  A central problem in quantum field theory is the computation of scattering
amplitudes. However, traditional methods are impractical to calculate high
order phenomenologically relevant observables. Building on a few decades of
astonishing progress in developing non-standard computational techniques, it
has been recently conjectured that amplitudes in planar N=4 super Yang-Mills
are given by the volume of the (dual) amplituhedron. After providing an
introduction to the subject at tree-level, we discuss a special class of
differential equations obeyed by the corresponding volume forms. In particular,
we show how they fix completely the amplituhedron volume for next-to-maximally
helicity violating scattering amplitudes.
