Michael Aschbacher : Fusion systems and simple groups

Posted by Alexey Cheskidov , part of the Departmental Colloquium.

At

Sept. 9, 2011, 3 p.m.

In

SEO 636

Abstract

Fusion systems were introduced by Luis Puig as a tool in modular representation theory. Later homotopy theorists became interested in the work; in particular Broto, Levi, and Oliver defined the notion of a p-local finite group (consisting of a saturated fusion system and a linking system), and Levi and Oliver proved the existence of the exotic Solomon-Benson 2-local finite groups, which in some ways are analogous to sporadic finite simple groups. Most of the talk will consist of an introduction to fusion systems, with technicalities suppressed whenever possible. Near the end of the talk, I'll speculate about the possibility of simplifying the proof of the classification of the finite simple groups using fusion systems.