Federico Castillo: Discrete Volume of Partial Permutohedra

ABSTRACT: Counting integer points inside a polytope is a classic problem at the intersection of geometry, algebra, and combinatorics. In this talk we will take a tour of this problem. We will focus on the Ehrhart polynomial. This is related to counting integer points in dilations of a particular polytope. Computing this polynomial is complicated in general, but we will review some known cases, leading to a family called partial permutahedra. This is joint work with Roger Behrend, Anastasia Chavez, Alexander Diaz-Lopez, Laura Escobar, Pamela E. Harris, and Erik Insko.