9 problems

Let $X$ be a Poisson variety and let $U$ be its canonical quantization, the preferred quantization associated with Losev's classification. A quantization is simple if it has no non…

Let $M_{eq,reg}$ be the $D$-module of twisted traces, let $\mathcal{A}_0^2$ be the degree-$2$ part of the relevant quantization algebra, and let $s$ be the Artin--Schreier map defi…

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…

Simplicity conjecture. The algebra $\cA_0$ is simple.

$\mathcal{O}$-singular locus conjecture. The locus $\mathfrak{c}^{\mathcal{O}-\mathrm{sing}}$ coincides with the union of singular hyperplanes.

Let $Y=\mathbb{C}^2/\Gamma$, where $\Gamma$ is a finite subgroup of $\operatorname{SL}_2(\mathbb{C})$, and let $\mathfrak{h}_\Gamma^*$ be the Cartan space associated with the ADE t…

Let $\widetilde{\mathop{\mathrm{Gr}}{}^\lambda_\mu}$ be a smooth symplectic resolution equipped with a conic $\mathbb C^*$-action, and let $Y^\lambda_\mu(\mathbf R)$ be the associa…

Let $X$ be a symplectic resolution of the affine variety $X_0$, let $\mathfrak{p}=H^2(X)$, and let $\mathcal{A}_\lambda$ be the algebra of global sections of the quantization speci…

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…