Bücher der Reihe Mathematical Sciences Research Institute Publications

Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. In this book, originally published in 2000, leading experts provide the necessary background to understanding the model theory and mathematics behind these applications.

When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations". A seminar was organized whose audience consisted of graduate students of the University and mature mathematicians who are not experts in the field. This volume contains 18 of these lectures. An effort is made to have an adequate Bibliography for further information. The Editor wishes to take this opportunity to thank all the speakers and the authors of the articles presented in this volume for their cooperation. S. S. Chern, Editor Table of Contents Geometrical and Analytical Questions Stuart S. Antman 1 in Nonlinear Elasticity An Introduction to Euler's Equations Alexandre J. Chorin 31 for an Incompressible Fluid Linearizing Flows and a Cohomology Phillip Griffiths 37 Interpretation of Lax Equations The Ricci Curvature Equation Richard Hamilton 47 A Walk Through Partial Differential Fritz John 73 Equations Remarks on Zero Viscosity Limit for Tosio Kato 85 Nonstationary Navier-Stokes Flows with Boundary Free Boundary Problems in Mechanics Joseph B. Keller 99 The Method of Partial Regularity as Robert V.

This book considers a branch of Riemannian geometry called Comparison Geometry. Comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has recently received great attention. This is an up-to-date reflection of developments in this field.

The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups.

This comprehensive introduction for beginning graduate students contains articles by the leading experts in the field. It covers basic topics such as algorithmic aspects of number fields, elliptic curves, and lattice basis reduction and advanced topics including cryptography, computational class field theory, zeta functions and L-series, and quantum computing.

A collection of thirteen articles by many of the leading contributors in the field on the history of the Gross-Zagier formula and its developments. It touches on the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula.

This 1999 book is a collection of research and expository articles on convex geometry and probability, suitable for researchers and graduate students in several branches of mathematics coming under the broad heading of 'Geometric Functional Analysis'. It arises arises from an MSRI program held in the spring of 1996.

Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.

In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications. The main areas of concentration were homotopy theory, K-theory, and applications to geometric topology, gauge theory, and moduli spaces.

Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. In this book, originally published in 2000, leading experts provide the necessary background to understanding the model theory and mathematics behind these applications.

This book contains eight expository articles by well-known authors on the theory of Galois groups and fundamental groups, focusing on developments in the field. Among the subjects covered are elliptic surfaces, Grothendieck's anabelian conjecture, fundamental groups of curves and differential Galois theory in positive characteristic.

In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms.

This book presents expository accounts of six important topics in Finsler geometry suitable for a special-topics graduate course in differential geometry. They treat issues related to volume, geodesics, curvature and mathematical biology, and provide a good variety of instructive examples.

This book is based on lectures by six internationally known experts presented at the 2002 MSRI introductory workshop on commutative algebra. These focus on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics.

Covering the mathematical basis of signal processing and many areas of application, this book is based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute. Emphasis is on challenges in the subject, particular techniques adapted to particular technologies, and certain advances in algorithms and theory.

This 1999 book is a collection of research and expository articles on convex geometry and probability, suitable for researchers and graduate students in several branches of mathematics coming under the broad heading of 'Geometric Functional Analysis'. It arises arises from an MSRI program held in the spring of 1996.

This fascinating 2003 collection of articles runs the gamut from new theoretical approaches, both computational and mathematical, to other games such as Amazons, Chomp, Dot-and-Boxes, Go, Chess, and Hex. Includes an updated bibliography by A. Fraenkel and a list of combinatorial game theory problems by R. K. Guy.

First published in 2000, this book provides a clear and complete picture of research in Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry. The expository nature of the articles makes this an excellent introduction for students as well as a basis for continuing research.

The 1992/3 academic year at the Mathematical Sciences Research Institute was devoted to Complex Algebraic Geometry. This 1996 volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change.

A collection of thirteen articles by many of the leading contributors in the field on the history of the Gross-Zagier formula and its developments. It touches on the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula.

This book contains expository contributions by respected researchers on the rich combinatorial problems arising from the study of algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. It will continue to be of use to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.

This book consists of lectures that are part of the distinguished series of MSRI workshops and contains contributions by six different authors providing mathematics students and researchers with a bridge - or a window - into a portion of the intriguing world of theoretical physics, especially that which centers around Einstein gravitation and quantum field theory.

This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values.

These articles form a broad survey of this exciting field. Topics include pointed Hopf algebras, triangular Hopf algebras, Hopf algebra extensions and cohomology, quantum groups and groupoids, quantum symmetric pairs, monoidal categories, and the Brauer group of a Hopf algebra.

This 2005 volume, covering a broad range of topics, is an outgrowth of the synergism of Discrete and Computational Geometry. Its surveys and research articles explore geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms, and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension.

This book presents expository accounts of six important topics in Finsler geometry suitable for a special-topics graduate course in differential geometry. They treat issues related to volume, geodesics, curvature and mathematical biology, and provide a good variety of instructive examples.

Covering the mathematical basis of signal processing and many areas of application, this book is based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute. Emphasis is on challenges in the subject, particular techniques adapted to particular technologies, and certain advances in algorithms and theory.

In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms.

This book considers a branch of Riemannian geometry called Comparison Geometry. Comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has recently received great attention. This is an up-to-date reflection of developments in this field.

Surveys and research articles based on a 2004 MRSI research workshop, plus a commented problem list by leading experts cover several areas of dynamical systems that have recently experienced substantial progress, including symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory.