13 problems

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…

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…

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.

Let $(\Lambda V,{\operatorname{d}})$ be a minimal Sullivan algebra. Let … be a relative minimal model with $\deg t_i=2$ for $1\leq i\leq r$, and suppose that … is finite dimensiona…

Vanishing conjecture. The Grothendieck group of the singularity category vanishes:

In the $(p,q)$-system, let $\mathfrak g$ be defined by $2\mathfrak g=(p-1)(q-1)$, and let $\{\theta_a\}_{a=1}^{2\mathfrak g}$ denote the D-instanton and ghost D-instanton fugacitie…

Let $c=c{p,q} eq 0$ and let $L(c,h)$ be a minimal model. Let $V{\alpha,\beta}^{\prime}$ be an irreducible module from the intermediate series, and let an admissible triple mean a…

Let ${p\mathcal{A}ss}^n_d$ be the operad for degree-$d$ partially associative $n$-ary algebras, in the non-Koszul parity case $n \not\equiv d \pmod{2}$. A gap in a minimal model me…

Constant-term conjecture. This constant term equals

Let $F$ be a simply-connected Calabi–Yau manifold. A minimal model of $F$ is a minimal model in its birational class. Morrison–Kawamata finiteness conjecture. There are finitely ma…