15 problems

Homological 3d mirror symmetry conjecture. There are 3d mirror pairs $X$ and $X^{!}$ whose A-model 2-category and B-model 2-category are interchanged under mirror symmetry.

Let $X$ and $X^!$ be symplectically dual conical Hamiltonian symplectic resolutions, with equivariant and Kähler roots, rings of differential operators, and associated $D$-modules…

Let $T$ be a torus, let $\mathfrak{t}$ be its Lie algebra, and let $T^{\vee}_{\mathbb{C}}$ be the complex dual torus. Let $\mathrm{BFM}(T^{\vee})$ denote the associated BFN space.…

Dinkins–Smirnov conjecture. The vertex functions of zero-dimensional quiver varieties factorize into a product of $q$-binomials, each of which corresponds to a repelling weight spa…

Let $G$ be the gauge group, let $U$ be the algebra appearing in the description of bulk lines, and let $\operatorname{Mod}$ denote the category of modules. Arakawa's chiral univers…

Let boundary VOAs arise from topologically twisted $\mathcal{N}=4$ SQFTs, and let their associated varieties be the corresponding Poisson-geometric spaces. Let Slodowy varieties an…

Let a non-rank-zero 3d $\mathcal{N}=4$ SQFT be a three-dimensional supersymmetric quantum field theory with nonzero rank, and let its boundary VOA be obtained after a topological t…

Let $Y$ be a Hamiltonian $G$-manifold with maximal torus $T$, Weyl group $W$, and root system. Let $(Y^\vee,f)$ be its two-dimensional mirror Landau–Ginzburg model, let…

Let $Y$ be a Hamiltonian $G$-manifold, with maximal torus $T$ and Weyl group $W$, and suppose the $T$-action on $Y$ extends to a Hamiltonian $G$-action. Let…

Let $D_p^b(\mathfrak{sl}_N)$ be the Argyres–Douglas theory with maximal regular puncture, and let $m=\gcd(p,b)$, $n=b/m$, and $p=m(n+k)$. The 3d-mirror type I equivalence conjectur…

Let $X$ and $X'$ be 3d mirror varieties, and let the elliptic stable envelopes of $X$ and $X'$ be defined. Denote by “properly renormalized” the elliptic stable envelopes after the…

Let $X$ be a holomorphic symplectic quotient with vertex function $V(q,z,a)$, where $q$ is a complex number with $|q|<1$, $z$ denotes the Kähler parameters, and $a$ denotes the equ…

3d mirror vertex-function conjecture. The vertex functions of $X$ with vanishing equivariant parameters are given by the Taylor series expansions of

Vertex-function character formula. The vertex functions of $X$ with vanishing equivariant parameters are given by the Taylor series expansions of

$3d$-mirror symmetry. For every symplectic variety from this class, there exists a dual variety $X'$ called the $3d$-mirror of $X$.