Abstract: I will talk about my recent work (arxiv:1805.07884) which shows that, on a Kahler manifold

with positive Kodaira dimension, the scalar curvature of the normalized Kahler Ricci flow will converge

to minus the Kodaira dimension on the regular part.  This improves Song-Tian's result which bounds

such scalar curvature.  This means that the Kahler Ricci flow deforms any Kahler metric to almost cscK

(constant scalar curvature Kahler metric).  Using this as an evidence, we briefly discuss how to find

cscK near the first Chern class of a minimal model.