The theory of graph colouring has existed for more than 150 years. Historically, graph colouring involved finding the minimum number of colours to be assigned to the vertices so that adjacent vertices would have different colours. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications.

The nature of C ]*-algebras is such that one cannot study perturbation without also studying the theory of lifting and the theory of extenstions. Approximation questions involving representations of relations in matrices and C ]*-algebras are the central focus of this volume. A variety of approximation techniques are unified by translating them into lifting problems: from classical questions about transivity of algebras of operators on Hilbert spaces to recent results in linear algebra. One chapter is devoted to Lin's theorem on approximating almost normal matrices by normal matrices. The...

This volume describes in monograph form important applications in numerical methods of linear algebra. The author presents material and extended results from recent papers in a readable style. The main goal of the book is to study the behaviour of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essentially unchanged. This has...

Model theoretic algebra has witnessed remarkable progress in the 1990s. It has found profound applications in other areas of mathematics, notably in algebraic geometry and in singularity theory. Since Wilkie's results on the o-minimality of the expansion of the reals by the exponential function, and most recently even by all Pfaffian functions, the study of o-minimal expansions of the reals has become an increasingly interesting topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a direction to this research.

Discusses the connection between Calabi-Yau threefolds and modular forms. This title presents the general theory and brings together the known results. It features hundreds of examples of rigid and non-rigid Calabi-Yau threefolds, and the construction of c

A monograph that is concerned with Galois theoretical embedding problems of so-called Brauer type with a focus on 2-groups and on finding explicit criteria for solvability and explicit constructions of the solutions. It also considers questions of reducing

This is a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.

Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.

Model theory has had remarkable success in solving important problems as well as in shedding new light on our understanding of them. The three lectures collected here present recent developments in three such areas: Anand Pillay on differential fields, Patrick Speissegger on o-minimality and Matthias Clasen and Matthew Valeriote on time congruence theory.

This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of C*-algebras and von Neumann algebras, together with recent work on the classification of C*-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.