Generalized Hamilton-Tian conjecture for the Kähler-Ricci flow

Let $X$ be Fano, let $T_0<\infty$, and suppose $\omega\rein-T_0[K_X]$. Consider the normalized Kähler-Ricci flow

$$\frac{\partial\tilde{\omega}}{\partial s}=-\operatorname{Ric}(\tilde{\omega})+\frac{1}{T_0}\tilde{\omega}.$$

Generalized Hamilton-Tian conjecture. As $s\to\infty$, the flow starting from $\omega$ converges in the Gromov-Hausdorff sense to a Kähler-Ricci soliton $(X_\infty,\omega_{KR})$. The source records announced or partial results in special cases, including Kähler-Einstein manifolds and Fano manifolds admitting a Kähler-Ricci soliton, but the general conjecture remains open.