Speaker: Spencer Backman (Georgia Tech)
Title: Riemann-Roch for directed graphs
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