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.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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