16 problems

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

Hypertoric Fukaya-category equivalence conjecture. There is a natural equivalence between

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…

Enhanced abelian localization conjecture. With a suitable choice of the shifts $hat{\Upsilon}$ that depends on the choice of $E$, for every generic $theta\to C$ and…

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

Abelian localization conjecture. Suppose that $(*)$ holds. Then the following two conditions are equivalent: (1) abelian localization holds for the quantization…

Singular hyperplane conjecture. The algebra $\mathcal{A}_lambda$ has infinite homological dimension if and only if $lambda$ lies in a singular hyperplane.

Finite homological dimension conjecture. The following two conditions are equivalent: (1) the algebra $\mathcal{A}_lambda$ has finite homological dimension; (2) derived localizatio…

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 $\mathfrak g$ be a semisimple simply-laced Lie algebra, let $\lambda$ and $\mu$ be dominant coweights, let $\overline{\mathop{\mathrm{Gr}}{}^\lambda_\mu}$ be the corresponding…

Let $X$ be a symplectic resolution, let $\mathfrak{A}$ be its universal quantization, and let $\mathcal{A}_\lambda$ be the specialized algebra of global sections. McGerty–Nevins lo…

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…