4 problems

Let $\mathbb{N}_{\infty}$ denote the infinite integers. Infinite-integer ratio transfer conjecture. There exist ratios of infinite integers of the form … that can be transferred to…

For a base $\beta>1$, let $T_\beta$ and $T_{-\beta}$ denote the positive- and negative-base transformations, respectively. The measurable-isomorphism conjecture. Among all…

Let $\Sigma$ be a subshift, let $Q(\Sigma)$ be the quantity associated with the iterative system in the paper, and let $\Sigma_{\mathcal W}\subset\Sigma$ be an interval shift. None…

Let $A$ be the alphabet, let $A^{\omega}$ denote the set of infinite words over $A$, let $\mathbb{T}$ be the circle, and let $F_{w_{[0,n)}}$ be the Möbius transformation associated…