5 problems

High-temperature uniqueness conjecture. For $\lambda\leq 0$, $\mu^\lambda$-cscK metrics are unique modulo the automorphism group.

Let $\pi: (X,H)\to (B,L)$ be a holomorphic fibration, where $H$ and $L$ are the relevant polarisation classes. An optimal symplectic connection is a connection associated with the…

Let $(X,L)$ be a polarized variety. Denote by $\mathcal{H}^{\mathbb{R}}_{\mathrm{NA}}(X,L)$ the space of non-archimedean metrics and by $\mathcal{H}(X,L)$ the space of Kähler metri…

Let … be the punctured disk, and let $h_{\mathrm{can},\Delta^{*}}$ be the canonical singular hermitian metric on $K_{\Delta^{*}}$ constructed from pluricanonical forms. Punctured-d…

Let $f:X\to S$ be a surjective proper Kähler morphism with connected fibers between connected complex manifolds, let $S^{\circ}$ be the complement of the discriminant locus, and le…