Quantitative arithmetic equidistribution I

For an endomorphism F of projective space P^N (or for any polarized endomorphism of a smooth projective variety) defined over a number field, there is a canonical height function on P^N whose zeroes are the preperiodic points. It is known, by a theorem of Xinyi Yuan (2008), that the Galois orbits of sequences of points with small height will uniformly distribute to the equilibrium measure of F. In these two talks, we work through details of a proof of a new, quantitative version of this result and present various applications of this stronger form of equidistribution.