Long curves and random hyperbolic surfaces

We will fix some topological data, a pants decomposition, of a closed surface of genus g and build hyperbolic structures by gluing hyperbolic pairs of pants along their boundary. The set of all hyperbolic metrics with a pants decomposition having a given set of lengths defines a (3g-3)-dimensional immersed torus in the (6g-6)-dimensional moduli space of hyperbolic metrics, a twist torus. Mirzakhani conjectured that as the lengths of the pants curves tend to infinity, that the corresponding twist torus equidistributes in the moduli space. In joint work-in-progress with Aaron Calderon, we confirm Mirzakhani`s conjecture. I will give a brief summary of the results.