# Rank 2 Amalgams and Fusion Systems

GR2W02 - Simple groups, representations and applications

Saturated fusion systems capture abstract conjugacy in $p$-subgroups of finite groups and have found application in finite group theory, representation theory and algebraic topology. One of the ways to approach saturated fusion systems and their classification is by understanding their essential subgroups. In this talk, we classify fusion systems $\mathcal{F}$ in which there are two $\mathrm{Aut}_{\mathcal{F}}(S)$-invariant essential subgroups whose normalizer systems generate $\mathcal{F}$. We employ the amalgam method and, as a bonus, obtain $p$-local characterizations of certain rank $2$ group amalgams whose parabolic subgroups involve strongly $p$-embedded subgroups, generalizing work of Delgado and Stellmacher.

This talk is part of the Isaac Newton Institute Seminar Series series.