Timothy Bates, Rutgers University

Abstract

In this talk, I will go over everything I know about the current progress on Fox's trapezoidal conjecture on alternating links. The conjecture states that the sequence of coefficients in the Alexander polynomial of an alternating knot forms a trapezoidal sequence. The conjecture has been proven for many families of alternating links, and some more recent investigations by Kálmán, Mészáros, and Postnikov suggest that matroids may play a role in its resolution.