Projective Structures and Mobility on 30th January 2013 in Canberra

It has been known for at least 2,500 years that different Riemannian metrics can have the same geodesics (as unparameterised curves). However, this phenomenon is quite rare: the generic metric has little "mobility." More generally, one could try to fit a metric to a system of curves that one would like to be its geodesics but generically this is hopeless: no "mobility" at all! I'll explain some of this classical area (Beltrami 1865, Liouville 1889) from a modern perspective (tractor bundles and the like).

My notes for the talk
Projective symmetries A follow-up exposition of the PDE controlling the infinitesimal symmetries of a projective structure.