Karen Vogtmann: Automorphisms of free groups, hairy graphs and modular forms

In order to understand automorphisms of finitely generated groups, a natural place to start is by studying the automorphisms of a free group.  The group of (outer) automorphisms of a free group  acts on a space of finite graphs known as Outer space, and the quotient of Outer space by this action can be used to compute group invariants.  I will show how to find new invariants (homology classes) using finite graphs with extra ``hairy" structure.  These classes are related to standard modular forms for SL(2,Z).  They were discovered by exploiting a beautiful connection with Lie algebra cohomology originally found by Kontsevich. (This is joint work with Jim Conant and Martin Kassabov)