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Geodesic currents and counting problems

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NPCW05 - Group actions and cohomology in non-positive curvature

We show that, for every filling geodesic current, a certain scaled average of the mapping class group orbit of this current converges to multiple of the Thurston measure on the space of measured laminations. This has applications to several counting problems, in particular, we count the number of lattice points in the ball of radius R in Teichmüller space equipped with Thurston’s asymmetric metric. This is a joint work with Juan Souto.

This talk is part of the Isaac Newton Institute Seminar Series series.

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