Explore deep connections between cluster algebras and loop level scattering amplitudes in N=4 super Yang-Mills theory during this 47-minute conference talk from the Amplituhedra, Cluster Algebras, and Positive Geometry Conference. Delve into the mathematical relationships focusing specifically on cases involving 6 and 7 particles, where finite Grassmannian cluster algebras Gr(4,n) exhibit unique properties. Learn about key features of these amplitudes that are either proven or theorized to hold true across all loop orders. Presented by Brown University's Anastasia Volovich at Harvard CMSA, gain insights into this specialized intersection of mathematical physics and algebraic structures.