Mathematical Studies Sl Book Answer

The Arithmetic of Polynomial Dynamical Pairs: (AMS-214)

In The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given...

The Einstein-Klein-Gordon Coupled System: Global Stability of the Minkowski Solution: (AMS-213) Alexandru D. Ionescu and Benoît Pausader

This book provides a definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equations of general relativity. Along the way, a novel robust analytical framework is developed...

Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas: (AMS-212) Daniel Kriz

This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from...

The Structure of Groups with a Quasiconvex Hierarchy: (AMS-209) Daniel T. Wise

This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time...

A Course on Surgery Theory: (AMS-211) Stanley Chang and Shmuel Weinberger

Surgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. A Course on Surgery Theory offers a modern look at this important mathematical discipline and some of its applications. In this book...

Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations: (AMS-210) Jérémie Szeftel and Sergiu Klainerman

One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of...

Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208) Vadim Kaloshin and Ke Zhang

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...

What's Next?: The Mathematical Legacy of William P. Thurston (AMS-205) Edited by Dylan Thurston

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 areas of mathematics, from foliations, contact structures, and...

A Hierarchy of Turing Degrees: A Transfinite Hierarchy of Lowness Notions in the Computably Enumerable Degrees, Unifying Classes, and Natural Definability (AMS-206) Rod Downey and Noam Greenberg

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 in...

Berkeley Lectures on p-adic Geometry: (AMS-207) Peter Scholze and Jared Weinstein

Berkeley Lectures on p-adic 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...

Introductory Lectures on Equivariant Cohomology: (AMS-204) Loring W. Tu

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...

Eisenstein Cohomology for GL_N and the Special Values of Rankin–Selberg L-Functions: (AMS-203) Anantharam Raghuram and Günter Harder

This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions.

The authors study the cohomology of locally symmetric spaces for GL(N) where...

Arithmetic and Geometry: Ten Years in Alpbach (AMS-202) Edited by Gisbert Wüstholz and Clemens Fuchs

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...

The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, and Pierre-Louis Lions

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...

The Norm Residue Theorem in Motivic Cohomology: (AMS-200) Christian Haesemeyer and Charles A. Weibel

This book presents the complete proof of the Bloch-Kato 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...

Weil's Conjecture for Function Fields: Volume I (AMS-199) Dennis Gaitsgory and Jacob Lurie

A central concern of number theory is the study of local-to-global 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...

The Plaid Model: (AMS-198) Richard Evan Schwartz

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...

$The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures$ The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures: (AMS-197) Gui-Qiang G Chen and Mikhail Feldman

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

Asymptotic Differential Algebra and Model Theory of Transseries: (AMS-195) Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven

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...

Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time: (AMS-196) Philip Isett

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...

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) Isroil A. Ikromov and Detlef Müller

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

Algebraic Theory of Numbers. (AM-1), Volume 1 Hermann Weyl

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...

Scattering Theory for Automorphic Functions. (AM-87), Volume 87 Peter D. Lax and Ralph S. Phillips

The application by Fadeev and Pavlov of the Lax-Phillips 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...

Discontinuous Groups and Riemann Surfaces (AM-79), Volume 79: Proceedings of the 1973 Conference at the University of Maryland. (AM-79) Edited by Leon Greenberg

Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian...

Contributions to the Theory of Games (AM-24), Volume I Edited by Harold William Kuhn and Albert William Tucker

The description for this book, Contributions to the Theory of Games (AM-24), Volume I, will be forthcoming.

Introduction to Algebraic K-Theory. (AM-72), Volume 72 John Milnor

Algebraic K-theory 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...

Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67 Stephen S. Shatz

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 Calculi of Lambda Conversion. (AM-6), Volume 6 Alonzo Church

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

Advances in Game Theory. (AM-52), Volume 52 Edited by Melvin Dresher, Lloyd S. Shapley, and Albert William Tucker

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

Beijing Lectures in Harmonic Analysis. (AM-112), Volume 112 Edited by Elias M. Stein

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...

Convergence and Uniformity in Topology. (AM-2), Volume 2 John W. Tukey

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

An Introduction to Linear Transformations in Hilbert Space. (AM-4), Volume 4 Francis Joseph Murray

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

Topics in Topology. (AM-10), Volume 10 Solomon Lefschetz

Solomon Lefschetz pioneered the field of topology--the 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...

Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121 Victor Guillemin

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 light-like geodesics are periodic? A surprising fact is that such...

Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 Douglas C. Ravenel

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...

Complex Dynamics and Renormalization (AM-135), Volume 135 Curtis T. McMullen

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...

Automata Studies. (AM-34), Volume 34 Edited by C. E. Shannon and J. McCarthy

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

The Action Principle and Partial Differential Equations. (AM-146), Volume 146 Demetrios Christodoulou

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...

Functional Integration and Partial Differential Equations. (AM-109), Volume 109 Mark Iosifovich Freidlin

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...

Cohomology Operations (AM-50), Volume 50: Lectures by N.E. Steenrod. (AM-50) David B.A. Epstein

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

Normal Two-Dimensional Singularities. (AM-71), Volume 71 Henry B. Laufer

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

Characteristic Classes. (AM-76), Volume 76 John Milnor and James D. Stasheff

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...

Invariant Forms on Grassmann Manifolds. (AM-89), Volume 89 Wilhelm Stoll

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...

A Theory of Cross-Spaces. (AM-26), Volume 26 Robert Schatten

The description for this book, A Theory of Cross-Spaces. (AM-26), Volume 26, will be forthcoming.

Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57 Edited by Richard S. Palais

The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57, will be forthcoming.

Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116 Nicholas M. Katz

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...

Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 Walter Edwin Sewell

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

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) Herbert Busemann

The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.

The Two-Valued Iterative Systems of Mathematical Logic. (AM-5), Volume 5 Emil L. Post

The description for this book, The Two-Valued Iterative Systems of Mathematical Logic. (AM-5), Volume 5, will be forthcoming.

Exponential Sums and Differential Equations. (AM-124), Volume 124 Nicholas M. Katz

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...

Commensurabilities among Lattices in PU (1,n). (AM-132), Volume 132 Pierre Deligne and G. Daniel Mostow

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

Prospects in Topology (AM-138), Volume 138: Proceedings of a Conference in Honor of William Browder. (AM-138) Edited by Frank Quinn

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...

Contributions to the Theory of Nonlinear Oscillations (AM-45), Volume V Edited by Lamberto Cesari, J. LaSalle, and Solomon Lefschetz

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-45), Volume V, will be forthcoming.

Contributions to the Theory of Nonlinear Oscillations (AM-29), Volume II Solomon Lefschetz

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...

Recent Developments in Several Complex Variables. (AM-100), Volume 100 John Erik Fornaess

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

Radically Elementary Probability Theory. (AM-117), Volume 117 Edward Nelson

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...

Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 Mariano Giaquinta

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

Lectures on P-Adic L-Functions. (AM-74), Volume 74 Kinkichi Iwasawa

An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet.

Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 George Lusztig

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 Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 L. Boutet de Monvel and Victor Guillemin

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...

Seminar on Differential Geometry. (AM-102), Volume 102 Edited by Shing-Tung Yau

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

Lectures on Fourier Integrals. (AM-42), Volume 42 Salomon Bochner Trust
Translated by Morris Tenenbaum and Harry Pollard

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

Topology Seminar Wisconsin, 1965. (AM-60), Volume 60 Edited by R. H. Bing and Ralph J. Bean

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

Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III Solomon Lefschetz

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III, will be forthcoming.

Fourier Transforms. (AM-19), Volume 19 Salomon Bochner Trust and Komaravolu Chandrasekharan

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

Probleme General de la Stabilite du Mouvement. (AM-17), Volume 17 Alexandr Mikhailovich Liapounoff

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

Calculus on Heisenberg Manifolds. (AM-119), Volume 119 Richard Beals and Peter Charles Greiner

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

An Extension of Casson's Invariant. (AM-126), Volume 126 Kevin Walker

This book describes an invariant, l, of oriented rational homology 3-spheres 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...

Ramification Theoretic Methods in Algebraic Geometry (AM-43), Volume 43 Shreeram Shankar Abhyankar

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

Entire Holomorphic Mappings in One and Several Complex Variables. (AM-85), Volume 85 Phillip A. Griffiths

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.

Seminar on Transformation Groups. (AM-46), Volume 46 Armand Borel

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

Seminar on Micro-Local Analysis. (AM-93), Volume 93 Victor Guillemin, Masaki Kashiwara, and Takahiro Kawai

Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of...

Topics in Transcendental Algebraic Geometry. (AM-106), Volume 106 Edited by Phillip A. Griffiths

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

Lie Equations, Vol. I: General Theory. (AM-73) Antonio Kumpera and Donald Clayton Spencer

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...

Morse Theory. (AM-51), Volume 51 John Milnor

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....

Generalized Feynman Amplitudes. (AM-62), Volume 62 Eugene R. Speer

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...

Lectures on Differential Equations. (AM-14), Volume 14 Solomon Lefschetz

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

Flows on Homogeneous Spaces. (AM-53), Volume 53 Louis Auslander, F. Hahn, and L. Green

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

Differential Systems and Isometric Embeddings.(AM-114), Volume 114 Phillip A. Griffiths and Gary R. Jensen

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

Introduction to Mathematical Logic (PMS-13), Volume 13 Alonzo Church

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...

Introduction to Non-Linear Mechanics. (AM-11), Volume 11 Nikolai Mitrofanovich Krylov and Nikolai Nikolaevich Bogoliubov

The description for this book, Introduction to Non-Linear Mechanics. (AM-11), Volume 11, will be forthcoming.

Topological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15 Marston Morse

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

Harmonic Analysis in Phase Space. (AM-122), Volume 122 Gerald B. Folland

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...

The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 C. Bushnell and P. C. Kutzko

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 non-Archimedean local field F in terms of the structure of these representations when they...

Hyperfunctions on Hypo-Analytic Manifolds (AM-136), Volume 136 Paulo Cordaro and François Treves

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...

Composition Methods in Homotopy Groups of Spheres. (AM-49), Volume 49 Hiroshi Toda

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

K-Theory of Forms. (AM-98), Volume 98 Anthony Bak

The description for this book, K-Theory of Forms. (AM-98), Volume 98, will be forthcoming.

Stationary Processes and Prediction Theory. (AM-44), Volume 44 Harry Furstenberg

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

Smoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 Morris W. Hirsch and Barry Mazur

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...

Contributions to the Theory of Nonlinear Oscillations (AM-41), Volume IV Edited by Solomon Lefschetz

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-41), Volume IV, will be forthcoming.

Seminar On Minimal Submanifolds. (AM-103), Volume 103 Edited by Enrico Bombieri

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

Functional Operators (AM-21), Volume 1: Measures and Integrals. (AM-21) John von Neumann

Geometry of orthogonal spaces.

Contributions to the Theory of Games (AM-28), Volume II Edited by Harold William Kuhn and Albert William Tucker

Continuous Model Theory. (AM-58), Volume 58 Chen Chung Chang and H. Jerome Keisler

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

Contributions to the Theory of Games (AM-39), Volume III Melvin Dresher, Albert William Tucker, and Philip Wolfe

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....

Existence Theorems in Partial Differential Equations. (AM-23), Volume 23 Dorothy L. Bernstein

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

Order-Preserving Maps and Integration Processes. (AM-31), Volume 31 Edward J. McShane

The description for this book, Order-Preserving Maps and Integration Processes. (AM-31), Volume 31, will be forthcoming.

An Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18 Clifford Truesdell

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

Automorphic Representation of Unitary Groups in Three Variables. (AM-123), Volume 123 Jonathan David Rogawski

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...

Introduction to Toric Varieties. (AM-131), Volume 131 William Fulton

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...

Rigid Local Systems. (AM-139), Volume 139 Nicholas M. Katz

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)...

Elementary Differential Topology. (AM-54), Volume 54 James R. Munkres

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

The Neumann Problem for the Cauchy-Riemann Complex. (AM-75), Volume 75 Gerald B. Folland and Joseph John Kohn

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

Riemann Surfaces Related Topics (AM-97), Volume 97: Proceedings of the 1978 Stony Brook Conference. (AM-97) Edited by Irwin Kra and Bernard Maskit

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

On Knots. (AM-115), Volume 115 Louis H. Kauffman

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

Consistency of the Continuum Hypothesis. (AM-3), Volume 3 Kurt Gödel

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...

Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 Nicholas M. Katz and Barry Mazur

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...

On Group-Theoretic Decision Problems and Their Classification. (AM-68), Volume 68 Charles F. Miller III

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...

Degrees of Unsolvability. (AM-55), Volume 55 Gerald E. Sacks

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

Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 David Eisenbud and Walter D. Neumann

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

Theory of Formal Systems. (AM-47), Volume 47 Raymond M. Smullyan

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

Combinatorial Group Theory and Topology. (AM-111), Volume 111 Edited by S. M. Gersten and John R. Stallings

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...

Contributions to the Theory of Partial Differential Equations. (AM-33), Volume 33 Lipman Bers, Salomon Bochner Trust, and Fritz John

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

Functional Operators (AM-22), Volume 2: The Geometry of Orthogonal Spaces. (AM-22) John von Neumann

Measures and integrals

Surface Area. (AM-35), Volume 35 Lamberto Cesari

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

Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120 James Arthur and Laurent Clozel

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...

Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 Gerd Faltings

The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. 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...

An Introduction to G-Functions. (AM-133), Volume 133 Bernard Dwork, Giovanni Gerotto, and Francis J. Sullivan

Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series...

Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104 Eric M. Friedlander

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...

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 Robion C. Kirby and Laurence C. Siebenmann

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

Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91 Lars Hörmander

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 1977-1978. While some of the lectures were devoted to the analysis...

Lectures on Modular Forms. (AM-48), Volume 48 Robert C. Gunning

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...

Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 Joan S. Birman

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 low-dimensional topology.

Singular Points of Complex Hypersurfaces. (AM-61), Volume 61 John Milnor

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

Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63), Volume 63 Elias M. Stein

This work deals with an extension of the classical Littlewood-Paley 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...

Contributions to Fourier Analysis. (AM-25) Antoni Zygmund and W. Transue

The description for this book, Contributions to Fourier Analysis. (AM-25), will be forthcoming.

Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56 Lee Paul Neuwirth

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

Algebraic Topology and Algebraic K-Theory (AM-113), Volume 113: Proceedings of a Symposium in Honor of John C. Moore. (AM-113) Edited by William Browder

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,

Curvature and Betti Numbers. (AM-32), Volume 32 Salomon Bochner Trust and Kentaro Yano

The description for this book, Curvature and Betti Numbers. (AM-32), Volume 32, will be forthcoming.

Meromorphic Functions and Analytic Curves. (AM-12) Hermann Weyl

The description for this book, Meromorphic Functions and Analytic Curves. (AM-12), will be forthcoming.

Transcendental Numbers. (AM-16) Carl Ludwig Siegel

The description for this book, Transcendental Numbers. (AM-16), will be forthcoming.

C*-Algebra Extensions and K-Homology. (AM-95), Volume 95 Ronald G. Douglas

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...

Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130: Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems. (AM-130) James Eells and Andrea Ratto

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...

Modern Methods in Complex Analysis (AM-137), Volume 137: The Princeton Conference in Honor of Gunning and Kohn. (AM-137) Edited by Thomas Bloom, David W. Catlin, John P. D'Angelo, and Yum-Tong Siu

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

Contributions to the Theory of Nonlinear Oscillations (AM-20), Volume I Solomon Lefschetz

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-20), Volume I, will be forthcoming.

Knots, Groups and 3-Manifolds (AM-84), Volume 84: Papers Dedicated to the Memory of R.H. Fox. (AM-84) Lee Paul Neuwirth

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

Period Spaces for p-divisible Groups (AM-141), Volume 141 Michael Rapoport and Thomas Zink

In this monograph p-adic period domains are associated to arbitrary reductive groups. Using the concept of rigid-analytic period maps the relation of p-adic period domains to moduli space of p-divisible groups is investigated. In...

Automorphic Forms on Adele Groups. (AM-83), Volume 83 Stephen S. Gelbart

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...

Prospects in Mathematics. (AM-70), Volume 70 Friedrich Hirzebruch, Lars Hörmander, John Milnor, Jean-Pierre Serre, and I. M. Singer

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...

Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 George Lusztig

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...

Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 G. Daniel Mostow

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...

The Equidistribution Theory of Holomorphic Curves. (AM-64), Volume 64 Hung-his Wu

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

Linear Inequalities and Related Systems. (AM-38), Volume 38 Harold William Kuhn and Albert William Tucker

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

Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 David Mumford

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of...

Contributions to the Theory of Games (AM-40), Volume IV Edited by Albert William Tucker and Robert Duncan Luce

The description for this book, Contributions to the Theory of Games (AM-40), Volume IV, will be forthcoming.

Finite Dimensional Vector Spaces. (AM-7), Volume 7 Paul R. Halmos

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

Symposium on Infinite Dimensional Topology. (AM-69), Volume 69 R. D. Anderson

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...

Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118 David A. Vogan Jr.

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...

Combinatorics of Train Tracks. (AM-125), Volume 125 R. C. Penner and John L. Harer

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

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 Louis H. Kauffman and Sostenes Lins

This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the...

Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92 Ib Madsen and R. James Milgram

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...

Isoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27 G. Polya and G. Szegö

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

Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 Michael B. Marcus and Gilles Pisier

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 non-Abelian groups. They also obtain many related...

Non-Archimedean Tame Topology and Stably Dominated Types (AM-192) Ehud Hrushovski and François Loeser

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 p-adic Simpson Correspondence (AM-193) Ahmed Abbes, Michel Gros, and Takeshi Tsuji

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

Classification of Pseudo-reductive Groups (AM-191) Brian Conrad and Gopal Prasad

In the earlier monographPseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go...

Descent in Buildings (AM-190) Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss

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

Multi-parameter Singular Integrals. (AM-189), Volume I Brian Street

This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial...

The Real Fatou Conjecture. (AM-144), Volume 144 Jacek Graczyk and Grzegorz Swiatek

In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all 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...

Surveys on Surgery Theory (AM-149), Volume 2: Papers Dedicated to C.T.C. Wall. (AM-149) Edited by Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg

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...

Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 Christine Lescop

This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S
3. In Global Surgery Formula for the Casson-Walker Invariant, a function F...

Surveys on Surgery Theory (AM-145), Volume 1: Papers Dedicated to C. T. C. Wall. (AM-145) Edited by Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg

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...

Triangulated Categories. (AM-148), Volume 148 Amnon Neeman

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

Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142 Curtis T. McMullen

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 fixed-points for renormalization and...

Euler Systems. (AM-147), Volume 147 Karl Rubin

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 p-adic Galois representations....

Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) Christopher D. Sogge

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...

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187) Claire Voisin

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...

Spaces of PL Manifolds and Categories of Simple Maps (AM-186) Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory 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...

Degenerate Diffusion Operators Arising in Population Biology (AM-185) Charles L. Epstein and Rafe Mazzeo

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...

The Gross-Zagier Formula on Shimura Curves: (AMS-184) Xinyi Yuan, Shou-wu Zhang, and Wei Zhang

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

The Decomposition of Global Conformal Invariants (AM-182) Spyros Alexakis

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...

Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183) Mark Green, Phillip A. Griffiths, and Matt Kerr

Mumford-Tate 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 Mumford-Tate groups and...

Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181) Umberto Zannier

This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book...

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179) Joram Lindenstrauss, David Preiss, and Jaroslav Tišer

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: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) Nicholas M. Katz

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

The Ambient Metric (AM-178) Charles Fefferman and C. Robin Graham

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...

Cycles, Transfers, and Motivic Homology Theories. (AM-143), Volume 143 Vladimir Voevodsky, Andrei Suslin, and Eric M. Friedlander

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...

Hypoelliptic Laplacian and Orbital Integrals (AM-177) Jean-Michel Bismut

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: Type A Combinatorial Theory (AM-175) Ben Brubaker, Daniel Bump, and Solomon Friedberg

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...

Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176) Edited by Bas Edixhoven and Jean-Marc Couveignes

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 tau-function as a typical example, have deep...

Dynamics in One Complex Variable. (AM-160): (AM-160) - Third Edition John Milnor

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...

Introduction to Ramsey Spaces (AM-174) Stevo Todorcevic

Ramsey theory is a fast-growing 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 Ramsey-type...

On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) Sophie Morel

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 on Kites (AM-171) Richard Evan Schwartz

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 so-called...

The Ergodic Theory of Lattice Subgroups (AM-172) Alexander Gorodnik and Amos Nevo

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 Topos Theory (AM-170) Jacob Lurie

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

Lectures on the Theory of Games (AM-37) Harold William Kuhn

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...

Mathematical Aspects of Nonlinear Dispersive Equations (AM-163) Edited by Jean Bourgain, Carlos E. Kenig, and Sergiu Klainerman

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...

Twisted L-Functions and Monodromy. (AM-150), Volume 150 Nicholas M. Katz

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 Taylor-Wiles in...

Lectures on Resolution of Singularities (AM-166) János Kollár

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...

Radon Transforms and the Rigidity of the Grassmannians (AM-156) Jacques Gasqui and Hubert Goldschmidt

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...

Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) Kazuya Kato and Sampei Usui

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....

The Structure of Affine Buildings. (AM-168) Richard M. Weiss

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

The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167) Jean-Michel Bismut and Gilles Lebeau

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

Spherical CR Geometry and Dehn Surgery (AM-165) Richard Evan Schwartz

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...

Discrete Orthogonal Polynomials. (AM-164): Asymptotics and Applications (AM-164) J. Baik, T. Kriecherbauer, Kenneth D.T-R McLaughlin, and Peter D. Miller

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

Integration of One-forms on P-adic Analytic Spaces. (AM-162) Vladimir G. Berkovich

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily...

Modular Forms and Special Cycles on Shimura Curves. (AM-161) Stephen S. Kudla, Michael Rapoport, and Tonghai Yang

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

Moments, Monodromy, and Perversity. (AM-159): A Diophantine Perspective. (AM-159) Nicholas M. Katz

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" algebro-geometric families of character sums...

On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) Mark Green and Phillip A. Griffiths

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

Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) Jean Bourgain

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

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154) Spyridon Kamvissis, Kenneth D.T-R McLaughlin, and Peter D. Miller

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...

Markov Processes from K. Itô's Perspective (AM-155) Daniel W. Stroock

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

Finite Structures with Few Types. (AM-152), Volume 152 Gregory Cherlin and Ehud Hrushovski

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 4-tuples. Primitive permutation groups of...

The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151), Volume 151 Michael Harris and Richard Taylor

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

Infinite Loop Spaces (AM-90), Volume 90: Hermann Weyl Lectures, The Institute for Advanced Study. (AM-90) John Frank Adams

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...

Advances in the Theory of Riemann Surfaces. (AM-66), Volume 66 Lars Valerian Ahlfors and Lipman Bers

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.

Contributions to the Theory of Riemann Surfaces. (AM-30), Volume 30 Edited by Lars Valerian Ahlfors, E. Calabi, Marston Morse, Leo Sario, and Donald Clayton Spencer

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