Manin conjectures for K3 surfaces

The Manin conjectures describe for geometrically easy varieties how the number of their rational points of bounded height should grow as the height bound varies. In this talk I will describe recent computations that suggest a similar statement for K3 surfaces, which are geometrically more complicated. Part of the talk will focus on how to count the number of points in a specific example, using a variation of an algorithm by Noam Elkies.