10 problems

Half-index conjecture. These inner products can be computed by a careful deformation and a chain of dualities that maps them to Schur half-indices, namely twisted partition functio…

WZW wave-function conjecture. The wave-functions $\mathcal Z(\mathbf{x})$ can be identified with the partition functions of WZW models with target $G_\mathbb{C}/G$. This proposes a…

Let $B_c$ be the boundary condition used to construct the state $|1\rangle$ in the Hilbert space of complex Chern–Simons theory, and let $W_a$ denote the boundary-skein operators.…

Schur-quantization isomorphism conjecture. The isometry is an isomorphism, so Schur quantization of theories of class $\mathcal S$ provides a consistent quantization of complex Che…

Let $G$ be a gauge group with Langlands dual group $G^{\vee}$, and let $\rho_a$ denote an abelian flat $G$-connection. Let $\rho_b$ and $\rho_c$ denote, respectively, abelian and n…

Let $\alpha$ and $\beta$ be critical points, let $\tau(\alpha)$ and $\tau(\beta)$ denote their corresponding torsions, and let $\mathcal{S}_{\alpha}^{\beta}$ be the Stokes coeffici…

Let $M_3$ be a closed 3-manifold, and let $\widehat{Z}_b(M_3,q)$ denote its non-perturbative $q$-series. Let $\hbar$ be the variable of the perturbative expansion and set…

Let ${\cal K}$ be a hyperbolic knot, let $Z_{\cal K}(\tau)$ be its Andersen–Kashaev invariant at vanishing holonomy, and let $V_{\cal K}$ be the complexified volume of the three-sp…

3D-index entry conjecture. A distinguished entry of the Stokes automorphism matrix is the 3D-index of Dimofte–Gaiotto–Gukov.

Resurgence and Stokes factorization conjecture. These perturbative series are resurgent, their trans-series involve two non-perturbative variables, and their Stokes automorphism sa…