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Counting finite-order lattice points in Teichmüller space

Geometry of mapping class groups and Out(Fn) October 25, 2016 - October 28, 2016

October 25, 2016 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Spencer Dowdall (Vanderbilt University)
Location: MSRI: Simons Auditorium



I will discuss a counting problem for the orbit of the mapping class group in Teichmüller space. Athreya, Bufetov, Eskin, and Mirzakhani have shown that the number of orbit points in a Teichmüller ball of radius R grows like e^{hR}, where h is the dimension of Teichmüller space. Maher has shown that pseudo-Anosov mapping classes are "generic" in the sense that the proportion of these points that are translates by pseudo-Anosovs tends to 1 as R tends to infinity. We aim to quantify this genericity by showing that the number of translates by finite-order and reducible elements have strictly smaller exponential growth rate. In particular, we find that the number of finite-order orbit points grows like e^{hR/2}. Joint work with Howard Masur.


27133?type=thumb Dowdall. Notes 281 KB application/pdf Download
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