## Pacific Dynamics Seminar: James Farre

• Date: 04/29/2021
• Time: 10:00
Lecturer(s):
James Farre (Yale/Heidelberg)
Location:

Online

Topic:

Conjugating flows on the moduli of hyperbolic and flat surfaces [video]

Description:

A measured geodesic lamination on a hyperbolic surface encodes the horizontal trajectory structure of certain quadratic differentials. Thurston’s earthquake flow along such a lamination induces a dynamical system on the moduli space of hyperbolic surfaces sharing many properties with the classical Teichmüller horocycle flow. Mirzakhani gave a dynamical correspondence between the earthquake and horocycle flows, defined Lebesgue-almost everywhere. In this talk, we extend Mirzakhani’s conjugacy and define an extension of the earthquake flow to an action of the upper triangular group P in PSL(2,R) mapping certain flow lines to Teichmüller geodesics. We classify the P-invariant ergodic probability measures as those coming from affine invariant measures on quadratic differentials and show that our map is a measurable isomorphism between P actions with respect to these measures. This is joint work with Aaron Calderon.

Organizers:
Other Information:

This event took place via zoom and a recording is available on mathtube.org.