13 problems

Let $M$ be a Calabi–Yau threefold, and let $\beta$ be a nonzero curve class in $M$. The symbols $\operatorname{Z_{GW}^{\prime}}(M;u)_\beta$ and $\operatorname{Z_{PT}}(M;q)_\beta$ d…

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…

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.

Pandharipande–Thomas rationality conjecture. The partition function $\operatorname{Z_{PT}}\left(M;q\mid\prod_{i=1}^r\tau_{k_i}(\gamma_i)\right)_\beta$ is the Laurent expansion of a…

MNOP correspondence. The invariants

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…

Let $X$ be a Calabi–Yau $3$-fold, let $\beta>0$ be an effective curve class, and let $\mathop{\rm DT}\nolimits'_{\beta}(X)$ and $\mathop{\rm PT}\nolimits_{\beta}(X)$ denote the deg…