  This paper introduces new operations on the string topology of a smooth
manifold: gravitational descendants of its cotangent bundle, which are
augmentations of the Chas-Sullivan $L_\infty$ algebra structure of the loop
space. The definition extends to Liouville domains. Descendants of the
$n$-torus are computed.
  To a monotone Lagrangian torus in a symplectic manifold, one associates a
Laurent polynomial called the Landau-Ginzburg potential, by counting
holomorphic disks. This paper proves the following mirror symmetry prediction:
the constant terms of the powers of an LG potential are equal to descendant
Gromov-Witten invariants of the ambient manifold.
