# The AJ conjecture for SU(2) and SL(2,C)

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Alessandro MalusÃ

created by daniele on 18 Jun 2018

21 jun 2018
-- 15:00

**Abstract.**

Given a knot K in S^{3,} one can consider as invariants the A-polynomial and the coloured Jones polynomial. After illustrating the original AJ conjecture, as formulated by Garoufalidis, I will specify its motivation from quantum SU(2)-Chern-Simons theory, and attempt to make sense of the statement that the two invariants mentioned above are classical and quantum in nature, respectively. This opens the question as of whether one can formulate an analogous conjecture for different Lie groups. For SL(2,C), the existence of an invariant corresponding to the coloured Jones polynomial has been conjectured by Andersen and Kashaev; I will discuss how a construction similar to the one by Garoufalidis leads to an AJ-conjecture for this invariant.