K3 surfaces are equipped with an area form and dynamically interesting automorphisms which preserve the area form. All this data (the surface, the area form, and the automorphism) can be made explicit using polynomial functions. On the other hand, K3s admit Ricci-flat metrics which arise from solving Monge-Ampere equations. I will discuss some applications of these Ricci-flat metrics to understanding the automorphisms of K3 surfaces. In the converse direction, I will also discuss some applications of K3 automorphisms to regularity properties of Monge-Ampere equations on K3s. Joint work with Valentino Tosatti.