Khovanskii-Pukhlikov theory and toric vector bundles

A convex chain is an integer linear combination of indicator functions of convex polytopes. We give a review of Khovanskii-Pukhlikov theory of convex chains and the Hirzebruch-Riemann-Roch theorem for convex polytopes. We also discuss applications to computation of Euler characteristic of a torus equivariant vector bundle on a toric variety. This is based on a joint work with Suhyon Chong and Shaoyu Huang.