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.