Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves. (Jointly with the MPI-Oberseminar)

We establish a new and surprisingly strong link between
two previously unrelated theories: the theory of moduli spaces of
curves (which, according to Penner, is controlled by the ribbon
graph complex) and the homotopy theory of operads (controlled
by ordinary graph complexes with no ribbon structure, introduced
first by Kontsevich). The talk is based on a joint work with Thomas
Willwacher.