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Watch a 53-minute lecture by Federico Ardila of San Francisco State University titled "Intersection theory and combinatorics: variations on a theme" presented at IPAM's LatMath 2025 Workshop at UCLA. Explore beautiful objects called "Chow rings of toric varieties" that exist at the intersection of combinatorics, geometry, and algebra. Learn about three different approaches to understanding these rings: through algebra, polyhedral geometry, and numerical analysis. Discover how combinatorialists have recently used these rings to prove several conjectures from the 1970s and 80s about map colorings. No prior knowledge of these objects is required. The lecture covers work by multiple researchers, including Ardila's joint work with Carly Klivans, Graham Denham, and June Huh. Recorded on March 6, 2025.
