Klara Stokes: Inner and outer automorphisms through incidence geometry

Abstract: Groups are often represented through linear actions, permutation actions, or symmetries of combinatorial objects. In this talk I will discuss a different kind of representation, in which both the inner and outer automorphisms of a group are encoded by an incidence geometry. The idea is to associate an incidence system to a group (G) so that inner automorphisms act as type-preserving automorphisms of the geometry, while outer automorphisms are realised geometrically as correlations, permuting the types of the incidence structure. This gives a way of viewing the distinction between inner and outer automorphisms through geometry. The talk is based on joint work with Dimitri Leemans and Philippe Tranchida.