8 problems

Algebraic-integrability or logarithmic-component conjecture. If

Ekedahl–Shepherd-Barron–Taylor conjecture. The foliation $\mathcal F$ is algebraically integrable if and only if $\mathcal F_{\mathfrak p}$ is $p$-closed for every closed point…

Let $\ell\ge 2$ and let $L=\partial^\ell+a_2(z)\partial^{\ell-2}+\dots+a_\ell(z)$ be a rational differential operator invariant under $\mathbb Z_\ell$, with coefficients vanishing…

Let $\ell\in\{3,4,6\}$, and let $L$ be an order-$\ell$ operator invariant under the group $\mathbb Z_\ell$ on an elliptic curve with the corresponding symmetry. Assume that its pol…

Consider algebraically integrable third-order differential operators $L$ with one pole, in the notation of the classification subsection, and let $q$ and $r$ be the associated gap…

Let $L$ be a rational algebraically integrable differential operator with gaps $q_1,\dots,q_{n-1}$, and call it fully cyclically symmetric when it has the stated cyclic symmetry. R…

Let $L$ be an algebraically integrable differential operator of order $n\ge 2$, with gaps $q_1,\dots,q_{n-1}$ in its local indices, and call $L$ fully cyclically symmetric when it…

Hirota–Kimura integrability conjecture. The Hirota–Kimura discretization remains algebraically completely integrable.