| Résume | Recently, there has been increasing interest in solving q-difference equations associated to quantum invariants of 3-manifolds as q-series. I will discuss an algorithmic approach to constructing such solutions, studied for example by Dreyfus, and relate such solutions to state integrals of Andersen-Kashaev. Along with exact computations of monodromy, this proves quantum modularity of such solutions in examples and, in particular, the quantum modularity of the q-Borel resummation of the coloured Jones polynomial. This is based on joint work with Garoufalidis, Gu and Mariño. |
