Speaker:  Joe Boninger (Boston College)

Title: Twisted knots and the perturbed Alexander invariant

Abstract: The perturbed Alexander invariant, defined by Bar-Natan and van der Veen, is an infinite family of polynomial invariants of knots in the three-sphere. The first invariant in the family, rho_1, is quick to compute and often superior to Khovanov homology at distinguishing knots. We will discuss the perturbed Alexander invariant and properties of the rho_1 invariant in particular. We will then explore the behavior of the rho_1 invariant and the Alexander polynomial under the operation of applying full twists to a knot. Our arguments use a model of random walks on knot diagrams.