17 problems

Let $\mathcal{T}$ be a four-dimensional $\mathcal{N}=2$ superconformal field theory, let $\mathbb{V}(\mathcal{T})$ be its associated vertex operator algebra, and let a surface defe…

Resummed dual-period conjecture. At every resonant point,

Resummed dual-period conjecture. On each lateral branch,

NS regularity conjecture.

Let $S$, $\rho$, and $\tau$ be the parameters appearing in the defect instanton partition function, and consider the dual transformation $S\to S-\tau$. Symmetry conjecture. This tr…

Entire-periodization conjecture. The function $G(\sigma)$ is well defined and is an entire function of $\sigma$. This analytic property would justify the periodization used to rewr…

Electric-magnetic integral-transform conjecture. At the level of the $\epsilon$ expansion,

Let $\Psi_N(z,t)$ denote the matrix-model insertion in, and let $Z^{\rm I}(z,t,\sigma)$ denote the type I surface-defect partition function in. The magnetic frame is the duality fr…

Let a codimension-two surface defect of general type be described by a parabolic structure, and let $\widehat{\mathfrak{sl}}_N$ denote the affine current algebra. Drinfeld–Sokolov…

Let $C$ be a Riemann surface, let $B$ be the base of the Hitchin fibration, let $\Sigma_b\subset T^*C$ be the spectral curve, and let $F_x$ be the cotangent fiber over $x\in C$. Su…

Let $\mathcal{T}$ be one of the class-$\mathcal{S}$ theories considered in the paper, let $\mathbb{V}(\mathcal{T})$ be its associated vertex operator algebra, and consider the Schu…

Consider the pure, non-conformal linear $SU(2)^{\times n}$ quiver system with functions $\tau_0$ and $\tau_1$ satisfying … … Their generalized Kiev ansatz has coefficients…

Consider the four-dimensional ${\mathcal N}=2$ supersymmetric gauge theory with gauge group $SU(2)$ and $N_f=4$ matter hypermultiplets in the fundamental representation. Let a regu…

Let $M$ be the three-manifold supporting a link $L$, and let ${{\mathbb S}}[L]$ denote the BPS observable associated with inserting the surface defect along $L$. Write $[L]$ for th…

Let $p$, $q$, and $t$ be superconformal-index fugacities, let $a_1$ and $a_2$ be fugacities for the $SU(3)$ flavor symmetry, and let $z$ be the gauge-integration variable. Write…

Let $\mathcal{S}^{2d-4d}_{\vartheta,\vartheta'}(X_{\gamma})$ be the $2d$-$4d$ spectrum generator for the BPS spectrum with central-charge phases in the wedge…

Consider $\mathcal{N}=2$ $\operatorname{SU}(N)$ gauge theories with a surface defect belonging to the class classified by partitions of $N$. Their dual conformal-block description…