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Tuesday, April 15, 2014

**Abstract:** During his 60th birthday conference, Thurston asserted that the growth rate of mapping class group is independent of genus. In this talk, we attempt to understand why and to what extend this is true. It turns out, given the right choice of generating sets, the mapping class group, Out(F_n) and SL(n,Z) all have uniform growth rates. We use the ideas and the work of Sleator-Tarjan-Thurston.