## Chip-firing on metric graphs

## Nathan Pflueger (Harvard University)

#### Abstract :

A chip distribution on a metric graph assigns an integer weight to finitely
many points on the graph. Chip distributions can be modified by a procedure
called chip-firing. Chip-firing, while purely combinatorial, bears several
striking similarities to the theory of divisor classes on algebraic curves.
I will survey some of the main results and open problems, including
combinatorial versions of the Riemann-Roch formula and Brill-Noether theory.