Liouville's Theorem through Symplectic Geometry

From a channel Lumen includes in full: This is a University of Maryland mathematics department channel, partially supported by the NSF. Every sampled transcript is a genuine lecture, proof walkthrough, research talk or applied-math tutorial (Hodge theory, Hopf-Rinow, Lie derivatives, quaternions, Voronoi diagrams), and the titles are plainly descriptive. The only uncertain items are the short interview clips with Scott Wolpert, which may be conversational rather than teaching, so they are excluded by title pattern.