Logic Seminar: Notions of tractability in the theory of discrete groups

Speaker: Peter Burton (ISU)

Abstract:

This talk will be a broad introduction to conditions which can be placed on a countable discrete group that make it in some sense ‘uncomplicated’ or ‘easily understood’. The motivating examples are requiring the group to be finite or abelian. We will illustrate why these can be regarded as contrasting properties, in that finite groups are globally small but can have extreme internal complexity while finitely generated abelian groups can be globally large but are internally straightforward. We then plan to discuss how these concepts generalize respectively to residually finite groups and amenable groups.