10 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

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 $\mathcal{D}$ be an integral quantization of a conical symplectic resolution, let $\mathcal{I}$ index the simple objects of its category $\mathcal{O}$, and define two indices t…

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…

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