Tommaso Rossi (Università di Bologna)

Operads were introduced by Peter May in the seventies to study the topology of iterated loop spaces. Thanks to his work many computations were carried out, for example Cohen and May computed the integral homology of the symmetric groups S_n and of the braid groups B_n. Interest in operads was considerably renewed in the early nineties with the work of Kontsevich, Ginzburg, Kapranov and Getzler, who find many applications of operad theory in algebra, geometry and mathematical physics.

In the first  part of the talk we will introduce operads providing many examples form algebra and geometry.

In the second part we explain a result of Getzler who used the theory of operads (in particular Koszul duality) to compute the Betti numbers of \overline{M}_{0,n}, the moduli space of genus zero stable curves (Getzler-"Operads and genus zero Riemann surfaces"). Time permitting we will discuss a refinement of this result due to myself and P. Salvatore (Rossi-Salvatore, "Chain level Koszul duality between the Gravity and Hypercommutative operads").