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It bui…
Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those…
Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its develop…
This book provides a comprehensive account of a key (and perhaps the most important) theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. The book begins with an overview of the theory of automorphic forms on linear algebraic…
The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds and harmonic analysis. The authors show how algebra, geometry and differential equations all play a more fundamental role in Euclidean Fourie…
This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce sp…
In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaul…
The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classificati…
This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetr…
The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter be…
This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding toge…
This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it rea…
Levy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of Levy processes, and…
The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not…
This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees t…
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 ne…
The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general re…
Calls for justice and reconciliation in response to political catastrophes are widespread in contemporary world politics. What implications do these normative strivings have in relation to colonial injustice? Examining cases of colonial war, genocid…
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style acces…
Originally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the t…
This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry foll…
This book is the first of a two-volume basic introduction to enumerative combinatorics at a level suitable for graduate students and research mathematicians. It concentrates on the theory and application of generating functions, a fundamental tool i…
This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topo…