Non-perturbative Amplituhedron Geometries

<!--HTML--><p><span style="color:rgb(0,0,0);">I will discuss some new developments in the context of the Amplituhedron construction for planar&nbsp;N=4&nbsp;SYM scattering amplitudes. I will define a negative Amplituhedron geometry which provides an all-loop order definition for a certain IR finite quantity, related to the ratio of null polygonal Wilson loops. Then I will show that the Amplituhedron picture suggests an interesting expansion of this quantity in terms of "loops of loops", unrelated to the usual small coupling expansion. In the leading order, I will provide an exact result to all orders in the coupling, and show the relation to the cusp anomalous dimension. Finally, I will discuss a certain interesting deformation of the geometric construction, and then conclude with future directions.</span></p>