11 problems

Let $\Gamma$ be the charge lattice of a four-dimensional $\mathcal N=2$ theory, with Dirac pairing $\langle\cdot,\cdot\rangle$, and let $\mathcal O(q)$ be the Kontsevich–Soibelman…

Let a four-dimensional ${\mathcal N}=2$ superconformal field theory have Schur index given by a formal power series in $q$. A modular linear differential equation (MLDE) is a linea…

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…

Let $A_\mathfrak{q}$ be the space on which the line defect Schur indices define a pairing, and let $I_{a,b}(\mathfrak{q})$ denote the Schur index associated with line defects $L_a$…

Let $\mathcal{T}$ be a four-dimensional $\mathcal{N}=2$ superconformal field theory, let $\mathcal{I}_{\mathcal{T}}(q)$ be its Schur index, and let $\mathbb{V}(\mathcal{T})$ be the…

Stabilization conjecture. For every fixed $k$, the coefficient of $q^k$ in $\operatorname{Tr}M(q)$ stabilizes to a limiting value for sufficiently large $N$.

Nonnegative-power conjecture. The series $S(q)$ and $\overline{S}(q)$ can be expanded as Taylor series in $q$, with no negative powers of $q$.

Generalized commutative-diagram conjecture. The commutative diagram relating line-defect Schur indices to vacuum expectation values at the $U(1)_r$-invariant vacua exists more gene…

Let $(A_{k-1},A_{N-1})$ be the generalized Argyres–Douglas theory with $\operatorname{gcd}(k,N)=1$, and let $\chi^{W_k,(k,k+N)}_0(q)$ denote the vacuum character of the $(k,k+N)$ m…

Let $\mathcal{I}_{A_{2n}}(q)$ be the Schur index of the $A_{2n}$ Argyres–Douglas theory, and let $\chi^{(2,2n+3)}_0(q)$ be the vacuum character of the $(2,2n+3)$ Virasoro minimal m…

Let $\I(q,z_1,\dots,z_n)$ be the flavor-refined Schur index of a four-dimensional $\mathcal{N}=2$ theory of Coulomb-branch rank $r$, let $\mathcal{O}(q)$ be its quantum-torus opera…