7 problems

Let $A,B\subset[0,1]$ be missing digits sets with bases $p_A$ and $p_B$, and define $T_x(y)=xy$. Universal interior conjecture. Suppose that … and … Then $A+T_x(B)$ contains a non-…

Let $A,B\subset[0,1]$ be missing digits sets. Palis' conjecture. Suppose that … Then, generically, $A+B$ contains a non-trivial interval. In the paper's missing-digits setting, the…

Let $C$ be the unit circle … For sufficiently large integers $p$, let $D\subset\{0,\dots,p-1\}^2$ satisfy $\#D\leq100$, and let $K_{p,D,l}$ denote the corresponding missing-digits…

Let $n\geq2$ be an integer and let $M\subset\mathbb{R}^n$ be a manifold of finite type. Neighbourhood estimate conjecture. There exists a number $\sigma=\sigma(M)>0$ such that, for…

Let $p>2$ be a prime number and let $\epsilon\in(0,1)$. Uniform Fourier-dimension conjecture. For every digit set $D$ with … we have … where the $o(1)$ term is uniform across all s…

Let $n\geq 1$ be an integer, let $M\subset\mathbb{R}^n$ be a strongly non-degenerate analytic manifold, let $p>2$ be an integer, and let $D\subsetneq\{0,\dots,p-1\}^n$ be a choice…

Let $K$ be a missing digits set, meaning a compact set determined by restricting the digits in a fixed integer base. Folklore conjecture. If … then $K\cdot K$ contains intervals. T…