Hollow polytopes of large width

The goal of this talk is to present the construction of hollow lattice polytopes of width larger than their dimension. After defining important properties of lattice polytopes, such as width and hollowness, we introduce the flatness constant and certain specializations of it, and discuss bounds and exact values of these in low dimension. We will then show how taking a direct sum of certain polytopes yields a hollow lattice polytope (resp. a hollow lattice simplex) of dimension 14 (resp. 404) and of width 15 (resp. 408). They are the first known hollow lattice polytopes of width larger than dimension. We will also present some asymptotic results which can be obtained with this method. The talk is based on joint work with Francisco Santos.