11 problems

Let $X$ and $X^!$ be symplectically dual varieties arising from Coulomb-branch and resolved Higgs-branch constructions for the gauge theory $(G,N)$. Let $\zeta$ be the relevant roo…

Let $X$ and $X^!$ be symplectically dual varieties arising respectively from Coulomb-branch and Higgs-branch constructions for the gauge theory $(G,N)$. Let $R$ be the coefficient…

Let $X$ and $X^!$ be symplectically dual, and let $\mathcal{A}$ be the universal quantization of $X$. The quantization exact sequence and the equivariant cohomology exact sequence…

Let $X$ and $X^!$ be symplectically dual, and let $Y$ be the affinization of $X$. Let $Y^T$ denote the scheme-theoretic fixed locus of $Y$ under the $T$-action, with grading induce…

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

Elliptic stable-basis duality conjecture. For any $p_1,p_2\in X^H$,

Let $I=(I_0,I_1)$ be a finite quiver with dimension vector ${\bf v}=(v_i)_{i\in I_0}$ and framing ${\bf w}=(w_i)_{i\in I_0}$. Let $A$ act on the Nakajima quiver variety…

Let $X\to X_0$ and $X^!\to X_0^!$ be symplectic dual conical symplectic resolutions, and let a torus $\mathbb{T}$ act on $X_0^!$. Denote by $H^*(X)$ the cohomology of $X$ and by th…

Let $\mathfrak{M}$ and $\mathfrak{M}^!$ be a symplectic dual pair, let $E$ be the Yoneda algebra of the category $\mathcal{O}$ for $\mathfrak{M}$, and let $\widetilde E$ be its uni…

Let $\mathfrak{N}$ and $\mathfrak{N}^!$ be as in the symplectic duality conjecture, let $A$ be a quantization of $\mathscr{N}$, and let $A_0$ be its central quotient quantizing…

Let $\mathfrak{N}$ and $\mathfrak{N}^!$ be a symplectic dual pair of cones admitting projective symplectic resolutions $\mathfrak{M}$ and $\mathfrak{M}^!$. Let $\mathscr{N}$ be the…