5 problems

Uniqueness conjecture. A Hermitian Einstein–Weyl structure on a compact complex manifold is unique, up to a holomorphic automorphism.

Correspondence conjecture. There exists a correspondence between solutions to the full KP equation and the Moyal deformations of ${\cal Z}$.

Let $m$ and $\phi$ define the Einstein–Weyl system above, and let $A$ and $B$ be matrix-valued fields satisfying … … Equivalently, locally write $A=K_t$ and $B=-K_y$, where $K$ is…

Generality conjecture. This system represents a general local form of monopole equations on an Einstein–Weyl background, up to coordinate transformations and a gauge.

LeBrun–Mason type correspondence conjecture. There is a natural one-to-one correspondence, at least in a neighborhood of the standard objects, between equivalence classes of space-…