14 problems

Contiguity conjecture. The transjective differences are contiguous in every affine type. Consequently, filling fails precisely when $m_r>m_t$; determining $m_t$ and $m_r$ from the…

Let $Q$ be a quiver of type $\widetilde{A}_{2n-1,1}$ with $n\geq 2$, and let $\mathcal{A}_q(Q)$ denote its quantum cluster algebra. Let $\mathcal{S}$ be the set of elements describ…

Consider the graded cluster algebras associated with the affine exceptional types $\widetilde{E}_6$, $\widetilde{E}_7$, and $\widetilde{E}_8$. Certain occurring degrees are shown t…

Let … be the graded cluster algebra considered for affine type $\widetilde{E}_7$, with two-dimensional degree vectors. $\widetilde{E}_7$ degree-$\pm(2,1)$ conjecture. The degrees…

Let $[\underline{p}]$ be the mutation path used in the $\widetilde{E}_6$ construction, and let $l([\underline{p}])$ denote its length. The desired property is that repeating this p…

Let $\mathcal{A}((1,0,1,0,1,0,1),\widetilde{E}_6)$ be the graded cluster algebra considered for affine type $\widetilde{E}_6$, with integer grading and degrees denoted by integers.…

Consider the exchange graphs of the graded cluster algebras associated with the affine exceptional types $\widetilde{E}_6$, $\widetilde{E}_7$, and $\widetilde{E}_8$. The paper desc…

Let $\mathcal M_C$ be the Coulomb branch of a framed affine quiver gauge theory. Affine instanton conjecture. Coulomb branches of framed affine quiver gauge theories are Uhlenbeck…

Suppose that $Q$ is an affine quiver, let $W$ be its Weyl group, let $\Pi$ be the associated preprojective algebra, and let $I_w$ be the ideal associated to $w\in W$. Let…

Minimal-polynomial conjecture for affine D and E. For each vertex $i$ of $Q$, the polynomial exhibited in the corresponding table is associated with the minimal linear recurrence r…

Minimal-recurrence conjecture for affine A. The linear recurrence relations obtained in the paper for frieze sequences of quivers of type $\tilde A$ are minimal.

Let $Q$ be an affine quiver of affine type, let $lambda displaystylein mathbb P^10(Q)$, and let $E$ be a quasi-simple module in an exceptional tube. For a dimension vector…

Let $Q$ be an affine quiver, let $mathcal A(Q)$ be its cluster algebra, and let $mathcal B'(Q)$ denote the set of all generic variables associated with $Q$. **The generic-variabl…

A quiver of affine type is a finite acyclic quiver whose underlying graph is an extended Dynkin diagram. Such a quiver satisfies the difference property when the difference identit…