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Selected Works of Phillip A. Griffiths with Commentary: Differential Systems
Edited by: Robert L. Bryant and David R. Morrison, Duke University, Durham, NC
A co-publication of the AMS and International Press.
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Collected Works
2003; 598 pp; hardcover
Volume: 18
ISBN-10: 0-8218-2089-3
ISBN-13: 978-0-8218-2089-6
List Price: US$109
Member Price: US$87.20
Order Code: CWORKS/18.4
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This item is also sold as part of the following set: CWORKS/18

Over the last four decades, Phillip Griffiths has been a central figure in mathematics. During this time, he made crucial contributions in several fields, including complex analysis, algebraic geometry, and differential systems. His books and papers are distinguished by a remarkably lucid style that invites the reader to understand not only the subject at hand, but also the connections among seemingly unrelated areas of mathematics. Even today, many of Griffiths' papers are used as a standard source on a subject. Another important feature of Griffiths' writings is that they often bring together classical and modern mathematics.

The four parts of Selected Works--Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems--are organized according to the subject matter and are supplemented by Griffiths' brief, but extremely illuminating, personal reflections on the mathematical content and the times in which they were produced.

Griffiths' Selected Works provide the reader with a panoramic view of important and exciting mathematics during the second half of the 20th century.

This book is jointly published by the AMS and the International Press.

Table of Contents

Part 4. Differential Systems
  • Introductory comments to part 4
Moving frames and differential geometry
  • On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry
Differential systems and Hodge structure
  • Poincaré and algebraic geometry
  • Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle
  • Reduction for constrained variational problems and \(\int\frac{1}{2} \kappa^2 ds\)
Integrability
  • Linearizing flows and a cohomological interpretation of Lax equations
The characteristic variety and its geometry
  • Some aspects of exterior differential systems
  • Characteristic cohomology of differential systems (I): General theory
  • Characteristic cohomology of differential systems II: conservation laws for a class of parabolic equations
  • Hyperbolic exterior differential systems and their conservation laws, Part I
  • Hyperbolic exterior differential systems and their conservation laws, Part II
  • Acknowledgments
  • Selected Titles
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