| Résume | Every hyperbolic surface (hence every Riemann surface or smooth algebraic curve over C) can be described by the lengths and twist of the curves of a pants decomposition. Fixing lengths and taking arbitrary twists creates an immersed, Lagrangian torus inside the moduli space of curves, which turns out to be related to the unipotent-like ``earthquake flow.’’ Mirzakhani asked if these twist tori equidistribute as lengths are taken to infinity: in this talk, I will explain joint work with James Farre in which analyze these limiting distributions. The key tool is a bridge that allows for the transfer of ergodic-theoretic results between flat and hyperbolic geometry. |
