4 problems

Sun–Zhang's conjecture. A polarized Fano fibration $(\pi:X\to Y,\xi)$ admits a Kähler–Ricci shrinker $(\omega,\xi)$, unique up to automorphisms of $X$ preserving $\xi$, if and only…

Fano-cone Ricci-flatness conjecture. On a Fano cone $X$, every Kähler-Ricci shrinker is a Ricci-flat Kähler cone metric.

Asymptotic conicity conjecture. A Kähler-Ricci shrinker is weakly asymptotically conical in the sense that it has a unique asymptotic cone at infinity, which is a Kähler cone metri…

K-polystability conjecture. A polarized Fano fibration $(\pi:X\rightarrow Y,\xi)$ with $X$ smooth admits a Kähler-Ricci shrinker, which is unique up to the action of…