Igor Khavkine
A conserved current for a PDE in $n$-variables can be thought of as a field dependent $(n-1)$-form that is closed on solutions. A similar definition can also be made in other form degrees. A field dependent $(n-p)$-form that is closed on solutions is called a higher current (or $p$-current). It is well known that, for variational PDEs, conserved currents (1-currents) correspond to symmetries via Noether's theorem. I will discuss a generalization of this result, which relates higher conserved currents to "higher stage symmetries". For simplicity, I will concentrate on the case of linear equations.
