Surveys and summaries of latest research in numerical analysis, optimization, computer algebra and scientific computing.

The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.

A graduate-level account of an important recent result concerning the Riemann zeta function.

This book contains surveys of recent important developments in combinatorics covering a wide range of areas in the field.

Leading researchers survey the latest developments in group theory and many related areas.

A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.

A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.

Review papers from experts in areas of active research into highly oscillatory problems, with an emphasis on computation.

This book brings the researcher up to date with recent applications of mathematical logic to number theory.

Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.