5 problems

Let $A$ be an algebra, and for dimension vectors $alpha_1,alpha_2$ let $\operatorname{Frep}_{\alpha_1\alpha_2}(A)$ denote the corresponding two-step flag representation variety. An…

Reineke's conjecture. The coefficients $b_i$ are non-negative.

Efimov's unimodularity conjecture. In the hypotheses of the positivity conjecture, the polynomial $P_\mathbf{e}^\mathbf{v}(q)$ is unimodular.

Rupel's positivity conjecture. The polynomial $P_\mathbf{e}^\mathbf{v}(q)$ has nonnegative integer coefficients.

Let $Q$ be an acyclic quiver, and let quiver Grassmannians be the varieties parametrizing subrepresentations of representations of $Q$. A counting polynomial for such a quiver Gras…