114 problems

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 $\Omega_{\gamma,\theta}(y)$ denote the refined, or motivic, Donaldson–Thomas invariant associated with charge $\gamma$ and stability parameter $\theta$. In a quantum torus, def…

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 $X$ be the Calabi–Yau threefold in the paper, and let $\mathcal{M}$ be the moduli stack of objects $E\in D^b\operatorname{Coh}(X)$ satisfying … For $[E]\in\mathcal{M}$, let $G$…

Let $K\subset S^3$ be a knot, let $U$ be the holonomy of the $U(N)$ Chern–Simons gauge field around $K$, and let $V$ be a source whose traces are summed over representations $r$. W…

Donaldson–Thomas crepant resolution conjecture. One has

MNOP conjecture. The rank-one Donaldson–Thomas theory of $X$ should be equivalent to the Gromov–Witten theory of $X$.

Joyce–Song multiple cover conjecture. We have

Asymptotic ADHM generating-series conjecture. The generating series satisfies

Let $X$) be a Calabi–Yau $3$-fold, let $\beta$ be a nonzero effective curve class, and let $\mathop{\rm DT}\nolimits'_{\beta}(X)$ denote the coefficient of $t^\beta$ in the reduced…

Let $X$ be a Calabi–Yau $3$-fold. The Donaldson–Thomas (DT) theory of $X$ counts stable coherent sheaves on $X$, while Gromov–Witten theory counts holomorphic curves in $X$. DT/Gro…

Let $X$ be a smooth projective three-fold. Write $Z_{DT}(X,q)_0$ for the degree-zero Donaldson–Thomas generating series, let $T_X$ be the tangent bundle, let $K_X$ be the canonical…

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

Let $X$ be a polarized Calabi-Yau threefold, let $\beta$ be a curve class, and let $S(X,\beta)$ be the moduli space whose Donaldson–Thomas invariant is … Let $N_\beta(X)$ denote th…

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…

Stokes-constant conjecture. The Stokes constant associated with the singularity … gammainGamma$.

Resurgence conjecture. For every analytic section of $E$ and each $\gamma\in\Gamma$, one can naturally associate a resurgent series in the standard coordinate $z$ on $\mathbb{C}$.

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 $\mathcal{M}^{\mathrm{vert}}(\mathbb{P})$ be the vertical moduli space of a good degeneration, equipped with the global $(-1)$-shifted potential function $\mathbb{W}=f\cdot g$.…

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 toric Calabi–Yau $4$-fold, let $\mathscr L$ be a $\mathbb T$-equivariant line bundle, and let $\mathsf{DT}_{X,\mathscr L}(m,q)$ denote the generating function of zero-…

Let a 4d $\mathcal{N}=2$ class $\mathcal{S}$ theory have a BPS spectrum encoded in a Kontsevich–Soibelman motivic wall-crossing formula, and let … can be generalized to all such 4d…

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…

The quadratic Donaldson–Thomas conjecture. In $W(\mathbb{R})[[q]]=\mathbb{Z}[[q]]$, one has