On hyperbolic perturbations of algebraic links and small Mahler measure

This paper surveys some results surrounding Lehmer's problem in the context of fibered links and Hopf plumbing. Topics addressed here are Mahler measures of fibered links, the relation between iterated Hopf plumbings and Salem-Boyd polynomials, and the question of when monotone growth occurs under iterated plumbing. Explicit calculations for certain "perturbations" of links associated to the ADE singularities are computed.