Date/Time
Date(s) - 20/11/2023
4:30 pm - 5:30 pm

Location: HH 312

Speaker: Joseph 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 polynomial, rho_1, is quick to compute and may be better at distinguishing knots than other practically computable invariant; it also has deep connections to both classical and quantum topology. We will discuss the perturbed Alexander invariant and properties of the rho_1 invariant in particular and explore the behavior of the rho_1 invariant and the classical Alexander polynomial under the operation of applying full twists to a knot. Our arguments use a model of random walks on knot diagrams.