Title:  Generalized flatness constants, spanning lattice polytopes, and the Gromov width

In this talk, I will present joint work in progress with Averkov, Balletti and Nill where we motivate some new directions of research regarding the lattice width of convex bodies. We show that convex bodies of sufficiently large width contain a unimodular copy of a standard simplex and discuss relations to recent results on spanning lattice polytopes and how this can be viewed as the starting point for studying generalized flatness constants. We will also briefly consider connections with symplectic geometry and the Gromov width. We conclude the talk with several open questions.The talk is aimed at an audience familiar with convex geometry. No background in symplectic geometry will be assumed.