Seminar in Algebraic Geometry and Number Theory

Abstract: The concept of associating a Chow-ring-like structure with a combinatorial object to extract combinatorial information is not new. The earliest successful instance of this approach was R. Stanley's proof of the g-conjecture in the 1970s. A more recent iteration of this idea is found in J. Huh's works on the Chow rings of matroids. Drawing inspiration from these ideas, I have defined Chow rings for unimodular triangulations. I will demonstrate how these constructions can be used to update the longstanding conjecture regarding the unimodality of the delta-vector of polytopes that admit triangulations of a special kind.