8 problems

Higher-dimensional Yang–Mills flow–Harder–Narasimhan conjecture. The relationship between the Yang–Mills flow and the Harder–Narasimhan filtration that holds on Riemann surfaces sh…

Atiyah–Bott convergence conjecture. The gradient flow of the Yang–Mills functional should converge at infinity, achieving the lower bound expressed above.

Three-dimensional Yang–Mills flow instanton conjecture. Some such regular connections will flow to instanton fixed points, rather than to flat fixed points.

Yang–Mills flow uniformization conjecture. From such an initial connection, the Yang–Mills flow converges to the flat connection corresponding to a Riemannian geometry with constan…

Let $(E,\bar{\partial}_{A})$ be a holomorphic vector bundle, and let $Gr^{HNS}(E,\bar{\partial}_{A})$ denote the associated graded object of its Harder–Narasimhan–Seshadri filtrati…

Finite-time defect measure conjecture. At time $\tau=T$, the singular set satisfies

Torsion-driven instability conjecture. The torsion inherent in the Yang–Mills flow is responsible for the instability of partially compactified hyperbolic three-dimensional space.

Bando–Siu's correspondence conjecture. There should be a correspondence, albeit far less detailed, between the Yang–Mills flow and the Harder–Narasimhan filtration in higher dimens…