Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Schubert calculus and Gelfand-Zetlin polytopes

Our goal is to give an interpretation of the Schubert calculus for a full flag variety in terms of the geometry of polytopes. For this we use the notion of Pukhlikov-Khovanskii ring. This ring can be constructed for any convex polytope; it was initially introduced to describe the cohomology ring of a smooth toric variety. It turns out that it also can be used for some non-toric varieties. In particular, the cohomology ring of a full flag variety can be identified with the Pukhlikov-Khovanskii ring of a Gelfand-Zetlin polytope. This identification provides a new approach to Schubert calculus. I will discuss some new results in this direction, recenlty obtained in a joint work with Valentina Kirichenko and Vladlen Timorin.