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Article

Virasoro constraints and topological recursion for Grothendieck's dessin counting

Letters in Mathematical Physics. 2015. Vol. 105. No. 8. P. 1057-1084.
Kazaryan M., Zograf P.

We compute the number of coverings of CP1∖{0,1,∞} with a given monodromy type over ∞ and given numbers of preimages of 0 and 1. We show that the generating function for these numbers enjoys several remarkable integrability properties: it obeys the Virasoro constraints, an evolution equation, the KP (Kadomtsev–Petviashvili) hierarchy and satisfies a topological recursion in the sense of Eynard–Orantin.