During the last decade the theory of fusion systems has evolved into an active area of mathematics of interest in at least three more established areas. The standard examples of fusion systems come from finite groups, but there are also exotic systems, realized in no finite group, playing a role in the theory akin to that of the sporadic groups in finite group theory.

The workshop will explore the role of fusion systems in algebraic topology, modular representation theory, and the local theory of finite groups. Aschbacher will describe a program in progress to classify most simple saturated 2-fusion systems of component type, and indicate why such a result should lead to a simplification in the proof of the theorem classifying the finite simple groups.