Jennifer Brown

The A-polynomial is a knot invariant built using the moduli space of flat connections on a knot's complement. It is the subject of a long-standing conjecture, which proposes that an appropriate quantisation of the A-polynomial precisely captures the recursion relations of another famous knot invariant known as the coloured Jones polynomial.

A major hurdle to resolving this conjecture is the lack of a good quantisation procedure. After introducing the A-polynomial, we will explain how the skein theory used to define the coloured Jones polynomial can be adapted to give a quantisation of the A-polynomial.