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Speaker:

Gaetan Borot
Affiliation:

MPIM
Date:

Mon, 2019-10-14 11:00 - 12:30
Location:

MPIM Lecture Hall 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.

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