10 February 2012
Professor Karen Vogtmann
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. I will give some general comments about geometric group theory and then describe the basic geometric object, called Outer space, associated to automorphism groups of free groups. This Colloquium talk is the first of a series of three lectures given by Professor Vogtmann, who is the European Mathematical Society Lecturer. In this series of three lectures, she will discuss groups of automorphisms of free groups, while drawing analogies with the general linear group over the integers and surface mapping class groups. She will explain modern techniques for studying automorphism groups of free groups, which include a mixture of topological, algebraic and geometric methods.