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As the title indicates, the content of these notes is a lengthy construction of techniques devised to study specific differential geometric problems. In this introduction we state our main objectives and illustrate by examples some of their geometric implications.

(Paperback)

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

(Paperback)

Offers an account of Kiyosi Ito's program. This book offers an account of integral curves on the space of probability measures. It provides a systematic development of Ito's theory of stochastic integration: first for Brownian motion and then for continuous martingales.

(Paperback)

A collection of papers on mathematical aspects of nonlinear dispersive equations, including both expository and technical papers that reflect a number of advances in the field. The expository papers describe the state of the art and research directions. The technical papers concentrate on a specific problem and the related analysis.

(Paperback)

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

(Paperback)

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

(Paperback)

Includes fifteen articles which focus on the developments in complex analysis. This work covers a spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. It covers topics that include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, and more.

(Paperback)

A 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 field of rational numbers.

(Paperback)

Develops techniques based on two ingredients: the theory of perverse sheaves and Larsen's Alternative. These techniques are then used to calculate the geometric monodromy groups attached to some specific universal families of (L-functions attached to) character sums over finite fields.

(Paperback)

One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. This book offers an exposition of Morse theory by John Milnor, recipient of the Fields Medal in 1962.

(Paperback)

This book develops a new theory of multi-parameter singular integrals associated with Carnot-Caratheodory balls. Brian Street first details the classical theory of Calderon-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Caratheodory geometry, where the main

(Paperback)

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

(Paperback)

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 provides a comprehensive exploration of Mumford-Tate groups and domains.

(Hardback)

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 provides a comprehensive exploration of Mumford-Tate groups and domains.

(Paperback)

Describes some major advances made in algebraic topology, centering on the nilpotence and periodicity theorems. This book begins with some elementary concepts of homotopy theory that are needed to state the problem. The latter portion provides specialists with a coherent and rigorous account of the proofs.

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Studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. The author also uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula.

(Paperback)

Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups.

(Paperback)

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

(Paperback)

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 Moser-Neumann question has been one of the central problems in the field. This title offers solution to the problem.

(Paperback)

A monograph that associates p-adic period domains to arbitrary reductive groups. Using the concept of rigid-analytic period maps, it investigates the relation of p-adic period domains to moduli space of p-divisible groups. It also establishes non-archimedean uniformization theorems for general Shimura varieties.

(Paperback)

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