Exceptionally simple super-PDE

In 1893, Cartan and Engel gave the first realizations of the exceptional simple Lie algebra G(2) as symmetry algebra of various geometric structures. I will report on generalizations of this story to the exceptional simple Lie superalgebras G(3) and F(4), in particular on a supersymmetric extension of the Hilbert–Cartan equation. Joint works with Kruglikov & The