Fu Liu (University of California, Davis)
MSRI: Simons Auditorium
We say a polytope is Ehrhart positive if its Ehrhart polynomial has positive coefficients. There are different examples of polytopes shown to be Ehrhart positive using different techniques. We will survey some of these results. Through work of Danilov/McMullen, there is an interpretation of Ehrhart coefficients relating to the normalized volumes of faces. We try to make this relation more explicit in the particular case of the regular permutohedron. The goal is to prove Ehrhart positivity for generalized permutohedra. If time permits, I will also discuss some related questions. This is joint work with Federico Castillo.