Uniform Potential Density for Rational Points on Algebraic Groups and Elliptic K3 Surfaces

A collection of varieties satisfies uniform potential density if each of them contains a dense subset of rational points after extending its ground field by a bounded degree. In this paper, we prove that uniform potential density holds for connected algebraic groups of a fixed dimension over fields of characteristic zero as well as elliptic K3 surfaces over number fields.
Final version, accepted by International Mathematics Research Notices