9 problems

Let $Q$ be a connected quiver with at least one frozen vertex, and let $\mathbf M$ be a reduced (weakly) balanced and monotone mutation sequence. Write $Q^{(j)}_{\mathbf M}$ for th…

Greenness conjecture. The sequence of vertices of $\Gamma_{\overline{w}}$ mutated by $\mu_\bullet$ is a green sequence with respect to $\Gamma_{\overline{w}}$.

Let $B$ be a skew-symmetrizable matrix indexed by $\mathcal I={1,\ldots,n}$. For a mutation sequence $\boldsymbol{w}$, let $r_i^{\boldsymbol{w}}$ be the associated reflections, let…

Berenstein–Geiss–Muller conjecture. The following are equivalent:

Let $P$ and $P'$ be plabic graphs, and associate to each its quiver. Two plabic graphs are move equivalent when they are related by local moves and changes of the colors of boundar…

Let $(C,z)$ and $(C',z')$ be real isolated plane curve singularities, and choose real morsifications of them. Each morsification has an associated quiver; two quivers are mutation…

Let $T_i$ denote the Lusztig isomorphisms associated with the simple roots of the quantum group, and let quiver mutations act on the corresponding quantum cluster structure. Luszti…

Quiver and mutation conjecture. For every semisimple, simply connected, complex Lie group $G$, there exists a quiver $Q_G$ and quiver mutations $\mu_G^{\operatorname{rot}}$ and…

The non-trivially valued mutation-periodicity conjecture. Corollary … and … , also hold when $Q$ is non-trivially valued.