5 problems

Infinite-dimensional vortex conjecture. There should be a way to view the family Hermite–Einstein equation as an infinite-dimensional version of the vortex equations, for example a…

Adiabatic-limit conjecture. Over an open subset away from the bubbling loci, the limiting connection on $X \times B$ should solve the family Hermite–Einstein equation.

Family Hermite–Einstein conjecture. The family Hermite–Einstein equation determines the geometry of such collapsing families away from singularities.

Let $X$ be a compact Kähler normal space with klt singularities, and let $\mathcal{F}$ be a stable sheaf on $X$. The Bogomolov-type inequality established in the three-dimensional…

Let $X$ be a projective manifold, let $f$ be the parabolic curve under consideration, and suppose the stability hypothesis stated immediately before the claim holds. Let $\omega_k$…