Plenary: Roots of Combinatorial Polynomials

We discuss why studying roots of combinatorial polynomials plays an important role in understanding the underlying combinatorics of the structures these polynomials encode. We highlight the author’s recent proof that real roots of all-terminal reliability polynomials of simple graphs are dense in [-1,0]U{1}; refining the same theorem proved for multigraphs by Brown and Colbourn (1992).