4 problems

Harmonic metric conjecture. There exists a harmonic metric $h$ on ${\cal B}$ if and only if ${\cal B}$ is a direct sum of $\nabla$-stable bundles. If ${\cal B}$ itself is $\nabla$-…

Hyperkähler metric conjecture. There exists a hyperkähler metric on ${\cal M}^s$ such that $\Omega$ is the associated holomorphic symplectic form.

Let $(E,\nabla)$ be a bundle with a non-Hermitian Yang–Mills connection $\nabla$. A bundle is $\nabla$-stable if it is stable with respect to the connection $\nabla$, and a harmoni…

Let $M$ be a hyperkähler manifold, let $\mathcal M^s$ be the smooth moduli space of stable non-Hermitian Yang–Mills connections, and let $\Omega$ be its natural closed holomorphic…