4 problems

Lissajous–Fourier knot conjecture. Any knot in $\mathbb{R}^3$ is isotopic to a Fourier knot of type $(1,1,2)$.

Torus-knot Fourier representation conjecture. The torus knot $T_{p,q}$, with $0<p<q$, can be represented as a Fourier-$(1,1,2)$ knot with frequencies $n_x=p$, $n_y=q$, $n_{z,1}=p$,…

Torus-knot representation conjecture. The torus knot $T_{2,q}$ can be represented as a Fourier-$(1,1,2)$ knot with frequencies $n_x=2$, $n_y=q$, $n_{z,1}=2$, and $n_{z,2}=q-2$, and…

2-bridge Fourier representation conjecture. Every 2-bridge knot can be expressed as a Fourier-$(1,1,k)$ knot with $n_x=2$ and $k\leq 2$.