Jet-determination of symmetries of parabolic geometries
  We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries - in particular torsion-free, parabolic contact, and several other classes. 
Boris Kruglikov and Dennis The
math.DG