Quantitative recurrence and hyperbolicity for the Teichmüller flow.
Ian Frankel (Toronto)
Monday 1st April 16:00-17:00 Maths 311B
We will explain how quantitatively recurrent geodesics for the Teichmüller metric on the moduli space of Riemann surfaces behave like geodesics in a negatively curved space. More precisely,
Let be the family of quadratic differentials corresponding to a length segment of a Teichmüller geodesic, parametrized by the metric. Let be a compact subset of the moduli space of Riemann surfaces. If the set of times for which belongs to has measure at least , and contains and , we will explain why the unit neighborhood of in its strongly stable leaf is contracted by in some metric, where the constants depend on and but not .