6 problems

Structural factorization conjecture. For odd $p\ge 5$ in the nontrivial range, the BPS generating function has the form

Gap conjecture. For any collection of plumbed $3$-manifolds $Y$, gaps between consecutive $q$-series exponents at the beginning of the series are statistically more significant tha…

Consider the BPS spectra of local $\mathbb{P}^1\times\mathbb{P}^1$ and local $dP_1$ in their respective limiting or collimation chambers. The limiting spectrum is described by the…

Let a collimation chamber be a region in the stability-condition space of the BPS system, and consider the TBA equation for the functions $\mathcal{X}_\gamma(\epsilon)$ and its cor…

Stabilization conjecture. For every fixed $k$, the coefficient of $q^k$ in $\operatorname{Tr}M(q)$ stabilizes to a limiting value for sufficiently large $N$.

Nonnegative-power conjecture. The series $S(q)$ and $\overline{S}(q)$ can be expanded as Taylor series in $q$, with no negative powers of $q$.