Recently, tropical geometry has emerged as a tool for studying classical moduli spaces by
associating to every variety a polyhedral complex which comes as its nonArchimedean skeleton.
Classically, it is known that the dth symmetric power of a smooth, projective algebraic curve X
is again a smooth, projective algebraic variety which functions as the moduli space of effective
divisors of degree d on X. In this talk, I will discuss two ways to tropicalize this statement.
The first way is to take the dth symmetric power of the tropicalization of X, and the second is
to tropicalize the dth symmetric power of X itself. In recent work with Martin Ulirsch, we show
that in fact the two agree. I will present all necessary definitions for understanding the above
statement and I will sketch the proof.
