54 problems

Let $(Q,W)$ be a self-dual quiver with potential, and let $\tau$ and $\widetilde{\tau}$ be self-dual weak stability conditions on the associated self-dual abelian category. Let…

Let $Q=(\bullet\rightrightarrows\bullet)$ be the self-dual $\tilde{A}_1$ quiver with its two vertices exchanged by the contravariant involution, and write $\tilde{A}_1^{u,v}$ for t…

In the orthogonal vector-space situation, let $\binom{x}{n}$ denote the generalized binomial coefficient, let $\boldsymbol{D}_n$ and $\boldsymbol{B}_n$ denote the corresponding Dyn…

Let $\mathcal{T}'$ be a $\Gamma$-labelled tree. In the Gaiotto–Moore–Neitzke asymptotic expansion, consider the total contribution to wall crossing obtained by choosing every possi…

MNOP dimension-zero Donaldson–Thomas conjecture. For any smooth projective threefold $X$, the dimension-zero Donaldson–Thomas series has the form

Fix $\mathbb K=\mathbb C$. Let $P$ be a Calabi–Yau $3$-fold, set $\mathcal A=\operatorname{coh}(P)$, and let $\mathfrak F_{\mathcal A}$ and $K(\mathcal A)$ be as in the source. Let…

Let $X$ be a Calabi–Yau threefold, fix $g\ge0$, and suppose $I_{1-g}(X,\beta)$ parametrizes ideals of local complete intersection curves of arithmetic genus $g$. Let…

Let $X$ be a Calabi–Yau threefold, meaning that $K_X$ is trivial. For curve classes $\beta\ne0$, let $Z^{\mathrm{DT}}(X)'$ be the reduced Donaldson–Thomas partition function, and l…

Let $Y$ be a Calabi–Yau $4$-fold, let $\beta\in H_2(Y,\mathbb{Z})$ be a curve class, and let $\mathbf{M}_{\beta}(Y)$ be the moduli space of one-dimensional stable sheaves $F$ on…

Let $M$ be a closed, oriented $3$-manifold, and write its skein partition function as an Euler expansion with integer exponents $c_k$. Positivity conjecture for skein partition fun…

Let $r$ be a positive integer, let $[[200~\mathbb C^4/\mathbb Z_r]$ be the quotient Calabi–Yau $4$-orbifold considered in the source, and let $q_0,\ldots,q_{r-1}$ be variables. Wri…

Let $X$ be a projective Calabi–Yau $4$-fold. Write $\operatorname{Hilb}^n(X)$ for the Hilbert scheme of $n$ points on $X$, let $L\to X$ be a line bundle, and distinguish Gromov–Wit…

For integers $n\ge 0$ and $\delta\in\frac12\mathbb Z$, let … where $\mathrm{PP}$ is the set of plane partitions and $w_-$, $w_0$, and $w_+$ are the sums of the entries strictly bel…

The genus zero log/local/open correspondence. The invariants satisfy

Local Fano threefold genus-zero correspondence. One has

Cao–Toda's genus-one descendent correspondence conjecture. Via some suitable choice of orientation on the moduli space, one has, for all $\gamma\in H^2(X,\mathbb Z)$,

Cao–Maulik–Toda's genus-zero correspondence conjecture. Via some suitable choice of orientation on the moduli space, one has

Let $X$) be a projective Calabi–Yau $4$-fold and let $L$ be a line bundle on $X$. Define … Here $M(q)=\prod_{i=1}^{\infty}(1-q^i)^{-i}$ is the MacMahon function. Cao–Kool's conject…

Let $Q$ be the quiver for the local phase labelled $\mathrm{PdP}_2$, let $e_i$ be its vertex dimension vectors, and let $\mathrm{d}$ be the dimension vector of a single D0-brane. L…

Let $Q$ be the quiver for the local Hirzebruch surface $K_{\mathbb{F}_0}$, let $e_i$ be its vertex dimension vectors, and let $\mathrm{d}=(1,1,1,1)$ be the dimension vector of a si…

Let $(Q,W)$ and $(Q',W')$ be quivers with potential related by mutation at a vertex $k$, and let $d,d'$ and stability weights $\theta,\theta'$ be related by the mutation formulas i…

Let $X$ be a Calabi–Yau $4$-fold and let $M_1(X,\beta)$ be the moduli scheme of one-dimensional stable sheaves $F$ with $[F]=\beta\in H_2(X,\mathbb Z)$ and $\chi(F)=1$. Let…

Let $\mathcal{C}_{\mathfrak{g},\Sigma}$ be the mutation class associated to an admissible pair $(\Sigma,\mathfrak{g})$. Let $\mathbf{w}_0=(w_0,\ldots,w_0)\in W(\mathfrak{g})^p$ be…

Let $(\beta,n)\in\mathbb{Z}^2$ satisfy … Assume $\beta\neq 0$ or $n>0$. Fourier–Mukai wall-avoidance conjecture. For every integer solution $(c,d)$ of … one has … This is a constra…

Let $(A,H)$ be a principally polarized abelian threefold with Picard rank $\rho(A)=1$. For nonzero $(\beta,n)\in\mathbb{Z}^2$, define…