**BILKENT **

**FUSION SYSTEMS
SEMINAR**

**"A Gentle Introduction to Fusion Systems"**

By

# MATTHEW GELVIN

# (Bilkent University)

** **

**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**

**Time: ****15.40**

**Place: ****Mathematics Seminar Room,
SA-141**

** **

**All are most cordially invited.**

Tea and biscuits: before the seminar