Based on courses held at the Feza GUrsey Institute, this collection of survey articles introduces advanced graduate students to an exciting area on the border of mathematics and mathematical physics. Including articles by key names such as Calogero, Donagi and Mason, it features the algebro-geometric material from Donagi as well as the twistor space methods in Woodhouse's contribution, forming a bridge between the pure mathematics and the more physical approaches.

This introduction to the conformal differential geometry of surfaces and submanifolds covers those aspects of the geometry of surfaces that only refer to an angle measurement, but not to a length measurement. Different methods (models) are presented for analysis and computation. Various applications to areas of current research are discussed, including discrete net theory and certain relations between differential geometry and integrable systems theory.

This two-volume set contains selected papers from the conference Groups St. Andrews 2001 in Oxford. Contributed by leading researchers, the articles cover a wide spectrum of modern group theory. Contributions based on lecture courses given by five main speakers are included with refereed survey and research articles.

This two-volume set contains selected papers from the conference Groups St. Andrews 2001 in Oxford. Contributed by leading researchers, the articles cover a wide spectrum of modern group theory. Contributions based on lecture courses given by five main speakers are included with refereed survey and research articles. The Groups St. Andrews proceedings volumes represent a view of the state of the art in group theory and often play an important role in future developments in the subject.

This volume covers the proceedings of an international conference held in Oxford in June 2002. In addition to articles arising from the conference, the book also contains the famous as-yet-unpublished article by Graeme Segal on the Definition of Conformal Field Theories. It is ideal as a view of the current state of the art and will appeal to established researchers as well as to novice graduate students.

This collection of articles from the Independent University of Moscow is derived from the Globus seminars held there. They are given by world authorities, from Russia and elsewhere, in various areas of mathematics and are designed to introduce graduate students to some of the most dynamic areas of mathematical research. The seminars aim to be informal, wide-ranging and forward-looking, getting across the ideas and concepts rather than formal proofs, and this carries over to the articles here. Topics covered range from computational complexity, algebraic geometry, dynamics, through to number...

Classical string theory is concerned with the propagation of classical one-dimensional curves, i.e. "strings," and has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac-Moody and Virasoro algebras has been used for such quantization. In this book, the authors give an introduction to global analytic and probabilistic aspects of string theory, bringing together and making explicit the necessary mathematical tools....

The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book provide a picture of current ideas and methods in the ongoing investigations into the structure of the computable and noncomputable universe. A number of the articles contain introductory and background material that will make the volume an invaluable resource for mathematicians and computer scientists.

This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and...

This volume discusses the whole spectrum of number theory with many contributions from some of the world's leading figures. Contributors cover the very latest research developments and much of the work presented here will not be found elsewhere. Also included are surveys that will guide the reader through the extensive published literature. This text will be a necessary addition to the libraries of all workers in number theory.