Intersection Theory and Combinatorics: Variations on a Theme
Federico Ardila-Mantilla, San Francisco State University
MAA Invited Address

Thursday, August 7
MAA MathFest 2025

Abstract: My talk will discuss some beautiful objects at the intersection of combinatorics, geometry, and algebra called "Chow rings of toric varieties”. I will discuss three ways of thinking about them: they can be approached using algebra, polyhedral geometry, or numerical analysis. I will then explain how combinatorialists have recently used these rings to prove several conjectures from the 1970s and 80s about the colorings of a map.

My talk will not assume that you know anything about these objects. I will talk about the work of many people, including my joint work with Carly Klivans, Graham Denham, and June Huh.

Biography: Federico Ardila-Mantilla is a Colombian-American mathematician and musician who works in combinatorics and geometry. He was an ICM 2022 speaker and has received the NSF CAREER Award for research, the MAA National Haimo Award for teaching, and the AMS "Mathematics Programs that Make a Difference" Award for service. He serves as Professor at San Francisco State University and founder of the SFSU-Colombia Combinatorics Initiative, and co-directed the MSRI-UP REU program for students from minoritized groups, and has mentored more than 50 thesis students. Federico is always searching for ways to grow and foster an increasingly diverse, equitable, welcoming, and joyful community of mathematicians that empowers and serves the needs of all.