Karen Vogtmann (Cornell)

"Hairy graphs, automorphisms of free groups and modular forms"

The group  of outer automorphisms of a free group  acts on a space of finite graphs known as Outer space, and a classical theorem of Hurwicz implies that the homology of the quotient by this action is an invariant of the group. A more recent theorem of Kontsevich relates the homology of this quotient to the Lie algebra cohomology of a certain infinite-dimensional symplectic Lie algebra.  Using this connection, S. Morita discovered a series of new homology classes for Out(F_n).  In joint work with J. Conant and M. Kassabov, we reinterpret Morita's classes in terms of hairy graphs, and show how this graphical picture then leads to the construction of large numbers of new classes, including some based on classical modular forms for SL(2,Z).