23 problems

Formal convergence conjecture. In the $x_i$ variables, the partition functions converge as formal power series expansions.

Let ${\mathfrak X}$ be a toric Calabi–Yau 3-fold, with a Lagrangian brane $L$ and framing parameters $\mathbf t$. Let $\mathcal W_{g,n}({\mathfrak X},L,\mathbf t;x_1,\dots,x_n)$ de…

Let $X$ be a toric Calabi–Yau 3-fold, and let $(Q,W)$ be a quiver with potential constructed from $X$ such that … Here, trivial attractor DT invariants means that all attractor Don…

Let $X$ be a smooth local toric Calabi–Yau $3$-fold, and let the Drinfeld double of its equivariant spherical Cohomological Hall algebra act on the cohomology of the moduli spaces…

Let $X$ be a smooth local toric Calabi–Yau $3$-fold, and let the Drinfeld double of its equivariant spherical Cohomological Hall algebra act on the cohomology of the moduli spaces…

For a toric Calabi–Yau threefold, let $\mathsf{Y}_{(Q,W)}$ denote the quiver Yangian associated with its quiver $Q$ and superpotential $W$, and let $\operatorname{CoHA}$ denote the…

Let the quantum distribution be the Wigner transform of the reduced density matrix of the non-interacting Fermi gas obtained by quantizing the mirror curve of a toric Calabi--Yau m…

Let $Z(N,\hbar)$ be the canonical partition function of the non-interacting Fermi gas associated with the quantized mirror curve of a genus-one toric Calabi--Yau manifold, where…

Cagnazzo–Grassi–Mariño conjecture. The non-perturbative topological string partition function on the $Y^{N,0}$ geometry in the conifold frame is given by

Sufficiency conjecture. There are at least $g$ inequivalent sets of $B$-fields for which the compatibility formula holds.

BKMP remodeling conjecture. All-genus B-model topological-string amplitudes on $(\check{\mathcal{X}},\Omega)$ are essentially equal to the Eynard–Orantin invariants of $C_q$.

Let the space be a toric Calabi–Yau 3-manifold or 3-orbifold with Aganagic–Vafa outer D-branes, let its partition function be the corresponding brane partition function, and let it…

Let $Z(N,\xi,\hbar)$ be the fermionic traces of the operator $\rho_{\mathbb{F}_2}$. In the ’t Hooft limit, scale the parameter appearing in the operator as … where $t_B$ is a gener…

Spectral determinant conjecture. The spectral determinant is

The remodeling conjecture. The topological recursion should calculate the open Gromov–Witten invariants of $X$ for all genera.

Let $X$ be a toric Calabi–Yau manifold with mirror family $\check{X}_y$, and let … be the SYZ map, defined by … where $1+\delta_i(q)$ are generating functions of the genus $0$ open…

Let $X$ be a toric Calabi–Yau threefold with mirror curve, and let the Eynard–Orantin topological recursion applied to that curve produce free energies $F_g$. For $X=\mathbb{C}^3$,…

Let an isoradially embedded dimer have an $R$-dimer determined by the superconformal $R$-charges, with modular parameter $\tau_R$. Let $(X,\beta)$ be the corresponding Belyi pair,…

Let $\mathfrak{X}$ be a toric Calabi–Yau threefold, let $\hat{\mathfrak{X}}$ be its mirror, and let $\mathcal{S}_{\hat{\mathfrak{X}}}$ be the mirror curve defined by … Denote by…

BKMP conjecture. These integrated correlators are equal to the A-model framed open Gromov–Witten potentials of $(X,L)$, where $L$ is the mirror brane to $\Gamma_X\subset\widehat X$…

The topological string partition function is associated with a toric Calabi–Yau manifold and its mirror curve. The remodeling conjecture. The topological string partition function…

Let the mirror of a toric Calabi–Yau manifold be equipped with its mirror curve and the modified topological recursion using … The recursion produces open and closed B-model quanti…

The recursion relation of Eynard and Orantin associates generating functionals to a spectral curve. A suitable generalization replaces the spectral-curve data by the mirror curve o…