Moduli Space Tilings in Combinatorics, Tropical Geometry and Quantum Field Theory

In this talk, I will give a gentle overview of recent developments at the intersection of theoretical particle physics with real, complex, tropical and algebraic geometry -- all held together with deep combinatorics from the theory of matroids and their subdivisions. The beating heart of the construction is the Cachazo-He-Yuan (CHY) integral and its generalization by Cachazo-Early-Guevara-Mizera (CEGM) to moduli spaces of points in higher dimensional projective spaces. The CHY and CEGM integral evaluates to a richly structured rational function which is closely related to the (positive) tropical Grassmannian, a very richly structured object in combinatorial and tropical geometry. I will explain how the notion of "color" in physics motivated Cachazo-Early-Zhang (CEZ) to introduce the chirotopal tropical Grassmannian, which is constructed from realization spaces of oriented matroids other than the that of the positive Grassmannian.