13 problems

Let $Z_{PT}(q)$ denote the stable-pairs partition function, and let … be the weighted generating function of labelled box configurations, with boundary partitions $(,,)$. Pandharip…

Let $\vec{\lambda}_{A,+}$ be $n$-tuples of plane partitions and $\vec{\lambda}_{A,-}$ be $m$-tuples of plane partitions for the six surfaces. Let $v_\alpha=e^{\mathfrak{a}_\alpha}$…

Let $\vec{\pi}_{a,+}$ be $n$-tuples of plane partitions and $\vec{\pi}_{a,-}$ be $m$-tuples of plane partitions for each of the four legs. Let $v_\alpha=e^{\mathfrak{a}_\alpha}$,…

Let $n,m$ be nonnegative integers indexing D8/D8$'$ and opposite-brane pairs, and let $v_\alpha=e^{\mathfrak{a}_\alpha}$, $w_\alpha=e^{\mathfrak{b}_\alpha}$,…

Let $\vec{\pi}_a$ be $n$-tuples of plane partitions for the four legs, and let $\vec{v}=(v_1,\ldots,v_n)$ and $\vec{w}=(w_1,\ldots,w_n)$ be the flavor fugacities of the $n$ D8 and…

Let $\pi_{1,2,3,4}$ be plane partitions. Denote by $\mathcal{Z}^{\mathrm{DT}\\,\mathrm{JK}}_{\pi_1\pi_2\pi_3\pi_4}[\mathfrak{q},\mu;q_{1,2,3,4}]$ and…

Three-legs PT3 $qq$-character collision conjecture.

Let $S$ be an elliptic surface, let $C$ be a curve of genus $h$, and let $S_z$ denote the specified relative divisors in $S\times C$. For curve data $(\beta,n)$, insertions…

Relative descendent GW/PT correspondence.

MNOP correspondence. The invariants

PT-DT correspondence. The Donaldson–Thomas and Pandharipande–Thomas generating functions are equal up to a factor of MacMahon's generating function for plane partitions.

Let $V_{,,}$ be the DT topological vertex and let $W_{,,}$ be the weighted labelled-box vertex. Let … be the plane-partition generating function. Pandharipande–Thomas topological v…

Let $X$ be a Calabi–Yau $3$-fold, let $\beta>0$ range over effective curve classes, and let $\mathop{\rm PT}\nolimits(X)$ be the Pandharipande–Thomas generating series. Katz produc…