Annals of Mathematics Studies^{202}
SunYung Alice Chang, Phillip A. Griffiths, and Elias M. Stein, Series Editors
Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of our time.

Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it...

William Thurston (1946–2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of mathematical fields, from foliations, contact structures, and...

Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications suitable...

Berkeley Lectures on padic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the...

This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with...

This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of Lfunctions.
The authors study the cohomology of locally symmetric spaces for GL(N) where...

Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the tenth anniversary of...

This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it...

This book presents the complete proof of the BlochKato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of...

A central concern of number theory is the study of localtoglobal principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a...

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex...

This book offers a survey of recent developments in the analysis of shock reflectiondiffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related...

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers...

Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below...

This is the first book to present a complete characterization of SteinTomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all realanalytic hypersurfaces. The range of...

In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields...

The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM105), Volume 105, will be forthcoming.

An especially timely work, the book is an introduction to the theory of padic Lfunctions originated by Kubota and Leopoldt in 1964 as padic analogues of the classical Lfunctions of Dirichlet.
Professor Iwasawa reviews the classical...

This book presents a classification of all (complex)
irreducible representations of a reductive group with
connected centre, over a finite field. To achieve this,
the author uses etale intersection cohomology, and
detailed information on... 
The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic...

This collection of papers constitutes a wideranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of...

The description for this book, Lectures on Fourier Integrals. (AM42), Volume 42, will be forthcoming.

During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing. Twentyfive of these lectures are included in this study, among them Professor Bing's...

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM36), Volume III, will be forthcoming.

The description for this book, Fourier Transforms. (AM19), Volume 19, will be forthcoming.

The description for this book, Probleme General de la Stabilite du Mouvement. (AM17), Volume 17, will be forthcoming.

The description for this book, Calculus on Heisenberg Manifolds. (AM119), Volume 119, will be forthcoming.

This book describes an invariant, l, of oriented rational homology 3spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of...

The description for this book, Ramification Theoretic Methods in Algebraic Geometry (AM43), Volume 43, will be forthcoming.

The present monograph grew out of the fifth set of Hermann Weyl Lectures, given by Professor Griffiths at the Institute for Advanced Study, Princeton, in fall 1974.
In Chapter 1 the author discusses Emile Borel's proof and the classical...

The description for this book, Seminar on Transformation Groups. (AM46), Volume 46, will be forthcoming.

The description for this book, Recent Developments in Several Complex Variables. (AM100), Volume 100, will be forthcoming.

Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard...

The description for this book, Topics in Transcendental Algebraic Geometry. (AM106), Volume 106, will be forthcoming.

In this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that...

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse....

This book contains a valuable discussion of renormalization through the addition of counterterms to the Lagrangian, giving the first complete proof of the cancellation of all divergences in an arbitrary interaction. The author also...

The description for this book, Lectures on Differential Equations. (AM14), Volume 14, will be forthcoming.

The description for this book, Flows on Homogeneous Spaces. (AM53), Volume 53, will be forthcoming.

The theory of exterior differential systems provides a framework for systematically addressing the typically nonlinear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of...

Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number...

The description for this book, Introduction to NonLinear Mechanics. (AM11), Volume 11, will be forthcoming.

The description for this book, Topological Methods in the Theory of Functions of a Complex Variable. (AM15), Volume 15, will be forthcoming.

This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes...

This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N,F) of a nonArchimedean local field F in terms of the structure of these representations when they...

In the first two chapters of this book, the reader will find a complete and systematic exposition of the theory of hyperfunctions on totally real submanifolds of multidimensional complex space, in particular of hyperfunction theory in...

The description for this book, Composition Methods in Homotopy Groups of Spheres. (AM49), Volume 49, will be forthcoming.

The description for this book, KTheory of Forms. (AM98), Volume 98, will be forthcoming.

Based on a seminar sponsored by the Institute for Advanced Study in 19771978, this set of papers introduces microlocal analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of...

The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied...

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM41), Volume IV, will be forthcoming.

The description for this book, Seminar On Minimal Submanifolds. (AM103), Volume 103, will be forthcoming.

Geometry of orthogonal spaces.

These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games...

This is a study of the theory of models with truth values in a compact Hausdorff topological space.

A new group of contributions to the development of this theory by leading experts in the field. The contributors include L. D. Berkovitz, L. E. Dubins, H. Everett, W. H. Fleming, D. Gale, D. Gillette, S. Karlin, J. G. Kemeny, R....

The description for this book, Existence Theorems in Partial Differential Equations. (AM23), Volume 23, will be forthcoming.

The description for this book, OrderPreserving Maps and Integration Processes. (AM31), Volume 31, will be forthcoming.

The description for this book, An Essay Toward a Unified Theory of Special Functions. (AM18), Volume 18, will be forthcoming.

The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first...

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as...

Riemann introduced the concept of a "local system" on P1{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions)...

The description for this book, Elementary Differential Topology. (AM54), Volume 54, will be forthcoming.

Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a selfcontained exposition of the Neumann problem for the CauchyRiemann complex and...

The description for this book, Stationary Processes and Prediction Theory. (AM44), Volume 44, will be forthcoming.

Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics...

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was...

Part exposition and part presentation of new results, this monograph deals with that area of mathematics which has both combinatorial group theory and mathematical logic in common. Its main topics are the word problem for groups, the...

The description for this book, Degrees of Unsolvability. (AM55), Volume 55, will be forthcoming.

This book gives a new foundation for the theory of links in 3space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3manifolds. The basic construction is a method of obtaining any link by...

This book serves both as a completely selfcontained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.

Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work...

The description for this book, Contributions to the Theory of Partial Differential Equations. (AM33), Volume 33, will be forthcoming.

Measures and integrals

The description for this book, Surface Area. (AM35), Volume 35, will be forthcoming.

A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the...

The arithmetic RiemannRoch Theorem has been shown recently by BismutGilletSoul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present...

Written for advanced undergraduate and firstyear graduate students, this book aims to introduce students to a serious level of padic analysis with important implications for number theory. The main object is the study of Gseries...

This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications...

Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of thesethe TOP manifoldsremained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling...

The description for this book, Riemann Surfaces Related Topics (AM97), Volume 97: Proceedings of the 1978 Stony Brook Conference. (AM97), will be forthcoming.

On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideasideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first...

New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H. C. Gunning's book surveys...

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in lowdimensional topology.
In Chapter 1 the author is concerned with the concept of a braid as a group of...

The description for this book, Singular Points of Complex Hypersurfaces. (AM61), Volume 61, will be forthcoming.

This work deals with an extension of the classical LittlewoodPaley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of...

The description for this book, Contributions to Fourier Analysis. (AM25), will be forthcoming.

The description for this book, Knot Groups. Annals of Mathematics Studies. (AM56), Volume 56, will be forthcoming.

This book contains accounts of talks held at a symposium in honor
of John C. Moore in October 1983 at Princeton University, The work
includes papers in classical homotopy theory, homological algebra,
rational homotopy theory, algebraic... 
The description for this book, Curvature and Betti Numbers. (AM32), Volume 32, will be forthcoming.

The description for this book, Meromorphic Functions and Analytic Curves. (AM12), will be forthcoming.

The description for this book, Transcendental Numbers. (AM16), will be forthcoming.

Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows...

The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the...

The fifteen articles composing this volume focus on recent developments in complex analysis. Written by wellknown researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial...

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM20), Volume I, will be forthcoming.

There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers...

Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 19771978. While some of the lectures were devoted to the analysis...

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents...

Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic...

In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes.
The book gives an explicit construction of one distinguished member, D(V), of...

Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity...

This work is a fresh presentation of the AhlforsWeyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna theory and several complex variables. The treatment is differential geometric throughout...

The description for this book, Linear Inequalities and Related Systems. (AM38), Volume 38, will be forthcoming.

These lectures, delivered by Professor Mumford at Harvard in 19631964, are devoted to a study of properties of families of algebraic curves, on a nonsingular projective algebraic curve defined over an algebraically closed field of...

The description for this book, Contributions to the Theory of Games (AM40), Volume IV, will be forthcoming.

As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938even though he did not have a fellowshipto study among the many giants of mathematics who had recently joined the faculty. He eventually became...

In essence the proceedings of the 1967 meeting in Baton Rouge, the volume offers significant papers in the topology of infinite dimensional linear spaces, fixed point theory in infinite dimensional spaces, infinite dimensional...

This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing...

Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in twoand threedimensional topology, geometry, and dynamical systems. This book...

This book offers a selfcontained account of the 3manifold invariants arising from the original Jones polynomial. These are the WittenReshetikhinTuraev and the TuraevViro invariants. Starting from the Kauffman bracket model for the...

Beginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more...

The description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM27), Volume 27, will be forthcoming.

In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact nonAbelian groups. They also obtain many related...

In this monograph padic period domains are associated to arbitrary reductive groups. Using the concept of rigidanalytic period maps the relation of padic period domains to moduli space of pdivisible groups is investigated. In...

Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 2125, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian...

The description for this book, Contributions to the Theory of Games (AM24), Volume I, will be forthcoming.

Algebraic Ktheory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to...

In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon...

The description for this book, The Calculi of Lambda Conversion. (AM6), Volume 6, will be forthcoming.

The description for this book, Advances in Game Theory. (AM52), Volume 52, will be forthcoming.

Based on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular...

The description for this book, Convergence and Uniformity in Topology. (AM2), Volume 2, will be forthcoming.

The description for this book, An Introduction to Linear Transformations in Hilbert Space. (AM4), Volume 4, will be forthcoming.

Solomon Lefschetz pioneered the field of topologythe study of the properties of many�sided figures and their ability to deform, twist, and stretch without changing their shape. According to Lefschetz, "If it's just turning the...

The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose lightlike geodesics are periodic? A surprising fact is that such...

Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved...

Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex...

The description for this book, Automata Studies. (AM34), Volume 34, will be forthcoming.

This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and...

The application by Fadeev and Pavlov of the LaxPhillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the...

Written and revised by D. B. A. Epstein.

A survey, thorough and timely, of the singularities of twodimensional normal complex analytic varieties, the volume summarizes the results obtained since Hirzebruch's thesis (1953) and presents new contributions. First, the singularity...

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential...

This work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann...

The description for this book, A Theory of CrossSpaces. (AM26), Volume 26, will be forthcoming.

The description for this book, Seminar on AtiyahSinger Index Theorem. (AM57), Volume 57, will be forthcoming.

The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now...

The description for this book, Degree of Approximation by Polynomials in the Complex Domain. (AM9), Volume 9, will be forthcoming.

The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM8), will be forthcoming.

The description for this book, The TwoValued Iterative Systems of Mathematical Logic. (AM5), Volume 5, will be forthcoming.

This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with...

The first part of this monograph is devoted to a characterization of hypergeometriclike functions, that is, twists of hypergeometric functions in nvariables. These are treated as an (n+1) dimensional vector space of multivalued...

This collection brings together influential papers by mathematicians exploring the research frontiers of topology, one of the most important developments of modern mathematics. The papers cover a wide range of topological specialties...

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM45), Volume V, will be forthcoming.

These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games...

This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for...

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the...

The padic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all padic representations of the fundamental group of a proper smooth variety over a padic field in terms of linear algebra—namely Higgs...

In the earlier monograph Pseudoreductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudoreductive groups. In this new book, Classification of Pseudoreductive Groups, Conrad and Prasad go...

Descent in Buildings begins with the resolution of a major open question about the local structure of BruhatTits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point...

This book develops a new theory of multiparameter singular integrals associated with CarnotCarathéodory balls. Brian Street first details the classical theory of CalderónZygmund singular integrals and applications to linear partial...

This book presents a new result in 3dimensional topology. It is well known that any closed oriented 3manifold can be obtained by surgery on a framed link in S
3. In Global Surgery Formula for the CassonWalker Invariant, a function F... 
Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra...

The first two chapters of this book offer a modern, selfcontained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters...

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixedpoints for renormalization and...

One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to padic Galois representations....

In 1920, Pierre Fatou expressed the conjecture thatexcept for special casesall critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the...

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of...

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution...

In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is...

Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic Ktheory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence...

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance...

This comprehensive account of the GrossZagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of Lseries. The formula will have new applications for the...

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant...

MumfordTate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of MumfordTate groups and...

This book considers the socalled Unlikely Intersections, a topic that embraces wellknown issues, such as Lang's and ManinMumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book...

This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related...

Convolution and Equidistribution explores an important aspect of number theorythe theory of exponential sums over finite fields and their Mellin transformsfrom a new, categorical point of view. The book presents fundamentally...

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation...

The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum. This is achieved in the book's fourth paper, using results of...

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate...

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number...

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's taufunction as a typical example, have deep...

This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures...

Ramsey theory is a fastgrowing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramseytype...

This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a...

Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the socalled...

The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically...

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinitycategories, higher categories in which all higher morphisms are assumed to be invertible. In...

This book is a spectacular introduction to the modern mathematical discipline known as the Theory of Games. Harold Kuhn first presented these lectures at Princeton University in 1952. They succinctly convey the essence of the theory, in...

For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and TaylorWiles in...

Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves...

This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. Its primary...

This collection of new and original papers on mathematical aspects of nonlinear dispersive equations includes both expository and technical papers that reflect a number of recent advances in the field. The expository papers describe the...

In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory....

In The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of BruhatTits buildings first completed by Jacques Tits in 1986. The book includes numerous results about...

This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a secondorder operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the...

This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction...

This book describes the theory and applications of discrete orthogonal polynomialspolynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and...

Among the many differences between classical and padic objects, those related to differential equations occupy a special place. For example, a closed padic analytic oneform defined on a simplyconnected domain does not necessarily...

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zerocycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the...

It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebrogeometric families of character sums...

In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodgetheoretic constructions such as the cycle class and the AbelJacobi map....

This book presents an overview of recent developments in the area of localization for quasiperiodic lattice Schrödinger operators and the theory of quasiperiodicity in Hamiltonian evolution equations. The physical motivation of these...

This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model...

Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the KolmogorovFeller theory of Markov processes. Starting with the geometric ideas that guided him, this...

This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4tuples. Primitive permutation groups of...

This book aims first to prove the local Langlands conjecture for GLn over a padic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the ladic cohomology of the "simple" Shimura...

The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology...

Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.

The description for this book, Contributions to the Theory of Riemann Surfaces. (AM30), Volume 30, will be forthcoming.