"A Gentle Introduction to Fusion Systems"
Abstract: Fusion systems are an encoding of the p-local structure of a finite group. In this talk we will introduce the basic notions of fusion systems and give motivation for why their study is important in the context of finite group theory and algebraic topology. We will discuss Alperin's fusion theorem, which says that finite groups exhibit certain "local-to-global" structure. This in turn will lead to Puig's notion of an abstract fusion system, which we can think of as the p-local data of a group with the group stripped away. These abstract fusion systems will be one of our fundamental objects of study for the semester. At the end, I would like discuss the Martino-Priddy conjecture, which says that there is a direct link between the algebra of fusion systems and the topology of classifying spaces of finite groups. This will require introducing the notion of a linking system, a sort of rigidified version of the fusion system on which it is based. This final section will also serve as a a preview of some interesting topics to come.
Date: Tuesday, October 6, 2015
Place: Mathematics Seminar Room, SA-141
All are most cordially invited.
Tea and biscuits: before the seminar