5 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).

Oh's conjecture. The Lagrangian torus $T(\boldsymbol{b})$ in $\mathbb C^n$ is Hamiltonian volume minimizing.