Asymptotics for pseudo-Anosovs in the Teichmuller lattice

Joseph Maher, CUNY Staten Island

Given a point in Teichmuller space, we call the orbit of the point under the mapping class group a Teichmuller lattice.
We show that the asymptotic growth rate of the number of pseudo-Anosov lattice points in a ball of radius r is the same as the asymptotic growth rate of the total number of lattice points in the ball of radius r. This uses recent work of Athreya, Bufetov, Eskin and Mirzakhani.