Karen Vogtmann: The topology and geometry of automorphism groups of free groups Mini course (lecture 1)

Free groups, free abelian groups and fundamental groups of closed orientable surfaces are the most basic and well-understood examples of infinite discrete groups. The automorphism groups of these groups, in contrast, are some of the most complex and intriguing groups in all of mathematics. In these lectures I will concentrate on groups of automorphisms of free groups, while drawing analogies with the general linear group over the integers and surface mapping class groups. I will explain modern techniques for studying automorphism groups of free groups, which include a mixture of topological, algebraic and geometric methods.