Matthew Harper
Michigan State University
Title
Coincidences of Links-Gould and other Quantum Invariants of Knots and Links
Abstract
I will survey several recent results on the Links-Gould polynomial, invariants of Garoufalidis-Kashaev, and the quantum invariant associated to Uq(sl3) at a fourth root of unity. This includes the affirmation of a conjecture of GK which proves their invariants recover the Links-Gould and sl3 invariants. We also prove a conjecture of Geer and Patureau-Mirand that the Links-Gould invariant admits a specialization to ADO3 (Uq(sl2) at a sixth root of unity). Finally, we'll discuss some cabling results for Links-Gould and other non-semisimple quantum invariants. These results are joint with subsets of Stavros Garoufalidis, Rinat Kashaev, Ben-Michael Kohli, Jiebo Song, Guillame Tahar, and Emmanuel Wagner.