Florian Eisele (University of Manchester) – Block theory of profinite groups

Profinite groups are a class of topological groups with close ties to finite groups. Many of the questions around group rings of finite groups and their representation theory have profinite analogues. I will report on results that generalise block fusion systems and Puig's theory of nilpotent blocks to the profinite setting, and a resulting description of blocks with infinite dihedral defect groups. This is joint work with MacQuarrie and Franquiz Flores.