Karen Vogtmann: Unstable cohomology of automorphism groups of free groups

The rational cohomology of Out(F_n) vanishes in high and low dimensions, but the middle range remains quite mysterious.  In this talk I will summarize what we do know  and then show how tools from topology and representation theory can be used to construct a large number of new cocycles. Those within range of computer calculations have been shown to give nontrivial cohomology classes, and it is conjectured that essentially all of them should. The talk is based partly on joint work with Jim Conant, Allen Hatcher and Martin Kassabov.