  These are expository notes from the 2008 Srni Winter School. They have two
purposes: (1) to give a quick introduction to exterior differential systems
(EDS), which is a collection of techniques for determining local existence to
systems of partial differential equations, and (2) to give an exposition of
recent work (joint with C. Robles) on the study of the Fubini-Griffiths-Harris
rigidity of rational homogeneous varieties, which also involves an advance in
the EDS technology.
