Abstract: For a finite (simple) group G, the normalizers of its nonidentity p-subgroups generally constitute the largest of its (proper) subgroups that can be predicted to exist having knowledge of the order of G alone. So perhaps it is no surprise that, historically, these so-called "p-local subgroups" and the concomitant "p-local analysis" of them have played an important role in investigations of the structure of finite groups. A modern setting for p-local analysis is the category of p-fusion systems. I'll explain what a fusion system is, revisit some classical p-local-to-global theorems in finite groups, and describe some of the quite beautiful connections between fusion systems, cohomology, and the homotopy theory of classifying spaces.

(Reception to precede at 3:30 p.m.)