Bøger i Mathematical Sciences Research Institute Publications serien

In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u).

In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u).

The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution.

Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups.

We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects.

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.

During late June and early July of 1987 a three week program (dubbed "microprogram") in Commutative Algebra was held at the Mathematical Sciences Research Institute at Berkeley.

During the week of September 13, 1988 the Mathematical Sciences Research Institute hosted a four day workshop on Arboreal Group Theory. Topics include the theory of length functions, structure of groups acting freely on trees, spaces of hyperbolic structures and their compactifications, and moduli for tree actions.

The volume is the outgrowth of a workshop with the same title held at MSRI in the week of November 13-17, 1989, and for those who did not get it, Logic from Computer Science is the converse of Logic in Computer Science, the full name of the highly successful annual LICS conferences.

This volume, based on a workshop by the MSRI and addressed to both beginners and experts, offers an expository overview of the state of the art in many areas of algebraic geometry. Many chapters present approaches to long-standing open problems by means of modern techniques currently under development and contain questions and conjectures to help spur future research.

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.

The three main themes of this book reflect the range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the papers here demonstrate a variety of techniques for solving problems, often outside of the standard methods.

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.

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.

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.

Appearance of singularities is pervasive in many problems in topology, differential geometry and algebraic geometry. This book concerns the study of singular spaces using techniques from a variety of areas of geometry and topology and the interactions among them.

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 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.

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.

The three main themes of this book reflect the range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the papers here demonstrate a variety of techniques for solving problems, often outside of the standard methods.

First published in 2000, this expository volume of surveys and research results covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.

This 1997 book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The first paper is an unfinished but insightful survey of the field of tight immersions and maps by Nicolaas H. Kuiper.

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.