| One of the starting points of tropical geometry is the deep analogy between Riemann surfaces and metric graphs, or more generally of tropical curves. Many constructions on the side of Riemann surfaces have natural counterparts on the side of tropical curves and vice versa. In this talk I will focus on two topics: the moduli space of tropical curves and the theory of harmonic maps between tropical curves. After explaining the basic story, I will, in particular, focus on the process of tropicalization which connects this to the world of Riemann surfaces. |