Khovanskii–Pukhlikov rings and divided difference operators

Schubert calculus was originally developed to answer purely geometric questions. For instance, how many lines intersect 4 given lines in a 3-space? However, main tools of Schubert calculus such as cohomology rings of flag varieties and push-pull operators can be defined and studied in purely algebraic terms. In the last decade, an algebraic side of Schubert calculus was partially interpreted in convex geometric terms (in the spirit of the theory of Newton polytopes). I will talk about algebraic methods and results of Schubert calculus from this convex geometric perspective. All necessary definitions will be given in the talk.