Numerical Semigroups and Kunz Polyhedra: A Bijective Love Story

A numerical semigroup is a subset of the natural numbers that contains 0 and is closed under addition. Recently attention has been given to a family of rational polyhedra whose integer points lie in bijection with numerical semigroups. In this talk we introduce the Kunz polyhedra by reframing an open conjecture, explore a combinatorial interpretation of their faces, and ask ourselves just how much geometry (and posets!) have to say about the structure of a numerical semigroup.