Let S be a closed hyperbolic surface. The commutator length of a homologically trivial curve in S is the minimal number of commutators one needs to multiply to represent the associated element in the fundamental group. In this talk I will discuss for fixed k the asymptotic behaviour, when L tends to infinity, of the number of closed geodesics in S of length at most L and commutator length equal to k. This is joint work with Viveka Erlandsson.
