4 problems

Let $(M^{4},g)$ be a compact anti-self-dual Einstein manifold with negative scalar curvature. Anti-self-dual Einstein vanishing conjecture. All the Seiberg–Witten invariants vanish…

Let $Y$ be a hyperbolic rational homology $3$-sphere, and let $H^{1,-}_0(Y\times\mathbb R)$ denote the relevant space of bounded solutions on the cylindrical anti-self-dual space…

Singer's conjecture. If the Yamabe invariant of $(M^4,g)$ is positive, then $(M^4,g)$ is unobstructed; equivalently,

Generality conjecture. The conformal structure defined by this bivector, with coefficients satisfying the vector-field part of the commutation relations for the extended Lax pair,…