DP-coloring (also called correspondence coloring) of graphs is a generalization of list coloring of graphs that has been widely studied in recent years after its introduction by Dvorak and Postle in 2015. Intuitively, DP-coloring is a variation on list coloring where each vertex in the graph still gets a list of colors, but identification of which colors are different can change from edge to edge. DP-coloring has been investigated from both the extremal (DP-chromatic number) and the enumerative (DP-color function) perspectives.
In this talk, we will give an overview of questions arising with regard to when the DP-color function equals the chromatic polynomial (or any polynomial), and how the polynomial method, through the Combinatorial Nullstellensatz and the Alon-Furedi theorem for the number of non-zeros of a polynomial, can be applied to both extremal and enumerative problems in DP-coloring. Many open problems and conjectures will be presented.