5 problems

In a four-dimensional theory with a line defect $L$, let $\mathcal{H}_{L,u,\gamma}^{BPS}$ be the framed BPS Hilbert space at Coulomb-branch point $u$ and charge $\gamma$, and defin…

Framed quiver conjecture. The framed BPS indices of the defect with core charge $\gamma_c$ are

Let $\mathcal C$ be a $3CY$ triangulated category and let $\mathcal M^{sfr}$ be the moduli space of stable framed objects. Vanishing-cycle conjecture. There is a formal manifold…

Let $L_\zeta$ be a line defect determined by the noncompact D4-brane $N_j$, let $u$ be a Coulomb-branch point, and let $\gamma$ be a charge. Let…

Let $X_N$ be the geometric-engineering Calabi–Yau threefold, let $N_j=\mathcal O_{D_j}(D_j)[1]$ be the noncompact D4-brane for a fixed $1\leq j\leq N-1$, and let $(P_i,Q_i)$ be the…