Por Xavier Blot (GFM-UL).

In 1991, Witten conjectured a relation between the moduli space of curves and the KdV hierarchy via the so-called Witten-Kontsevich series. This conjecture was proved in 1992 by Kontsevich. The first goal of the talk is to clearly present this statement.

Then, I will explain how the recent developments of the Double Ramification hierarchies allow to define a quantum version of the Witten-Kontsevich series. I will finish by explaining a surprising connection  between coefficients of the quantum Witten-Kontsevich series and Hurwitz theory.