4 problems

Let $\Omega_{E_{12}^{\gamma}}$ be the tiling space associated with a generalized 12-fold tiling with parameter $\gamma$. For generic parameters, meaning those with the maximal numb…

Canonical-transversal preservation conjecture. There is a homeomorphism $h'$ isotopic to $h$ such that, for any canonical transversal $\Xi$ in $\Omega$, $h'(\Xi)$ is a canonical tr…

Let $E_\parallel$ be a $d$-dimensional linear subspace of ${\mathbb R}^n$ with irrational orientation, and let $\mathcal L(E_\parallel)$ be the associated cut-and-project Delone se…

Let $A$ be a finite alphabet, and let a tiling in ${\mathbb R}^d$ have a suitably defined notion of linear repetitivity. Its transversal is the tiling space consisting of tilings l…