**Patrice Philippon**

Institut de Mathématiques de Jussieu, France

November 30, 2017

**Arithmetic geometry of toric varieties**:
We will present results obtained in collaboration with J.Burgos and
M.Sombra. These extend the well known dictionary between the geometric
properties of toric varieties and convex geometry. In particular, we give combinatorial descriptions of classical invariants of arithmetic geometry, such as metric, height, essential minimum, positivity properties and equidistribution.