Title: Equidistribution of rational points on weighted projective stacks     Abstract: Studying rational points on varieties is a central topic in number theory. When there are infinitely many rational points one can ask how are they distributed. Are they all clumping together? Do most of them tend to lie on a special sub-variety? Or do they distribute equally over the entire variety? In this talk I will focus on a particularly nice set of spaces, weighted projective stacks. We will see that rational points on these spaces satisfy certain strong equidistribution properties. Finally, I will survey some applications of equidistribution to the arithmetic of elliptic curves.