Let F_n be the free group on n generators and H be its first rational homology group. The "bivariant" coefficients of the title are the representations of Aut(F_n) given by arbitrary tensor products of H and its linear dual. In recent work, I computed the stable cohomology of Aut(F_n) with these coefficients, i.e. the cohomology in degrees sufficiently small enough compared to n, building on previous work by Djament - Vespa and Randal-Williams. In this talk I will review this result and explain the description of the stable cohomology in terms of explicit cohomology classes that were introduced by Kawazumi. A particularly nice description can be given by describing the collection of the stable cohomology groups as a so-called "wheeled PROP". If time permits, I will also say something about the proof.
