10 problems

Let an RCFT have characters whose leading exponents are $-\frac{c}{24}+h_A$, and let the associated contour integrals have leading exponents $\frac12(p+\Delta_A)$. Suppose these ex…

Fixed-order MLDE conjecture. For any given 4d ${\cal N}=2$ superconformal field theory, ${\cal I}_k(q)$ solves a modular linear differential equation of fixed order and Wronskian i…

Let $H_{\mathfrak g}$ denote the rank-3 theory associated with a Lie algebra $\mathfrak g$, and let its Schur index be the protected generating function identified conjecturally wi…

Let $(E_{7+1/2})_k$ denote the affine vertex operator algebra associated with the intermediate Lie algebra $E_{7+1/2}$ at level $k$. Rationality conjecture. The affine VOA…

Let $p$ and $p'$ be odd integers greater than $13$. Let $\{\eta^{c_{\operatorname{eff}}}\operatorname{ch}_{\,2,\,p\,;\,1,\,s}\}$ and…

Let $V$ be a simple affine vertex algebra associated with one of the Lie algebras in the $\mathrm{DC}$ series … at level $-h^{\vee}/6-1$. Let $\chi^{\mathrm{twi}}(q)$ denote a norm…

Let $V_{-4/3}(A_2)$ be the admissible affine vertex operator algebra at level $-4/3$, and let $V_{-4/3}(A_2;2\varpi_1)$ and $V_{-4/3}(A_2;2\varpi_2)$ denote the corresponding modul…

Let $V=V_{-3/2}(G_2)$ be the affine vertex operator algebra at admissible level $-3/2$, and let $f_0$ and $7f_{4/5}$ be the solutions of the fourth-order modular linear differentia…

Indicial-root bound conjecture. For all $l$, every indicial root of this form satisfies $m<l$.

Existence conjecture. Such a component exists for all $l$.