Speaker: Spencer Backman (Georgia Tech)

Title: Riemann-Roch for directed graphs
Abstract: Chip-firing on graphs has been explored in various contexts for nearly 20 years. In 2007 Matthew 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 pursued. 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.