Faustin Adiceam

On the epsilon-density of a vector in the unit torus

A central question surronding the problem of constructing so-called dense forests in convex geometry is the following : consider a finite set of multiples of a vector in the unit torus. When does this set get epsilon-close to any point in the torus?
We will answer this question and, time permitting, show its relation with the aforementioned problem in convex geometry.