16 problems

Poisson linearization conjecture. If the restricted Lie algebroid $T^*_S M$ integrates to a compact, source 1-connected Lie algebroid, then $pi$ is linearizable around $S$.

Relative Poisson cohomology conjecture. Let $pi$ be a Poisson structure with a compact symplectic leaf $S\subset M$. If

Minor-matching conjecture. The sets of minors defining the $T$-orbits of symplectic leaves in $M_{m,n}$ should match the sets of quantum minors generating the winding-invariant pri…

Let $\mathbf{v}$ be a dimension vector, let $\GL_{\mathbf{v}}$ be the corresponding product of general linear groups, and let $\mathbf{N}_{\mathbf{v}}$ be the associated representa…

Let $G$ be a reductive group, let $\mathbf{N}$ be a representation, and let $\mathcal{M}(G,\mathbf{N})$ and $\mathcal{M}_{\mathsf{Higgs}}(G,\mathbf{N})$ denote the associated Coulo…

Let $W$ be a complex reflection group, let $\tau$ be a finite-order element of the normalizer of $W$ in ${\mathrm{GL}}_{\mathbb{C}}(V)$, and let $c\in{\mathcal{C}}$ satisfy…

Harish–Chandra compatibility conjecture. The maps from irreducible characters of the normalizer to Calogero–Moser fixed points, from those characters to unipotent representations v…

Cuspidality conjecture. Then $p$ is $\tau_d$-cuspidal.

Let $V$ be a complex reflection representation of a finite group $W$, let $\tau$ be an automorphism preserving the relevant structure, and assume that the natural morphism…

Classical symplectic-leaf conjecture. The classical limit of the construction describes the full family of symplectic leaves in the Poisson-Lie group obtained as the classical limi…

Let $\mathcal M_C(\lambda,\mu)$ be the Coulomb branch and let $\mathfrak M_0(\lambda,\mu)$ be the corresponding affine quiver variety. Leaf-bijection conjecture. There is a natural…

Let $\mathfrak{g}$ be a semisimple Lie algebra, let $e\in\mathfrak{g}$ be nilpotent, and let $\mathfrak{X}_{P,0}^e$ be the corresponding variety in the discussion. Special-leaf con…

Tikaradze's analogue of the Kac–Weisfeiler conjecture. Suppose that $A$ is a nonnegatively filtered $\bold{k}$-algebra such that $\operatorname{gr} A$ is a finitely generated commu…

Let $\mathcal{M}_{m,p}(\mathbb{C})$ be the Poisson variety of complex $m\times p$ matrices, and let $\mathcal{O}_q(\mathcal{M}_{m,p}(\mathbb{C}))$ be its quantized coordinate ring.…

Yakimov's conjecture. The symplectic cores in $V$ can be recovered from the closures of the symplectic leaves in this analogous manner.

Stability conjecture. If $\Phi$ vanishes, then any Poisson structure close enough to $\pi$ admits at least one nearby symplectic leaf diffeomorphic to $S$.