Toric varieties and combinatorics

There is a classical connection between toric varieties and combinatorics, and tools from algebraic geometry can be used to prove facts about combinatorics. For example, one can give a proof of Euler's formula for the Euler characteristic of a convex polyhedron using the cohomology of complex projective varieties. I will discuss the h polynomial of simplicial convex polytope and a related polynomial introduced by Stanley, the local h polynomial. I will then discuss how combinatorial results can be used to deduce algebro-geometric information about the associated varieties.