Strong irreducibility of Alexander polynomials
Evan Bullock, Rice

A polynomial f(t) in one variable over the rational numbers is strongly irreducible if f(t^k) is irreducible for all positive integers k. I will discuss a generalization of Eisenstein's irreducibility criterion to proving strong irreducibility and applications in knot theory to the study of the rational algebraic concordance group. (This is joint work with Chris Davis.)