Growth of the Weil-Petersson diameter of Moduli space

The Weil-Petersson metric on Teichmuller space is a negatively curved Kahler metric that relates in interesting ways to hyperbolic geometry in dimensions 2 and 3. Though this metric is incomplete, its completion is a CAT(0) metric space on which the mapping class group acts cocompactly, and the quotient of this completion by the mapping class group is the Deligne-Mumford compactification of moduli space M(g,n). I will give a brief introduction to Weil-Petersson geometry and discuss joint work with Hugo Parlier that computes the growth rate of the WP diameter of M(g,n) as g and n tend to infinity.