4 problems

Shen's conjecture. There are non-trivial positively complete, projectively flat Finsler metrics of constant curvature

Projective flatness conjecture. The vector bundles of completely filled quantum Hall states over geometric parameter spaces are projectively flat for an appropriate connection.

Let $M$ be an algebraic manifold with $\dim_{\mathbb{C}}M\geq3$, let $L$ be a very ample line bundle on $M$, and let $\omega\in K(M,L,x\,dy-y\,dx)$ be a foliation with normal bundl…

Local projective flatness conjecture. The metric $F$ must be locally projectively flat.