4 problems

Let $S$ be the marked surface, let $\mathcal{P}$ be its marked points, let $n$ be the relevant parameter, and let $\alpha\in(0,2\pi)^{\mathcal{P}}$ be the tuple of angle defects. F…

Uniform log Yau–Tian–Donaldson conjecture. The polarised pair $((X,L);D)$ admits a cscK cone metric if and only if it is uniformly log $K$-stable.

Admissible cone metric count conjecture. There are at least $g$ admissible cone metrics of the form $a(d_1,\ldots,d_n)$.

Donaldson's conjecture. There is a cone-singularity solution $\omega_\beta$ to this equation for every parameter $\beta\in(0,R(X))$. If $R(X)<1$, there is no solution for any param…