Open-problem statements, with their sources attached.

The Zariski Cancellation Problem: every polynomial ring over a field k of characteristic 0 is cancellative.

There are no indecomposable vector bundles of rank 2 on $\mathbb{P}^n$ for $n \ge 7$. This is Conjecture 6.3 in [Har1974].

The Jacobian Conjecture: any regular function (i.e. vector valued polynomial function from) kⁿ → kᵐ whose Jacobian is a non-zero constant has an inverse that is given by a regular function, where k is a field of characteristic 0

For $N = 6$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 6$ and $D = 4$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 6$ and $D = 5$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 6$ and all $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 8$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 10$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 10$ and $D = 4$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 10$ and $D = 5$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 10$ and $D = 6$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 10$ and $D = 7$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 10$ and $D = 8$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 10$ and $D = 9$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 12$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 14$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 16$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For all even $N \geq 6$ and $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 6$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{R}$?