5 problems

Canonical-weight criterion conjecture. Up to $\operatorname{SL}(2,\mathbb{Z})$, the condition

Consistency and perfect-matching conjecture. A brane tiling is consistent if and only if the corresponding toric diagram has maximally tempered coefficients for its boundary points…

Consider a four-dimensional $\mathcal{N}=1$ superconformal quiver theory described by a brane tiling, and let its superconformal index be the generalization of the Witten index. Le…

Let $Q$ be the quiver of a consistent brane tiling, with vertices $i,j\in Q_0$, and let $I$ be an extremal perfect matching. The preceding result for geometrically consistent brane…

Let $G$ be a consistent brane tiling, let $(Q,W)$ be the corresponding quiver with potential, and let $A=\mathbb{C}Q/(\partial W)$ be its quiver-potential algebra. Fix a vertex…