4 problems

Let $chat{X}$ be a Calabi–Yau threefold, and let … be a conifold transition. Let $(\Omega_t,\omega_t,h_t)$ denote the holomorphic volume form, Hermitian form, and bundle metric inv…

Let $M=\Gamma\backslash G$ be a compact non-Kähler homogeneous space. Suppose that $M$ admits an invariant solution of the heterotic equations of motion with slope parameter…

Classification conjecture. If $M$ admits such a solution, then $\nabla=\nabla^+$ and $M$ is one of the nilmanifold $\mathfrak h_3$, a quotient of $\operatorname{SL}(2,\mathbb C)$,…

Uniqueness conjecture. There is no other compact homogeneous space admitting an invariant solution to the heterotic equations of motion with respect to a connection in the ansatz…