Behavior of Weil-Peterson geodesics in the moduli space of Riemann surfaces

Masur-Minsky machinery of curve graphs and hierarchical structures of pants and marking graphs provide a combinatorial frame work to study Kleinian surface
groups, Mapping class groups and Teichmuller space.
My plan is to explain how using this machinery and local properties of Weil-Petersson(WP) metric and its geodesics one can construct WP geodesics with
certain behaviors. For example WP geodesic rays diverging in the moduli space or rays recurring to a compact set, as well as close geodesics which stay in a thin
part of moduli space.

I probably need to start with some background and then we’ll see how far we can
go.