Brown’s moduli spaces and the gravity operad

We will introduce Brown’s moduli spaces, which parametrize genus zero curves with marked points and arise in the geometric study of multiple zeta values.
We will explain the proof of two essentially equivalent results: on the one hand, the purity of the Hodge structure on the cohomology of these spaces;
on the other hand, the freeness of the non symmetric operad underlying Getzler’s gravity operad. This is joint work with Bruno Vallette.