Checking the complex AJ conjecture for the first hyperbolic knots

Alessandro Malusà
(AU)
Seminar
Wednesday, 7 February, 2018, at 16:15-17:15, in Aud. D3 (1531-215)
Abstract:
In his formulation of the AJ conjecture, Garoufalidis considered the action of a certain q-commutative algebra on the coloured Jones polynomial of a knot, arguing the existence of a preferred element, the non-commutative A-polynomial, annihilating it. In a recent work with Jørgen E. Andersen, we proposed a version of the AJ conjecture for the partition function of the Teichmüller TQFT, which holds true for the first two hyperbolic knots. The check of this fact was handled with the help of a computer, using a Gröbner-like elimination procedure to find a certain generator of the relevant ideal in a non-commutative algebra. In this presentation I intend to recall the formalism of the original AJ conjecture as stated by Garoufalidis, and its adaptation to the case of the quantum Teichmuller theory. I will discuss the process used for proving the conjecture for the knots 4_1 and 5_2, and the difficulties that arise in the case of more complicated knots.
Organised by: QGM
Contact person: Cristiano Spotti, Martin de Borbon & Roberta Iseppi