Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

In this talk I will show how it is possible to construct a second-order nonlinear PDE in two independent variables, with highly nontrivial symmetry group, by starting from a very simple datum - a generic three-form on a seven-dimensional linear space. The construction itself follows from the combination of several well-known ingredients, but it is hardly found in the literature in a concise self-contained form, which is the main goal of this talk. I will conclude by pointing out some related results recently obtained in collaboration with D. Alekseevsky, J. Gutt and G. Manno, as well as open problems.