This volume is a unique and comprehensive collection of works by some of the world's leading researchers. Papers on algebraic geometry, algebraic groups, and Lie groups are woven together to form a connection between the study of symmetry and certain algebraic structures. This connection reflects the interests of R. W. Richardson who studied the links between representation theory and the structure and geometry of algebraic groups. In particular, the papers address Kazhdan-Lusztig theory, quantum groups, spherical varieties, symmetric varieties, cohomology of varieties, purity, Schubert...

This book brings together a selection of the best lectures from many graduate workshops held at the Australian National Institute for Theoretical Physics in Adelaide. The lectures presented here describe subjects currently of great interest, generally at the interface between mathematics and physics, and also where suitable expositions did not previously exist at a level suitable for graduate students. Topics covered include quantum groups, the operator algebra approach to the integer quantum Hall effect, solvable lattice models and Hecke algebras, Yangevins, equivariant cohomology and...

This book presents the foundations of Euclidean geometry from the point of view of mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here, real affine space is characterized by a small number of axioms involving points and line segments making the treatment self-contained and thorough. This treatment is accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and...

This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces...

Here is a concise and accessible exposition of a wide range of topics in geometric approaches to differential equations. The authors present an overview of this developing subject and introduce a number of related topics, including twistor theory, vortex filament dynamics, calculus of variations, exterior differential systems and Backlund transformations. The book is an ideal starting point for graduate students embarking on research.

This book presents a new homological approximation theory in the category of equivariant modules, unifying the Cohen-Macaulay approximations in commutative ring theory and Ringel's theory of Delta-good approximations for quasi-hereditary algebras and reductive groups. The book provides a detailed introduction to homological algebra, commutative ring theory and homological theory of comodules of coalgebras over an arbitrary base. It aims to overcome the difficulty of generalizing known homological results in representation theory.

This book provides an easy introduction to the theory of differentiable manifolds.