Towards the amplituhedron volume

It has been recently conjectured that scattering amplitudes in planar $$ mathcal{n}=4 $$ super yang-mills are given by the volume of the (dual) amplituhedron. in this paper we show some interesting connections between the tree-level amplituhedron and a special class of differential equations. in particular we demonstrate how the amplituhedron volume for nmhv amplitudes is determined by these differential equations. the new formulation allows for a straightforward geometric description, without any reference to triangulations. finally we discuss possible implications for volumes related to generic n k mhv amplitudes.