Speaker: Matthew Harper, Michigan State University

Date: November 11, 2025

Abstract: Following the discovery of the Jones polynomial and the formalism by Reshetikhin and Turaev, a plethora of quantum link invariants emerged. Every representation of a quantum group corresponds to a potentially new link invariant, and relations between these invariants can be understood through representation theory. This talk will begin with an overview of quantum groups and the Reshetikhin-Turaev construction for the Jones polynomial. The two main examples discussed in the talk will be the Links-Gould and \Delta_{sl_3} polynomials derived from non-semisimple quantum groups. Both of these invariants generalize the Alexander polynomial from classical knot theory. I will survey some properties of these invariants and how they extend those of the Alexander polynomial. Notably, the Links-Gould polynomial of a cabling is observed to detect the genus of knots for all knots with up to 18 crossings.