The Johnson filtration is an important and mysterious sequence of subgroups of the mapping class group. I will prove that each term is finitely generated once the genus is sufficiently large. The main tool is the Bieri-Neumann-Strebel invariant. No prior knowledge of the mapping class group or the BNS invariant will be assumed. This is joint work with Tom Church and Mikhail Ershov. Speaker(s): Andy Putman (University of Notre Dame)