Prolongation 101
A whiteboard talk given at the Mini-workshop on Geometric Analysis, University of Wollongong, 5th September 2014

Abstract Prolongation is a process for augmenting a system of partial differential equations with further equations in order to produce an equivalent but more congenial system. This talk will be a beginner's guide starting with what turns out to be the Killing equation in Euclidean space. Prolongation is often regarded as more of an art than a science but, with the advent of parabolic geometry, some theory can be constructed.

At the talk I handied out (insufficiently many copies of)
T.P. Branson, A. Čap, M.G. Eastwood, and A.R. Gover, Prolongations of geometric overdetermined systems, Internat. Jour. Math. 17 (2006) 641-664,
M.G. Eastwood, Prolongations of linear overdetermined systems on affine and Riemannian manifolds, Rend. Circ. Mat. Palermo Suppl. 75 (2005) 89-108,
the second of which is a more expository version of the first with more examples. Please let me know if you would like hard copies. Here are my
very rough notes for the talk.