88 problems

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 $v_\alpha=e^{\mathfrak{a}_\alpha}$, $w_\alpha=e^{\mathfrak{b}_\alpha}$,…

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…

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

Fix $n\in\mathbb{Z}_{\geq 0}$, let $\mathrm{H}_n=\operatorname{Hilb}^n(\mathbb{A}^3)$ be the Hilbert scheme of ideals of colength $n$ in $\mathbb{C}[x,y,z]$, and let…

Let $\vec{\mathtt{q}}=(\mathtt{q}_0,\mathtt{q}_1,\mathtt{q}_2,\mathtt{q}_3)$ and $\mathtt{Q}=\mathtt{q}_0\mathtt{q}_1\mathtt{q}_2\mathtt{q}_3$. Define … where…

Let $G=\mathbb{Z}_r<\mathrm{SU}(2)<\mathrm{SU}(4)$ or $G=\mathbb{Z}_2\times\mathbb{Z}_2<\mathrm{SO}(3)<\mathrm{SU}(4)$. Let $X\to\mathbb{C}^4/G$ be the Nakamura $G$-Hilbert crepant…

Let $X_5$ be the quintic threefold, let $H$ be its hyperplane class, and set $\kappa=H^3=5$. Write $\overline{\Omega}_H$ for the rank-zero invariant with Chern-character arguments…

Integral rank-one conjecture. The $\mathbb{K}$-module $\mathrm{P}(nd)_{nv}$ is free of rank one.

Let $X$ be a holomorphic symplectic $4$-fold and let $M_\beta$ be the moduli scheme of one-dimensional stable sheaves $F$ on $X$ with $\operatorname{ch}_3(F)=\beta$ and $\chi(F)=1$…