### 20 september, Charles Favre (Université Denis Diderot):
Equidistribution of points of small heights
(joint work with Juan Rivera-Letelier)

**Abstract.**
Let R be a rational map with complex coefficients of degree
at least 2. For any point z on the Rieman sphere (with at most two
exceptions), the sequence of measures equidistributed on the preimages
of z under R^n converges to a measure m_R which is independent on z. Our
aim is to present an arithmetic analog of this result. Suppose R has
rational coefficients. It is then possible to construct a so-called
height function h_R on the algebraic closure of the field of rational
numbers. Our main result states that for any sequence of points z_n
such that h_R(z_n) tends to 0, the sequence of measures equidistributed
on the Galois conjugates of z_n converges to the measure m_R. The proof
of this result relies on basic properties of the Laplace operator on the
complex plane, as well as on the affine line associated to the p-adic
field C_p.