In 1995, Claude Roger conjectured that the universal central extension of the Lie algebra of exact divergence-free vector fields should have a particularly straightforward description in terms of the de Rham cohomolgy in codimension 2. We give an outline of a recent proof of this result, and use it to construct the universal central extension of the group of exact divergence-free diffeomorphisms of a compact 3-dimensional manifold. (Joint work with Leonid Ryvkin, Cornelia Vizman, Peter Kristel, Tobias Diez, and Karl-Hermann Neeb.)