6 problems

Toric-CY-four-fold magnificent-four conjecture. After suitable conditions, the deformation parameters reduce to at most three independent parameters; the D0/D8 operators are the st…

Edge-vertex sign rule. The sign relative to the square root $\mathsf{e}_lambda^i$ is $(-1)^{\sigma_i(\lambda)}$. This proposes an explicit sign rule for finite plane-partition edge…

Curve-vertex sign rule. The sign relative to the square root $\mathsf{v}_pi^{i\prime}$ is $(-1)^{\sigma_i(\pi)}$. This is a proposed orientation rule for curve-like toric Calabi–Ya…

Point-vertex sign rule. The sign relative to the square root $\mathsf{v}_pi^i$ is $(-1)^{\sigma_i(\pi)}$. This proposes an explicit orientation rule for the toric Calabi–Yau $4$-fo…

Let $X=\operatorname{Tot}_{\mathbb P^1}(\mathcal O\oplus\mathcal O(-1)\oplus\mathcal O(-1))$ and let $P_{n,d}(X;T)$ be the equivariant stable-pair invariant, where $d$ is the degre…

Let $\lambda,\mu,\nu,\rho$ be finite plane partitions, with at most two of them non-empty, and let $\mathsf V^{\operatorname{DT}}_{\lambda\mu\nu\rho}(q)$ and…