Flow by Mean Curvature inside a Moving Ambient Space

We will discuss some computations related in particular to the motion by mean curvature of a submanifold inside an ambient Riemannian manifold evolving by Ricci or backward Ricci flow. Special emphasis will be put on the analogous of Huisken's monotonicity formula and the connection with the validity of some Li-Yau-Hamilton Harnack-type inequalities in a moving manifold.