Finite Simple Groups: Thirty Years of the Atlas and Beyond

点击翻译按钮获取中文摘要

This award supports participation in the conference "Finite Simple Groups: Thirty Years of the Atlas and Beyond" taking place November 2-5, 2015, at Princeton University in Princeton, NJ. The concept of a group in mathematics grew out of the notion of symmetry. The symmetries of an object in nature or science are encoded by a group, and this group carries important information about the structure of the object itself. Group theory has had many important applications in physics and chemistry, particularly in quantum mechanics and in the theory of elementary particles. The main theme of the conference will be the interaction between theory and computation, and applications of group theory to other areas of mathematics. The list of invited participants features senior and junior researchers from across these fields and thus will foster further interaction and collaboration between them, during and after the conference. Conference activities will include informal working groups organized by experts in the field to discuss current and future research directions during the conference; a poster session; a webpage; and a wiki. The proceedings of the conference will be published.The classification of finite simple groups, one of the most monumental accomplishments of the modern mathematics, was announced to be completed in 1983. Since then, it has opened up a new and powerful strategy to approach and resolve many, previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy utilizes information about finite simple groups, some of which is catalogued in the "Atlas of Finite Groups" and "An Atlas of Brauer Characters." It is impossible to overestimate the roles of the atlases and the related computer algebra systems in everyday life of researchers in many areas of contemporary mathematics. The conference will bring together a diverse group of researchers in group theory, representation theory, and computational group theory. The objective of the conference is to discuss numerous applications of the Atlases and to explore recent developments and future directions of research.