Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=-1 (with T. Brendle and D. Margalit) - [pdf] [ps]
preprint 2012.

Abstract :
We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel of the Burau representation evaluated at t=-1 and also the fundamental group of the branch locus of the period mapping. One application is that each component in Torelli space of the locus of hyperelliptic curves becomes simply-connected when curves of compact type are added.