Katharina Jochemko: Points, Polytopes and Polynomials

Abstract

Ehrhart theory is concerned with the enumeration of lattice points in polytopes. Given a polytope with vertices in the integer lattice, the function counting the lattice points in its integer dilates agrees with a polynomial, the Ehrhart polynomial of the polytope. In this talk, I will give a brief overview of some of my research interests in Ehrhart theory, in particular, geometric models for enumerative problems, structural results for Ehrhart polynomials as well as ties to valuation theory.