Lecture 3: Geodesics on the diffeomorphism group - the EPDiff equation

In this lecture I will talk about the EPDiff equation, which governs the behaviour of solutions to the registration problem. It can be derived either from a variational principle or as a consequence of momentum preservation. The EPDiff equation is actually a family of equations, parametrized by the choice of the metric, which contains various PDEs known in physics. This lecture will explain how to geometrically derive the EPDiff equation and show some of its mathematical properties.