Abstract: The Tutte polynomial is a two-variable polynomial one may associate to a given graph. It's cool because it is universal among multiplicative graph invariants that respect certain deletion and contraction relations. Given a graph, one may also study an associated quiver algebra and count its modules over a finite field. Here we display a direct relation between the Tutte polynomial and this count of modules. The main result here is due to Hausel and Sturmfels but some methods may be new.
This joint work with Fernando Rodriguez Villegas and Anton Mellit.