Covering minima and non-hollow lattice polytopes

The covering minima of a convex body were introduced by Kannan and Lovasz to give a better bound on the constant in the flatness theorem, which states that the width of hollow convex bodies in a fixed dimension is bounded by a constant. These minima are similar in flavor to Minkowski's successive minima, and on the other hand generalize the covering radius and the width of a convex body. I will speak about recent joint work with Francisco Santos and Matthias Schymura, where we investigate extremal values of these covering minima for non-hollow lattice polytopes.