The work of Maryam Mirzakhani 18

Growth of the number of simple closed geodesics on hyperbolic surfaces

Random hyperbolic surfaces and measured laminations

We prove an equidistribution result for the level sets of the lengths of simple closed curves in the moduli spaceMg of hyperbolic surfaces of genus g. This result parallels known results regarding horocycle and horosphere flows on homogeneous spaces [Rat], [Dani].

Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces

The Boundary of an Affine Invariant Submanifold

Full Rank Affine Invariant Submanifolds