The positive orthogonal Grassmannian and scattering amplitudes in ABJM

I will talk about the positive orthogonal Grassmannian and its connection to scattering amplitudes in ABJM theory via on-shell diagrams. The on-shell diagrams can be characterized by permutation, which is the invariant information under equivalence moves. The functional map that arises from the moves satisfies the tetrahedron equations by Zamolodchikov, implying (2+1)-dimensional integrability. I will also present the solution to the BCFW recursion relation for loop amplitudes in ABJM theory, to all loop, four and six-point amplitudes can always be written in a dLog form.