4 problems

Model-set conjecture. Every unimodular substitution of Pisot type gives rise to a regular model set, though not necessarily a generic one.

Let $\Gamma \subset \mathbb{R}^m \times \mathbb{R}^n$ be a lattice, let $p_2$ denote projection onto the second factor, and let $W \subset \mathbb{R}^n$ be the half-open parallelot…

Szemerédi conjecture for model sets. Then $\Lambda$ contains arithmetic progressions of arbitrary length.

Let $(G\times H,\mathcal{L})$ be a cut and project scheme, let $W\subset H$ be a compact set, and let \text{\Large curlywedge}(W) denote the associated model set. Write…