5 problems

Kernel conjecture.

Let $K$ be the coefficient field, let $x,y$ be variables, and let $\partial_x$ and $\partial_y$ denote the corresponding formal partial derivatives. For $\alpha\in\mathbb{N}^*$ and…

Let $D$ be a nonzero derivation of ${\rm K}[x,y]$, where ${\rm K}$ is the underlying field, and let ${\mathbb e}(D)$ denote the eigenvalue-degree invariant used in the paper. Finit…

Finiteness conjecture. If $D$ is simple, then

Kernel-growth conjecture. The dimension $\dim K_m$ grows polynomially in $m$ of degree at most $N-2$.