6 problems

Cryo-EM sample-complexity conjecture. If $R\geq 3$ is large enough, then the minimal number of observations required for accurate recovery of the $\operatorname{O}(n)$ orbit of $f$…

Degree-three invariant conjecture. The invariants of degree at most three list resolve the generic orbit in $(\mathbb{C}^n)^d$ if and only if

Let $H=\mathbb{Z}/L\mathbb{Z}\subset\mathrm{SO}(3)$ be generated by rotation through $2\pi/L$ about the $z$-axis, and consider homogeneous projected cryo-EM with $S$ shells and $F$…

Let $\mathcal{F}$ be a finite set of nonzero spherical-harmonic frequencies, let $V$ be the corresponding $\mathrm{SO}(3)$ representation, and let…

Heterogeneous MRA recovery conjecture. Generic unique recovery is possible at degree $3$ if $\mathcal{U}>Kp+K-1$, while generic list recovery is possible at degree $3$ precisely if…

Let $p\geq 3$ be odd, let $V=\mathbb{R}^p$ with the cyclic-shift action of $G=\mathbb{Z}/p\mathbb{Z}$, and let the projection identify opposite entries as in MRA with projection. M…