Geometry & Topology Seminar

Alessandro Malusà, University of Saskatchewan

"Complex AJ conjecture"

The AJ conjecture was initially formulated as a relation between the A-polynomial and the coloured Jones of a knot. The statement has an informal motivation in terms of SU(2)-Chern-Simons theory, in which the two invariants have an interpretation as a constraint and a partition function, respectively. Since the A-polynomial has the same significance of the theory for SL(2,C), it is to be expected that an analogous statement should be made for the partition function of the complexified theory, once properly defined. One construction of such a partition function was proposed by Andersen and Kashaev through their Teichmüller TQFT, for which a version of the AJ conjecture is formulated in a joint work with Andersen via methods of geometric quantisation. In this talk I want to illustrate said construction and the key steps of the proof of the conjecture for the first two hyperbolic knots. Time permitting, I would like to mention some of my ongoing work with Ben Aribi and Piguet-Nakazawa, in which we are investigating on the conjecture for the so-called twist knots.

MC 5403