Lower bound for canonical heights and distribution of small points

In this talk we give an overview of the broad topic of lower bounds for heights.

We begin with the simple case of the Weil height of algebraic numbers, where interesting problems as Lehmer's conjecture are already still open. We then discuss similar questions for elliptic curves, where the geometry of the group variety gives rise to new challenges.

In the final part of the presentation, we focus on the distribution of points of small height, the so called small points, on a subvariety of an algebraic group of dimension >1.