Ralph Morrison: Tropical Geometry Mini-course, Part III: Abstract tropical curves and Berkovich spaces

In the previous talks, we looked at tropical curves as one-dimensional balanced polyhedral complexes in Euclidean space.  In this talk we will consider them more abstractly, as metric graphs with lengths on each edge.  We will build up a theory of rational functions and divisors on these abstract tropical curves in parallel with classical divisor theory.  We will close with a brief introduction to Berkovich spaces, which connect to both the abstract and embedded versions of tropical curves.