Michael Borinsky, a physicist at the Perimeter Institute, presents a research talk given at the IAS Amplitudes Group Meeting on tropicalizing scalar quantum field theory. He shows that the tropicalized massive scalar theory is exactly solvable, with the solution expressed as a non-linear recursion on the expansion coefficients of the quantum effective action. Geometrically this recursion computes volumes of moduli spaces of metric graphs, which Borinsky connects to Mirzakhani's volume recursions on moduli spaces of curves. He then builds on this result to construct a sampling algorithm that draws points from the moduli space of graphs in proportion to their perturbative weight, running in polynomial time and memory where existing Feynman integral methods scale exponentially. He demonstrates the method on the phi4 beta function at 50 loops and phi3 correlation functions in three dimensions up to 20 loops, using a proof-of-concept implementation. The talk assumes familiarity with perturbative quantum field theory and moduli space geometry.