Global Torelli theorem for hyperkahler manifolds

The global Torelli theorem for hyperkaehler manifolds is a statement about a diffeomorphism between the “birational moduli space”, obtained by gluing together certain birationally equivalent points in the coarse moduli space, and a quotient of the period domain by the mapping class group. I will state the theorem and explain how one computes the mapping class group using the Sullivan's theory of rational homotopy.