Johannes Hofscheier

Generalised flatness constants, spanning lattice polytopes, and the Gromov width

In this talk, I will present joint work with Averkov and Nill where we motivate some new directions of research regarding the lattice width of convex bodies. Based on the conclusion that convex bodies of large width contain a unimodular copy of a standard simplex, we will discuss relations to recent results on spanning lattice polytopes and how this can be viewed as the beginning of the study of generalised flatness constants. We will conclude the talk by outlining connections between the lattice width of a Delzant polytope and the Gromov width of its associated toric symplectic manifold.