Quantitative recurrence and hyperbolicity for the Teichmüller flow.
Ian Frankel (Toronto)
Monday 1st April, 2019 16:00-17:00 Maths 311B
Abstract
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 :%090%09%5Cleq%09t%09%5Cleq%09L%5C%7D "\{(X_t,q_t): 0 \leq t \leq L\}")
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  "(X_0,q_0)")
in its strongly stable leaf is contracted by 
in some metric, where the constants 
depend on and 
but not .
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 .Add to your calendar
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