9 problems

Let $[\gamma]$ be a knot type, let $U_C([\gamma])$ be the set of curves in that knot type whose distortion is at most $C$, and let $\delta([\gamma])$ be the distortion thickness of…

Compression lower bound from supertrunk. There is a universal constant $c>0$ such that for every knot type $K$,

Geometric decomposition conjecture. Every length-minimising unknot in $\mathcal{U}_\tau$ for $\tau\in(0,2)$ admits a decomposition into finitely many elementary geometric component…

Let $K$ be a ribbon knot, let $\operatorname{Rib}(K)$ denote its minimal ribbonlength, and let $c(K)$ denote its crossing number. Linear ribbonlength conjecture. The minimal ribbon…

Let $\Gamma_n$ denote the set of convex $n$-gons with each edge of length $1$, and let $E_n^\alpha$ be the energy associated with the increasing continuous function…

Let $[K]$ be a knot type, let $s_{sh}[K]$ denote its stick number in the simple hexagonal lattice, and let $c[K]$ denote its crossing number. Crossing-number bound conjecture. For…

Let $[K]$ be a knot type, let $s_{sh}[K]$ denote its stick number in the simple hexagonal lattice, and let $3_1$, $4_1$, $5_1$, and $5_2$ denote the indicated knot types. 13-stick…

Let $L$ be a link that is balanced in the sense of the paper's balance criterion, and let a link be nicely balanced when its kink measure is represented by a kink tension function…

Let $[K_1]$ and $[K_2]$ be isotopy classes of knots, and let $[K_1\sharp K_2]$ be their composite isotopy class. For an isotopy class $[K]$, write $E^{(2)}_{\circ}([K])$ for the in…