Squares
Squares

Author: A. R. Rajwade

Publisher: Cambridge University Press

Published: 1993-10-14

Total Pages: 302

ISBN-13: 0521426685

DOWNLOAD EBOOK

Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works of Pfister, Hilbert, Hurwitz and others are easily accessible to non-experts and undergraduates alike. The author deals with many different approaches to the study of squares; from the classical works of the late 19th century, to areas of current research. Anyone with an interest in algebra or number theory will find this a most fascinating volume.

Introduction to Subfactors
Introduction to Subfactors

Author: Vaughan F. R. Jones

Publisher: Cambridge University Press

Published: 1997-05-15

Total Pages: 178

ISBN-13: 0521584205

DOWNLOAD EBOOK

Subfactors have been a subject of considerable research activity for about 15 years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. A new pictorial approach to subfactors is presented in a late ch apter.

The Descriptive Set Theory of Polish Group Actions
The Descriptive Set Theory of Polish Group Actions

Author: Howard Becker

Publisher: Cambridge University Press

Published: 1996-12-05

Total Pages: 152

ISBN-13: 0521576059

DOWNLOAD EBOOK

In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces.

Double Affine Hecke Algebras
Double Affine Hecke Algebras

Author: Ivan Cherednik

Publisher: Cambridge University Press

Published: 2005-03-21

Total Pages: 449

ISBN-13: 0521609186

DOWNLOAD EBOOK

This is an essentially self-contained monograph centered on the new double Hecke algebra technique.

Groups St Andrews 2001 in Oxford: Volume 1
Groups St Andrews 2001 in Oxford: Volume 1

Author: C. M. Campbell

Publisher: Cambridge University Press

Published: 2003-11-06

Total Pages: 316

ISBN-13: 9781139437219

DOWNLOAD EBOOK

This first volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions from Marston Conder (Auckland), Persi Diaconis (Stanford) and Marcus Du Sautoy (Cambridge). The series of Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past twenty years. As with earlier volumes, these refereed volumes also contain accessible surveys of contemporary research fronts, as well as a diverse collection of short research articles. They form a valuable reference for researchers, especially graduate students, working in group theory.

Around Grothendieck's Esquisse D'un Programme
Around Grothendieck's Esquisse D'un Programme

Author: Leila Schneps

Publisher: Cambridge University Press

Published: 1997-07-10

Total Pages: 308

ISBN-13: 9780521596428

DOWNLOAD EBOOK

The first of two companion volumes on anabelian algebraic geometry, this book contains the famous, but hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. This work, written in 1984, fourteen years after his retirement from public life in mathematics, together with the closely connected letter to Gerd Faltings, dating from 1983 and also published for the first time in this volume, describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves; it is written in an artistic and informal style. The book also contains several articles on subjects directly related to the ideas explored in the manuscripts; these are surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.