47 problems

Finite-set bijection conjecture. There is a bijection

Let the diagonal unitary minimal model $(D_6,A_{10})$ be deformed by the relevant operator $\phi_{\frac9{11}}$, with no other relevant operators turned on, and suppose the flow is…

Admissible monomial basis conjecture. For $1\leq r\leq p-1$, the set of admissible monomials of the form defined in the source, where $r_L=r$, $r_0=1$, and $s=1$, is a basis of…

Monomial basis conjecture. In the general case $p<p'$, the monomials satisfying the quadratic exclusion condition

Let $(\Lambda V,d)$ be an elliptic minimal algebra whose differential has homogeneous length. Write … where $e$ is given by the formula of the theorem on homogeneous-length differe…

Let $p,q$ be positive integers, set … and for integers $m,n$ set … For the Lie superalgebra ${\mathcal L}_s$ and the irreducible module $L(c_{p,q},h_{p,q}^{m,n})$, finite-dimension…

Let $p$ and $q$ be parameters, define … and define … Let ${\mathcal L}_s$ be the Lie superalgebra introduced above, and let $L(c_{p,q},h_{p,q}^{m,n})$ denote the corresponding irre…

Let $p_+$ and $p_-$ be the parameters of the logarithmic $(p_+,p_-)$ model. Let ${\bar{\mathscr{C}}}$ be the space of generalized characters, let $\mathscr{G}$ be the subspace desc…

Magnonic pseudoenergy conjecture. Two magnonic pseudoenergies, $\varepsilon^{(1)}$ and $\varepsilon^{(2)}$, should be introduced to handle the non-diagonal nature of the kink scatt…

Generalized E-series limit conjecture. The limit

Universal structure-constant conjecture. Structure constants are given by a universal expression built from the double Gamma function, multiplied by polynomial functions of…

Let $C=M(p,p+1)$ be a unitary A-type Virasoro minimal model, and suppose the transition at $R_0=R_C$ is directly between the two-dimensional CFT $C$ and a two-dimensional TFT. Let…

Let $C=M(p,p+1)$ be a unitary A-type Virasoro minimal model, and let $R_C$ be a value such that for all $R<R_C$ the continuum model has the central charge of $C$. Low-cutoff contin…

Let $\mathrm{SM}(3,5)$ denote the fermionic minimal model and let $\mathrm{Majorana}$ denote the Majorana theory, with the conjugate taken at the level of the bulk TQFT. Consider t…

Let $\mathrm{SM}(3,5)$ denote the fermionic minimal model and let $\mathrm{SO}(1)_1$ denote the invertible spin-TQFT factor. Consider the bulk TQFT associated with the fourth-sheet…

Let $N$ be an integer coprime to $6$, let $r$ be as in the construction, and let $Z^\circ_{N,r}$ and $W_{N,r}^{\mathsf{small}}$ be the models defined in the nonsingular-model and g…

Let $N$ be an integer coprime to $6$, let $r$ be as in the construction, and let $Z^\circ_{N,r}$ and $W_{N,r}^{\mathsf{small}}$ be the nonsingular and closer-to-minimal models defi…

Consider the coset … which has central charge $57/40$. Here $W_k(E_7,f_\theta)$ denotes the indicated affine $W$-algebra. Effective minimal-model conjecture. This coset is isomorph…

A differential graded Lie algebra $L$ is connected if it is concentrated in non-positive cohomological degrees, and its cohomology is nilpotent when it is nilpotent as a graded Lie…

Let $(E_{7+1/2})_k$ denote the affine VOA at level $k$, and let $M_{\rm eff}(13,4)$ be the effective description of the minimal model $M(13,4)$ with effective central charge…

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

Let $X$ be a Calabi–Yau variety, and consider its movable cone and the minimal models birational to $X$. Movable-cone Cone Conjecture. The variety $X$ should have only finitely man…

Consider the simple topological defect lines in the relevant fermionic minimal models, with labels determined according to $m\bmod 4$. For $m=0,3\bmod 4$, the m-type lines are…

General dessin conformal-block conjecture. For a dessin satisfying the proposition's conditions, it corresponds to a family of 4-point CBs whose states follow the stated table.

Dessins' conformal-block information conjecture. The dessins in question should contain the full information for certain CBs.