Divided difference operators for convex polytopes

In this talk I will discuss new results and constructions of Kiritchenko-Smirnov-Timorin associating convex polytopes to representations of reductive groups which generalize the well-known Gelfand-Zetlin polytopes and encode information about Weyl and Demazure character formulas. These construction are very promising to give convex geometric formulae in Schubert calculus. The talk for the most part is accessible for anybody with basic background in algebra and representation theory.