Chromatic quasisymmetric functions

Richard Stanley initiated the study of the chromatic symmetric function X_G of a finite graph G.  This symmetric function encodes more information about G than the well-studied chromatic polynomial, and has been studied closely.  Michelle Wachs and I introduced a refined version of X_G.  For most graphs G, this refined version is quasisymmetric but not necessarily symmetric.  However, X_G is symmetric when G is an indifference graph.  Chromatic quasisymmetric functions of indifference graphs are related to previously studied objects from algebraic geometry and representation theory of symmetric groups.  After introducing  chromatic symmetric and quasisymmetric functions, I will discuss these relations.