Thursday, March 8 at 3:00 pm
in Milner 317
Title: Character varieties and the Tutte polinomial of graphs
Abstract: This talk will
be on work in progress joint with Tamas Hausel. I will discuss how the
Tutte polynomial of certain graphs naturally appears in relation to
counting absolutely indecomposable representations of quivers over a
finite field k. In turn, the number of such representations for the
quiver with one node and g loops is related to the number of points of
a certain character variety over k associated to a Riemann surface of
genus g. The Weil conjectures then indicate how the relation between
the various counts is a manifestation of underlying geometric facts
about these varieties.