4 problems

Ivrii's conjecture. The main part of the spectral asymptotics is given by ${\mathcal E}^{\rm {MW}}$, while: (i) for fixed $(g^{jk})$ and general $(V_j),V$, the remainder is…

Shen's conjecture. Some condition on $\nabla {\bf B}$ is necessary to prove Theorem 0.11 of Shen.

Magnetic gap-labelling conjecture for strongly minimal actions. If the action is strongly minimal, then the containment in the magnetic gap-labelling conjecture for minimal actions…

Magnetic gap-labelling conjecture. The magnetic gap-labelling group is contained in the subgroup of $\mathbb R$ given by