Dear all, This week, Friday August 21, David Pfefferle (UWA) will give a talk at 4pm (Sydney time) via Zoom. Zoom link: https://uni-sydney.zoom.us/j/97078333625 Meeting ID: 970 7833 3625 Title: Spinning tops and magneto-hydrodynamics: Part 2 Abstract: In part 1, we reviewed the constrained variational problem originating from the Euler-Poincare reduction of geodesics on Lie groups with left-invariant Riemannan metric and applied it to the case of SO(3) to derive the well-known Euler equations of a free rigid body. In this talk, we replicate those steps in the case of a semidirect product between the Lie-Frechet group of diffeomorphisms and the space of one-forms on a domain of real space. Working at a formal level, this infinite dimensional group is equipped with a right-invariant Riemannian metric, and out come incompressible ideal magneto-hydrodynamics equations from the Euler-Poincare reduction. Rather elegantly, Alfven’s frozen-in flux theorem is seen as a consequence of the semidirect product structure (which encodes advection), and relabelling symmetry is attributable to right-invariance. Link to Part 1: https://youtu.be/_TNWDtOIGcQ Past talks can be found on the YouTube channel: https://www.youtube.com/channel/UCZqgDJ21wbdzMbeIdealpUg/ I hope to see you all online. Lachlan