The Weil-Petersson metric is a Riemannian metric of non-negative sectional curvature on Teichmuller space. The mapping class group acts by isometries with respect to this metric. In this talk, we introduce the Weil-Petersson metric and sketch the proof by Masur and Wolf that shows that, in fact, the mapping class group constitutes its full group of isometries. Speaker(s): Didac Martinez-Granado (Indiana University)