Intersection Theory of Matroids - Variations on a Theme

Explore a mathematical lecture from the Workshop on Combinatorics of Enumerative Geometry that delves into the intersection theory of matroids through multiple computational approaches. Begin with a comprehensive survey of four distinct methods for computing Chow rings of toric varieties, developed by Billera, Brion, Fulton-Sturmfels, and Allermann-Rau. Examine how these computational techniques illuminate the proof of Huh and Huh-Katz's formula for calculating coefficients of reduced characteristic polynomials in matroids. Learn how each proof methodology reveals unique aspects of matroid combinatorics and provides foundational understanding for recent developments in matroid intersection theory. Gain insights into the mathematical beauty and computational power of these varied approaches while understanding their applications in modern matroid theory.