4 problems

Let $n\in\mathbb{Z}_{\geq 2}$ and define … Let $c_{\beta_n}$ denote the capacity function associated with the four-dimensional polydisk, and let $\operatorname{accum}(\beta_n)$ den…

Brahmagupta-move staircase conjecture. The functions $c_{\beta_i}$ have infinite staircases.

Usher's conjecture. Between the center of $A_{0,n}$ and $\mathrm{accum}(L_{n,0})$, the function $c_{L_{n,0}}$ equals

Staircase correspondence conjecture. For every $\beta\geq\sqrt{3}$, the function $c_\beta$ has an infinite staircase if and only if the function $c_{H_b}$ has an infinite staircase…