Counting finiteorder lattice points in Teichmüller space
Geometry of mapping class groups and Out(Fn) October 25, 2016  October 28, 2016
Location: SLMath: Eisenbud Auditorium
Mapping Class Group
Teichmüller space
Counting
00A35  Methodology of mathematics {For mathematics education, see 97XX}
0111  Research data for problems pertaining to history and biography
14624
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 pseudoAnosov mapping classes are "generic" in the sense that the proportion of these points that are translates by pseudoAnosovs tends to 1 as R tends to infinity. We aim to quantify this genericity by showing that the number of translates by finiteorder and reducible elements have strictly smaller exponential growth rate. In particular, we find that the number of finiteorder orbit points grows like e^{hR/2}. Joint work with Howard Masur.
Dowdall. Notes

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