  A new way of computing scattering amplitudes in a certain very important QFT
(N=4 SYM) has recently been developed, in which an algebraic structure called
the positive Grassmannian plays a very important role. The mathematics of the
positive Grassmannian involve, among other things, bipartite graphs, which also
appear in the formulation of a certain class of conformal field theories that
are currently being generalized into Bipartite Field Theories (BFT). The fact
that the same structures appear in two such different realms of physics
suggests a deeper connection between the two that is yet to be fully unveiled.
Here we explore that potential connection by looking at the graphs of a certain
class of BFTs, the brane tilings, in terms of the new mathematics developed for
the computation of the amplitudes. This way we produce a set of data that will
hopefully be useful in the development of that connection.
