88 problems

Bayer–Macrì–Toda Bogomolov–Gieseker inequality. For any $(b,w)\in U$ and $\nu_{b,w}$-semistable $E\in\mathcal D(X)$, one has

Let $X$ be a smooth 3-fold and let $\mathscr{L}_1,\mathscr{L}_2$ be line bundles on $X$ satisfying … Let…

Let $\vec{\pi}_a$ be $n$-tuples of plane partitions for the four legs, and let $\vec{v}=(v_1,\ldots,v_n)$ and $\vec{w}=(w_1,\ldots,w_n)$ be the flavor fugacities of the $n$ D8 and…

Independence conjecture. The series $\mathsf{DT}_{r,k}^{\rm ell}(\mathbb{A}^3,q,t,w;p)$ does not depend on the elliptic parameter $p$.

Let $\lambda,\mu,\nu,\rho$ be finite plane partitions, with at most two of them non-empty in the stable-pairs case. Let…

Katz's genus-zero GV/DT conjecture.

Let $\mathcal{Z}$ be a hard-Lefschetz $3$-orbifold, and let … be a crepant resolution. Let $DT_{mr}(-)$ denote the reduced, multi-regular Donaldson–Thomas potential, and let…

DT/PT $\mathbb{Z}_{n}$-orbifold vertex correspondence. If $\nu$ is multi-regular, then

Let $X$) be a smooth projective complex variety. Let $\mathfrak I_n(X,\beta)$ be the moduli space of $1$-dimensional closed subschemes $Z$ of $X$ satisfying the paper's fixed numer…

Derived skein–DT conjecture. There is an isomorphism

Skein–DT sheaf conjecture. There is an isomorphism

Let the orientation constructed by Joyce and Upmeier be the orientation used to define the motivic Donaldson–Thomas invariants in this paper, and let the orientation used by Behren…

Maulik–Ranganathan's conjecture. The generating functions satisfy

Let $\vec{\lambda}_{A,+}$ be $n$-tuples of plane partitions and $\vec{\lambda}_{A,-}$ be $m$-tuples of plane partitions for the six surfaces. Let $v_\alpha=e^{\mathfrak{a}_\alpha}$…

Let $\vec{\pi}_{a,+}$ be $n$-tuples of plane partitions and $\vec{\pi}_{a,-}$ be $m$-tuples of plane partitions for each of the four legs. Let $v_\alpha=e^{\mathfrak{a}_\alpha}$,…

Let $n,m$ be nonnegative integers indexing D8/D8$'$ and opposite-brane pairs, and let $v_\alpha=e^{\mathfrak{a}_\alpha}$, $w_\alpha=e^{\mathfrak{b}_\alpha}$,…

Gromov–Witten/Donaldson–Thomas correspondence conjecture. With this change of variables,

Stable-pair/Donaldson–Thomas correspondence conjecture.

Let $\bold X$ be a logarithmic Calabi–Yau 3-fold, let $D^{[\beta]}$ be the product of the relevant Hilbert schemes of points on the interiors of the boundary divisors, and let … be…

Let $\lambda$ be a Young diagram. For each box $\Box\in\mathbb{Z}^2_{\geq 0}$, let $p_{\lambda,\Box}=\prod_{\Box'\in H_\lambda(\Box)}q_{\Box'}$, where $H_\lambda(\Box)$ is the hook…

Let $\mathsf{T}_{\four}^{K}(x)$ denote the D8 $qq$-character and let $\mathsf{f}^{K_{1}|K_{2}}_{\four\four}(x_{1}/x_{2})$ be the corresponding one-loop factor. D8 quadratic commuta…

Let $G$ be a reductive group and $M$ a closed, connected, oriented $3$-manifold. Let $\Loc^{\ff}_{G}(M)$ be the representation variety of $G$-local systems, let…

Let $G$ be a reductive group, $G^{L}$ its Langlands dual, and $M$ a closed oriented $3$-manifold. Kapustin–Witten Langlands duality conjecture. There is an isomorphism … This is mo…

Let $X$ be a smooth projective threefold over $\mathbb{R}$, equipped with an isomorphism … for some line bundle $L$ on $X$. For $n\geq 0$, let $\tilde{I}_n$ be the quadratic degree…

MNOP correspondence. The invariants