I recently participated in the Nearly Carbon Neutral Geometric Topology Conference, speaking about work with James Farre in which we extend Mirzakhani’s conjugacy between the earthquake and horocycle flows. You can watch the videos below, and though the conference has ended, I’m happy to answer any questions over email.

Part 1 deals with coordinates for hyperbolic structures adapted to arbitrary measured laminations,
generalizing Fenchel-Nielsen coordinates and the shear coordinates of Bonahon and Thurston.
In part 2, I define both the earthquake and horocycle flows, and explain how to use the
orthogeodesic foliation map of part 1 to extend Mirzakhani’s conjugacy between them.