An algebraic renaissance for the chromatic polynomial

The chromatic polynomial has played a central role in graph theory for almost 100 years, but it is only now, in
work led by participants in this project, that an algebraic theory of these polynomials is being developed. This
project should lead to a new algebraic theory of these polynomials and their roots, as well as resolution of
some fundamental computational questions about them. Our aims are to relate the structure of graphs to the
most fundamental algebraic properties of their chromatic polynomials, namely their factors, their Galois
groups, and chromatic equivalence, and to determine which algebraic numbers can be roots of these
polynomials.