6 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.

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…

Let $X$ be the Fargues–Fontaine curve, and let $\mathcal{E}$ be a vector bundle on $X$. For each rational slope $mu$, write $\mathcal{E}^{geq mu}$ for the subbundle determined by t…

Let $C$ be a hyperbolic Riemann surface and let $H\to C$ be a local system arising from a variation of Hodge structure. The Lyapunov exponents of $H$ determine a polygon, and the H…

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…