Online Talk 

A p-local finite group (S, F, L) is a generalization of the p-local data of a finite group. The cohomology of a p-local finite group (S,F, L) is defined as the mod-p cohomology of the realization |L| of its centric linking system. There are three types of mod-p homology decompositions for |L| over the collection of F-centric subgroups. I will discuss some  open problems and recent results on the sharpness of these homology decompositions.