13 problems

Let $\Sigma^2\xrightarrow{\iota}X^6\xrightarrow{\pi}X^4$ be a fibration with monodromy representation $\rho:\pi_1(X^4)\to\operatorname{Sp}(2g,\mathbb{Z})$. Assume twisted Stiefel–W…

Mirror-symmetry conjecture. When $n>0$, there is a bijection between the simple modules $\{L_a\}$ of $V_{g,n}$ and the fixed manifolds $\mathcal{M}_{g,n}^T=\{M_a\}$ such that, for…

Consider two class $\mathcal{S}$ theories $T[\mathfrak{g}, C^{(1)}, D^{(1)}]$ and $T[\mathfrak{g}, C^{(2)}, D^{(2)}]$ on stable Riemann surfaces $C^{(1)}$ and $C^{(2)}$, with full…

Let $V_{g,n}$ be the vertex operator algebra associated with the genus-$g$ theory with $n$ regular punctures, and let $\{L_a\}$ be its simple modules. Let ${\cal M}_{g,n}$ be the m…

Let $V_{g,0}$ be the vertex operator algebra associated with the unpunctured genus-$g$ theory, with simple modules $\{L_a\}$ and conformal dimensions $h(L_a)$. Let ${\cal M}_{g,0}$…

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 $\Sigma_{g,p}$ be a genus-$g$ surface with $p$ punctures, let $\Gamma$ be the charge lattice, and let…

Let $\mathbb{V}(\mathcal{T}_{1,2})$ be the vertex operator algebra associated with the class-$\mathcal{S}$ theory $\mathcal{T}_{1,2}$, and let the free $bc\beta\gamma$ system be th…

Higher-genus VOA conjecture. The higher-genus VOAs will enjoy $\mathrm{USp}(2g)$ outer automorphism symmetries, and their $\mathrm{USp}(2g)$-invariant subVOAs will be isomorphic to

Let $C$ be an oriented Riemann surface with a pants decomposition determining a weak-coupling Lagrangian duality frame with gauge algebra … For a line defect $L({\cal P},\zeta)$ as…

Let $A_{N-1}$ theories be associated with Riemann surfaces having full punctures, and let a candidate BPS graph be constructed by replacing each branch point of an $A_1$ BPS graph…

Let $C_L$ and $C_R$ be Riemann surfaces with collections of defects $D_L$ and $D_R$, each containing at least one full defect whose global symmetry is a compact group $G$ with Lie…

Let ${\cal C}$ be the Riemann surface on which the six-dimensional $(2,0)$ theory is compactified, and suppose the resulting theory flows under the renormalization group to a four-…