11 problems

Moment-map fiber dimension conjecture. One has

Symplectic-singularities conjecture. Every fiber $Y$ of $\widetilde{\psi}_{G,X}/\!/G$ has symplectic singularities.

Nilpotent-model irreducibility conjecture. If $X=M_G(H,\eta,V)$, where $\eta$ is nilpotent, then $X$ satisfies (Irr).

Irreducibility conjecture. Every conical irreducible Hamiltonian $G$-variety $X$ satisfies (Irr).

Quadratic norm conjecture. The norm squared

Properness conjecture. The moment map $\bm\mu$ is proper.

Let $G$ be a real almost algebraic group, let $\pi$ be a discrete series representation attached to a coadjoint orbit $\mathcal{O}_{\pi}$, and let $H$ be a closed almost algebraic…

Compatibility conjecture. The following diagram commutes:

Flag Hilbert scheme conjecture. The following hold:

Let $\mathfrak{n}$ be a nilpotent Lie algebra, let $\mathfrak{t}(\mathfrak{n})$ be a maximal torus of diagonalizable derivations, let $\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}$ be…

Flow-closedness conjecture. If $\mu_\mathbb{C}$ is a complex moment map associated to a linear action by a compact group $K$ on a vector space, then $|\mu_\mathbb{C}|^2$ is flow-cl…