Chow Functions for Partially Ordered Sets

Explore a mathematics seminar that delves into the groundbreaking development of Chow functions for partially ordered sets. Learn about Stanley's 1992 foundational work on Kazhdan-Lusztig-Stanley (KLS) theory and how it unifies three key mathematical concepts: Kazhdan-Lusztig polynomials in Coxeter groups, toric g-polynomials of polytopes, and Kazhdan-Lusztig polynomials of matroids. Discover how these newly introduced Chow functions encode cohomological aspects of combinatorial objects, including descent-like statistics for Bruhat graph paths, chain enumeration in polytope faces, and Hilbert series of matroid Chow rings. Gain insights from this collaborative research presented by Luis Ferroni from the Institute for Advanced Study, working alongside Jacob P. Matherne and Lorenzo Vecchi.