7 problems

Refined BPS stabilization conjecture. The refined BPS number $n_\beta^{i,j}$ stabilizes when $\beta$ is sufficiently positive. This conjectures asymptotic stability of the refined…

For the local $\mathbb{P}^2$, let $\widetilde{n}_d^{i,j}$ denote the combinatorial refined BPS invariants obtained from the Nekrasov partition function, and let $n_d^{i,j}$ denote…

Modularity conjecture for refined BPS generating functions. The functions $h^{\rm ref}_{p,\mu}$ transform as vector-valued higher-depth Jacobi forms of the stated weight and index

Let $w^{\pm}$ denote the toric weights, and consider the scaling limit $w^{\pm}\longrightarrow\infty$ along a slope $s$. Let $y$ be the refinement parameter. Toric-weight refinemen…

Wild character-variety conjecture. The weighted Poincaré polynomial satisfies

Let $Z_\beta$ be the refined partition-function coefficient associated with a curve class $\beta$, and let the refined Gopakumar–Vafa-series condition and the denominator ansatz be…

Let $Z_\beta(\tau,\boldsymbol{t_m},\epsilon_1,\epsilon_2)$ be the coefficient indexed by the base curve class $\beta$ in the partition function, and let … Let $A(\tau,z)$ and…