Seminar talk, 7 May 2008

Speaker: Raffaele Vitolo

Title: On differential equations characterized by their Lie point symmetries

Abstract:

We study the geometry of differential equations determined uniquely by their point symmetries. The action of the infinitesimal group of point symmetries foliates the jet space where the equation live. Equations which are uniquely determined by their point symmetries are of two types: they either coincide with a leaf of the part of the jet space where the action is regular or they coincide with the singular subset of the action. Many examples are provided, ranging from minimal submanifolds and geodesics to Monge-Ampère equations and some of their generalizations.