University of Minnesota Combinatorics Seminar
Friday, October 21, 2011
3:35pm in 570 Vincent Hall



Chip-Firing and Riemann-Roch Theory for Directed Graphs

Spencer Backman

Georgia Tech


Abstract

Chip-firing on graphs has been studied in various contexts for nearly 20 years. In 2007 Matt Baker and Sergey Norine showed that by studying chip-firing, one may develop a Riemann-Roch formula for graphs analogous to the classical statement from algebraic geometry. Following their paper, many different extensions have been explored. We investigate two distinct generalizations of chip-firing for directed graphs and develop necessary and sufficient conditions for the Riemann-Roch formula to hold with respect to these models as well as an algorithm for testing whether these conditions are satisfied. Connections to the directed sandpile model, G-parking functions, and arithmetical graphs are presented. This is joint work with Arash Asadi.