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During the last few decades, significant strides have been made in the study of scattering amplitudes. New modern on-shell techniques have made calculations with a large number of particles and loops feasible. Many of the significant advancements in the field has come by studying $\mathcal N = 4$ super Yang-Mills (sYM) and using its planar, or large $\mathcal N$, limit as a sandbox to explore the underlying geometric structure. In recent years this has been studied using the positive Grassmannian, on-shell diagrams, and the Amplituhedron. A natural progression is to try and extend these discoveries beyond planar $\mathcal N = 4$ sYM to explore whether the geometric interpretation is a more general feature of quantum field theories. Similarly, considering theories with $\mathcal N \ne 4$ will teach us to what extent these geometric pictures apply to other field theories. The focus of our talk are these structures. Specifically we focus on using the dual formulation to probe how the amplitudes, or on-shell forms, behave in the ultra violet.

(Hopefully) enough pizza at 11:50am.