"Boundary Theory for Groups"
Abstract:A fruitful idea in (infinite) group theory is to associate a "boundary" to a group, which reflects its "behaviour at infiity". This idea is no orphan. Mother idea: Regard a Group as a Geometric Object. Father idea: Attach to a Geometric Object a Boundary. In my talk I will survey this family of ideas, and try to convince that having a boundary is for the groups own good (unless she/he is amenable), and convenient to group theorists too.