Irreducible Sp-representations and subgroup distortion in the mapping class group (with N. Broaddus and B. Farb) - [pdf] [ps]
Comment. Math. Helv. 86 (2011), 537-556.

Abstract :
We prove that various subgroups of the mapping class group $\Mod(\Sigma)$ of a surface $\Sigma$ are at least exponentially distorted. Examples include the Torelli group (answering a question of Hamenst\"adt), the ``point-pushing'' and surface braid subgroups, and the Lagrangian subgroup. Our techniques include a method to compute lower bounds on distortion via representation theory and an extension of Johnson theory to arbitrary subgroups of $\HH_1(\Sigma;\Z)$.