Abstract: I will start by explaining the Kummer K3 construction of Ricci-flat metrics of concentrated curvature. I will write down explicit estimates due to R. Kobayashi of these Ricci-flat metrics. As an application, I will discuss (stable), closed geodesics. If time permits, I will also discuss isometries of K3 surfaces and implications on the curvature. This is recently completed work, https://arxiv.org/abs/2209.04814.