6 problems

Let $\mathcal{P}\subseteq\mathcal{A}(n,k)$ be a set of affine $k$-planes, and consider unions $F=\bigcup_{P\in\mathcal{P}}P^\prime$ with $P^\prime\subseteq P$. Héra constructed exa…

Let $F=\bigcup_{P\in\mathcal{P}}P^\prime\subseteq\mathbb{R}^n$, where $\mathcal{P}$ is a set of $k$-planes and $P^\prime\subseteq P$. Assume that $k\geq 2$, that the elements of…

Let $X\subseteq\mathbb{R}^d$ be a Borel set. For a measure $\mu$ on $X$, let $\overline{F}_\mu(1)$ denote its upper Fourier spectrum at $1$, let $\operatorname{spt}(\mu)$ denote it…

Upper packing-dimension conjecture. For every $K\in\mathcal{K}$,

Let $\mu$ be a Bernoulli measure supported on a Bedford–McMullen carpet, and let $X_\alpha^{\rm symb}$ be the set of points whose symbolic local dimension with respect to $\mu$ equ…

Let $\Lambda$ be a self-affine Sierpiński sponge, and let $\mu$ be a Bernoulli measure on $\Lambda$ satisfying the Very Strong Separation Condition. The packing spectrum of $\mu$ i…