On the Diffraction Spectrum of the Set of Visible Points in Lattices and Certain Cut-and-Project Sets

Let $k \geq 2$ be an integer. In 2000, Baake, Moody, and Pleasants proved that the set of lattice points in $\mathbb{Z}^k$ visible from the origin has pure point diffraction. It is also known that irreducible cut-and-project sets—such as the Ammann-Beenker point set—exhibit pure point diffraction.

Let $S$ be a finite subset of $\mathbb{Z}^k$, and let $V(S)$ be the set of points simultaneously visible from $S$. We will discuss the diffraction spectrum of the set $V(S)$ and the diffraction spectrum of the set of visibility from the origin in certain classes of irreducible cut-and-project sets. Joint work with Carlos Ospina.