Virasoro constraints and topological recursion for grothendieck’s dessin counting

Maxim Kazarian, Peter Zograf

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


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.

Original languageEnglish
Article numberA002
Pages (from-to)1057-1084
Number of pages28
JournalLetters in Mathematical Physics
Issue number8
Publication statusPublished - 1 Aug 2015
Externally publishedYes


  • Grothendieck’s “dessins d’enfants”
  • Ribbon graphs
  • Topological recursion
  • Virasoro constraints


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