**BILKENT **

**FUSION
SYSTEMS SEMINAR**

**"Categories Associated to Fusion Systems"**

By

# MATTHEW GELVIN

# (Bilkent University)

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** **

**Abstract: **This
week we'll start off by completing our discussion of the Alperin-Goldschmidt-Puig
Fusion Theorem. We'll characterize the F-essential subgroups in terms of
the fusion system F, which will lead to the important notions of F-centric, F-radical,
and strongly p-embedded subgroups. The
characterization of F-essential subgroups leads naturally to the orbit category
of a fusion system, which roughly plays the role of the category of transitive
G-sets in the theory of finite groups. The analogy is not perfect,
however, and we will spend some time investigating the subtleties
involved. We will finish by introducing the linking system associated to
F and give some motivation for its importance from the point of view of homotopy theory.

**Date: ****Tuesday, October 13, 2015**

**Time: ****15.40**

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

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**All are most cordially invited.**

Tea and biscuits: before the seminar