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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 non-Archimedean skeleton.
Classically, it is known that the d-th 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 d-th symmetric power of the tropicalization of X, and the second is
to tropicalize the d-th 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.
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