Review: relations between Chern-Simons theory and topological recursion

Up to now, Chern-Simons theory has been related to topological recursion in two different regimes. Firstly, considering SU(N + 1) theory in Seifert fibered spaces, the large N expansion of the colored (in any fixed representation R) HOMFLY invariant of fiber knots, can be extracted from a topological recursion. Secondly, it is conjectured that the topological recursion can compute the semiclassical expansion (in $q = e^{\hbar} \rightarrow 1$) of a solution to the $q$-difference equation satisfies by the colored Jones polynomials $J_n(q)$ of a knot $K \subseteq \mathbb{S}_3$ --  this was checked in particular for the $8$-knot. We shall put this last aspect in perspective with Andersen and Eynard mini-courses, and informally summarize the relations we expect between geometric quantization of character varieties and topological recursion.