This collection of survey articles and research papers focuses on some of the most fruitful methods and ideas in the recently very active field of complex differential geometry and nonlinear differential equations. The topics found in this 1984 Summer Research Conference Proceedings include the local embedding of Cauchy-Riemann structures, minimal varieties, harmonic maps, Chern number inequalities for singular Kahler surfaces, the spectrum of the Laplacian for Kahler manifolds, foliations, vanishing theorems, and complex Finsler metrics. Papers of particular note include Mok's survey on foliation techniques and vanishing theorems, a succinct account of one of the most important methods in several complex variables which has recently produced some very good results, and the research articles by Cheng-Yau and Sampson, which contain highly significant new results. Both researchers and graduate students in the fields of several complex variables, differential geometry, and partial differential equations will find this material especially useful.

Complex Differential Geometry and Nonlinear Differential Equations: Proceedings of the Ams-Ims-Siam Joint Summer Research Conference, Held August ... Science Foundation (Contemporary Mathematics)

Science & Math

Society for Industrial and Applied Mathematics

Institute of Mathematical Statistics

Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie

American Mathematical Society

Mathematics

Amer Mathematical Society

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Graphs and Algorithms, held in 1987 at the University of Colorado in Boulder. The purpose of the conference was to foster communication between computer scientists and mathematicians, for recent work in graph theory and related algorithms has relied on increasingly sophisticated mathematics. Wagner's Conjecture, self-adjusting data structures, graph isomorphism, and various embedding and labelling problems in VLSI are examples of the kinds of questions now facing the field. With around 65 participants, the conference brought out the depth and diversity of current research in this area. The wide range of topics covered in this volume demonstrates the vitality of the activity in both mathematics and computer science and captures the diversity and excitement of the conference.

Graphs and Algorithms: Proceedings of the Ams-Ims Siam Joint Summer Research Conference Held June 28-July 4, 1987 With Support from the National Sci (Contemporary Mathematics, 89)

Computers & Technology

Graphics & Design

Category theory has had important uses in logic since the invention of topos theory in the early 1960s, and logic has always been an important component of theoretical computer science. A new development has been the increase in direct interactions between category theory and computer science. In June 1987, an AMS-IMS-SIAM Summer Research Conference on Categories in Computer Science and Logic was held at the University of Colorado in Boulder. The aim of the conference was to bring together researchers working on the interconnections between category theory and computer science or between computer science and logic. The conference emphasized the ways in which the general machinery developed in category theory could be applied to specific questions and be used for category-theoretic studies of concrete problems. This volume represents the proceedings of the conference. (Some of the participants' contributions have been published elsewhere.) The papers published here relate to three different aspects of the conference. The first concerns topics relevant to all three fields, including, for example, Horn logic, lambda calculus, normal form reductions, algebraic theories, and categorical models for computability theory. In the area of logic, topics include semantical approaches to proof-theoretical questions, internal properties of specific objects in (pre-) topoi and their representations, and categorical sharpening of model-theoretic notions. Finally, in the area of computer science, the use of category theory in formalizing aspects of computer programming and program design is discussed.

Categories in Computer Science and Logic: Proceedings of the Ams-Ims-Siam Joint Summer Research Conference Held June 14-20, 1987 With Support from T (Contemporary Mathematics, 92)

Gray, John W.

National Science Foundation

The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold--that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.

The Connection Between Infinite Dimensional and Finite Dimensional Dynamical Systems: Proceedings of the Ams-Ims-Siam Joint Summer Research Conferen (Contemporary Mathematics)

Foias, Ciprian

Nicolaenko, Basil

The study of Riemann problems has undergone a strong, steady growth in the last decade. The general direction of the research has headed toward understanding the wave structure of the solutions of more physically realistic systems. These systems fail either or both of the two main restrictions of the classical theory---that the system be strictly hyperbolic or genuinely nonlinear. The systems that have been studied tend to fall into the following broad classes: real gas dynamics (including combustion), visco-elastic materials, phase transitions, and multiphase flow in porous media. In addition to their usefulness in large-scale calculations, computational schemes have vastly improved the handling of discontinuity behavior. 
This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Current Progress in Hyperbolic Systems: Riemann Problems and Computations, held at Bowdoin College in July 1988. The papers presented here provide a complete picture of recent research by some of the leaders in this field. Graduate students and beginning researchers will find this book a useful introduction to current work in this area.

Current Progress in Hyperbolic Systems: Riemann Problems and Computations : Proceedings (Contemporary Mathematics)

Lindquist, W. Brent

Classical field theory has undergone a renaissance in recent years. Symplectic techniques have yielded deep insights into its foundations, as has an improved understanding of the variational calculus. Further impetus for the study of classical fields has come from other areas, such as integrable systems, Poisson geometry, global analysis, and quantum theory. This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory, held in July 1991 at the University of Washington at Seattle. The conference brought together researchers in many of the main areas of classical field theory to present the latest ideas and results. The volume contains thirty refereed papers, both survey and research articles, and is designed to reflect the state of the art as well as chart the future course of the subject.

Mathematical Aspects of Classical Field Theory: Proceedings of the Ams-Ims-Siam Joint Summer Research Conference Held July 20-26, 1991, With Support ... Mathematics (American Mathematical Society),)

MARSDEN, Jerrold E.

Moncrief, Vincent

Gotay, Mark J.

Physics

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