From ODEs to topological recursion: the case of Hurwitz numbers -- CANCELLED --

I will first explain the general theory due to Bergere, Eynard and myself to associate, to any finite order ODE, a kernel K(x,x') and a collection of (W_n)_{n > 0} satisfying loop equations. Under some assumptions on the semiclassical expansions of these quantities, this implies these expansions are computed by the topological recursion. 

Then, following the third paper of Alexandrov-Chapuy-Eynard-Harnad, I will describe the ODE that generating series of Hurwitz numbers satisfy, and show that in this case, the coefficients of the semiclassical expansion of W_n are generating series of Hurwitz numbers with fixed topology and ramification profile of length n over \infty.