Current Topics Seminar: Berkovich spaces and number theory

I will explain some interplay between non-archimedean/tropical geometry, number theory, and combinatorics. I will also give some applications to the theory of heights on abelian varieties. 
In the case of Jacobians, these relate to combinatorics, convex geometry, and potential theory (electrical network) of metric graphs. 
(Needless to say, the talk will be "self-contained".)