Symmetries and Overdetermined Systems of Partial Differential Equations

Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogeneous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order too. This three-week summer program considered the symmetries preserving various natural geometric structures. Often these structures are themselves derived from partial differential equations whilst …