5 problems

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…

Let $X$ be an irreducible affine Poisson variety admitting a symplectic resolution $\widetilde{X}\to X$. Let $A_\hbar$ be a deformation quantization of $\mathcal{O}_X$, and let…

Alev's completeness conjecture. For every integer $n\geq 2$, these $\pi(n)$ constructed graphs are the only solutions of the equation.

Simple-graph uniqueness conjecture. For every integer $n\geq 2$, there exists a unique polynomial of degree $4(n-1)$ in $S^W_{\mathfrak{sl}_2}$ solving the equation. It is represen…

Alev's conjecture.