Watch a 52-minute mathematics lecture exploring Roger's 1995 conjecture about the universal central extension of the Lie algebra of exact divergence-free vector fields, presented at the ESI's Thematic Programme on "Infinite-dimensional Geometry." Learn about a recent proof demonstrating how this extension can be described using de Rham cohomology in codimension 2, and discover its application in constructing the universal central extension of the group of exact divergence-free diffeomorphisms on compact 3-dimensional manifolds, based on collaborative research with Leonid Ryvkin, Cornelia Vizman, Peter Kristel, Tobias Diez, and Karl-Hermann Neeb.