14 problems

For a Calabi–Yau $A_\infty$ category, let the Gromov–Witten potential define a left ideal in the sheaf of Weyl algebras associated to its periodic cyclic chain complex, and let thi…

For $g\geq 0$ and $n\geq 1$, let $Z_{g;n}(q):=\sum_dN_{g,d;n}q^d$, where $N_{g,d;n}:=\sum_{(\beta,\sigma)=d,\,(\beta,F)=n}N_g(\beta)$. Let $E_2(q),E_4(q),E_6(q)$ be Eisenstein seri…

For integers $n,g\geq 0$ and positive degree $d_E>0$, let $\mathcal{F}^{(n,g)}_{d_E}$ denote the refined free energy in degree $d_E$, and let the conifold and orbifold points be th…

Let $\mathbf{r}_1,\ldots,\mathbf{r}_l$ be representations, let $\mathbf{r}_{i_1}\otimes\cdots\otimes\mathbf{r}_{i_l}$ be their tensor product, and let…

Let $\mathcal F$ be an $\mathcal N=(0,1)$ SQFT with cylindrical ends and boundary $\partial\mathcal F$, and suppose … Let $Z_{RR}(\mathcal F)(\tau,\bar\tau,a)$ be its conditionally…

Let $\widetilde{\mathcal{F}}^{\mathsf{B}}_g$ be the genus-$g$ series associated to the formal quintic, let $T=I^{\mathsf{Q}}_1(q)/I^{\mathsf{Q}}_0(q)$, and let $A_2$, $A_4$, $A_6$,…

Let $\widetilde{\mathcal{F}}^{\mathsf{B}}_g$ be the genus-$g$ series associated to the formal quintic, let $T=I^{\mathsf{Q}}_1(q)/I^{\mathsf{Q}}_0(q)$ be the mirror coordinate, and…

Let $K\mathbb{P}^3$ be the local projective three-space, let $T=I^{K\mathbb{P}^3}_1(q)$ be the mirror coordinate, and let $\mathcal{F}^{\mathsf{SQ}}_g$ and…

Let $K\mathbb{P}^3$ be the local projective three-space, let $T=I^{K\mathbb{P}^3}_1(q)$ be the mirror coordinate, and let $\mathcal{F}^{\mathsf{SQ}}_{g,a+b}a,b$ denote the stable q…

Let $K\mathbb{P}^2$ be the local projective plane, let $T=I^{K\mathbb{P}^2}_1(q)$ be the mirror coordinate, and let $\mathcal{F}^{\mathsf{SQ}}_g$ denote its genus-$g$ stable quotie…

Let $K\mathbb{P}^2$ be the local projective plane, let $q$ be the degree variable, and let $T=I^{K\mathbb{P}^2}_1(q)$ be the mirror coordinate with $Q(q)=\exp(T)$. Let…

Let $S$ be a Kähler surface, let $K_S$ denote its canonical class, and let $C(S)$ be the Kähler cone of $S$. Write $D_2$ for the differential operator,…

A chain of matrices defines formal free energies $F_g$ through its topological expansion, and modular transformations act on the associated spectral-curve data, including the Bergm…

Let $z_c$ denote the conifold-point value of the complex-structure coordinate $z$, and let $f^{(1,0)_k}$ be the holomorphic ambiguity associated with the Klein-bottle contribution…