The SL(2,R) action on Moduli space: Mordell Lecture
Meeting Room 2, CMS
We prove some ergodic-theoretic rigidity properties of the action of SL(2; R) on the moduli space of compact Riemann surfaces. In particular, we show that any ergodic measure invariant under the action of the upper triangular subgroup of SL(2; R) is supported on an invariant a ffine submanifold. The main theorems are inspired by the results of several authors on unipotent flows on homogeneous spaces, and in particular by Ratnerís seminal work. This is joint work with Maryam Mirzakhani and Amir Mohammadi.
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