Research Talk: Rigidity for Automorphism Groups of Free Groups
Martin Bridson (University of Oxford)
I will discuss various results describing how aspects of rigidity familiar from the setting of lattices in semisimple Lie groups can be transported to the setting of automorphism groups of free groups.
The (non)existence and complexity of algorithms has been a central theme in combinatorial and, later, geometric group theory since their inception, with low dimensional topology providing both motivation and a significant field of application. In this talk I will review some of the milestones in the development of decision problems in group theory, highlighting the geometry behind them. I shall then survey the current state of the art, with an emphasis on applications to geometry and topology and including decision problems for profinite groups