  We prove that a Kleinian surface groups is determined, up to conjugacy in the
isometry group of $\mathbb H^3$, by its simple marked length spectrum. As a
first application, we show that a discrete faithful representation of the
fundamental group of a compact, acylindrical, hyperbolizable 3-manifold $M$ is
similarly determined by the translation lengths of images of elements of
$\pi_1(M)$ represented by simple curves on the boundary of $M$. As a second
application, we show the group of diffeomorphisms of quasifuchsian space which
preserve the renormalized intersection number is generated by the (extended)
mapping class group and complex conjugation.
