8 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…

A one-dimensional tiling space has a map $F$ arising in the setting above, with rotation class $\mu$ when that class exists. Denjoy-type conjecture. Some version of Denjoy's theore…

A Pisot substitution is called homological when it satisfies the topological condition on the first rational Čech cohomology of its tiling space introduced for reducible non-unimod…

Let $A_{punc}$ be the $C^*$-algebra associated with the punctured tiling, let $H$ be the Hilbert space used in the spectral triples, and let $\mathcal{P}$ be the set indexing the f…

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…

Let a one-dimensional substitution tiling space have dilatation a degree $d$ Pisot number, and suppose that its first rational Čech cohomology has dimension $d$. For these homologi…