16:30
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.