Tropical curves are algebraic curves defined over the tropical
semi-ring. They essentially carry the same information as metric
graphs. There is a reasonable theory of divisors in this setting. For
example, there is a tropical analogue of the Riemann-Roch theorem. The
main technique in studying divisors on tropical curves is often to
look for nice canonical representatives in linear equivalence classes.
In this talk, we will describe various canonical representatives for
divisor classes on tropical curves.
We first revisit the concept of reduced divisors (which is the main
ingredient needed to prove the Riemann-Roch theorem) and explain their
various interpretations. We then discuss break divisors from
multiple points of view. If time permits we discuss the classical
analogues of these representatives and give some applications.
No prior knowledge in the subject will be assumed. This talk is based
on joint works with M. Baker, with M. Baker, G. Kuperberg, A. Yang,
and with Ye Luo.