| Over the past decade, there has been an great deal of interest in the development of a theory of divisors on graphs and tropical curves, which is analogous to the classical theory for algebraic curves. In the first half of the talk, I will give a survey of divisor theory for graphs and it's applications to algebraic geometry and number theory. The combinatorial language for studying linear equivalence of divisors on graphs is "chip-firing", a certain game which has been independently introduced in several mathematical fields. In the second half of my talk, I will explain how chip-firing may be viewed as a shadow of a certain process on partial graph orientations, and illustrate how this insight lends itself to a more conceptual, but still combinatorial, understanding of Baker and Norin's Riemann-Roch theorem for graphs. |