Tian's uniform Bergman kernel lower-bound conjecture for Kähler–Einstein manifolds

Let $\{(M_i,g^i)\}$ be a sequence of $n$-dimensional Kähler–Einstein manifolds with constant scalar curvature $n$. For each $M_i$, let $\rho_l(M_i,g^i)$ denote the Bergman kernel of $K_{M_i}^{-l}$ with respect to the metric induced by $g^i$. Tian's uniform Bergman kernel lower-bound conjecture. There exists an integer $l_0$ such that, for every integer $l>0$, there is a constant $c_l>0$, depending only on $l$ and $n$, for which

$$\rho_{ll_0}(M_i,g^i)\geq c_l$$

for every $i$. The conjecture concerns uniform partial $C^0$ estimates for sequences of positively curved Kähler–Einstein manifolds. It was proved independently by Donaldson–Sun and Tian, so the conjecture is solved.