10 problems

Noetherianity conjecture. For every $n\in\mathbb{N}$, the functor $P^{\otimes n}$ is noetherian: every ascending chain of subfunctors of $P^{\otimes n}$ stabilizes.

Let $H$ be the Hamiltonian and let $\gamma$ denote the relevant family of cycles. For each $k\in\mathbb{N}$, let $\nu_{H,\gamma}(k)$ be the Noetherianity index giving the optimal b…

Let $H$ be the Hamiltonian and let $cgamma$ be the associated family of cycles, with $n_r$ the universal Noetherianity index at level $r$ and $\nu_r$ the corresponding optimal Noet…

Draisma's conjecture. The affine infinite Grassmannian $\widetilde{\operatorname{Gr}}(\infty/2,V^*_\infty)$ is topologically $S_\infty$-noetherian: every descending chain of…

For $k>0$, let $cmathcal{GTM}_k$ be the full subcategory of topological minor morphisms spanned by graphs not admitting the Robertson chain $R_k$ as a topological minor, and let…

Let $cmathcal{GM}$ be the category of graphs and minor morphisms. A category is Noetherian over a ring if its associated module categories satisfy the relevant ascending-chain fini…

Let $W_{geq -1}$ be the Lie algebra of polynomial vector fields on the affine line with degrees at least $-1$, and let $U(-)$ denote the universal enveloping algebra. Non-noetheria…

Let $G$ be a group. An ${\mathscr{FI}}_G$-module is Noetherian when every submodule of a finitely generated ${\mathscr{FI}}_G$-module is finitely generated. The known result states…

Snowden's conjecture. A generalisation of the finite-dimensionality theorem for bounded $\Delta$-varieties should hold at the ideal-theoretic level, not only for equations of insta…

The conjecture. If $C$ has a left torsion rational functor, then $C$ is $\mathcal{F}$-Noetherian.