Topological recursion for irregular spectral curves

Norman Do, Paul Norbury

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5 Citations (Scopus)


We study topological recursion on the irregular spectral curve xy2 - xy + 1 = 0, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve xy2 = 1, which takes the place of the Airy curve x = y2 to describe asymptotic behaviour of enumerative problems associated to irregular spectral curves. In particular, we calculate all one-point invariants of the spectral curve xy2 = 1 via a new three-term recursion for the number of dessins d'enfant with one face.

Original languageEnglish
Pages (from-to)398-426
Number of pages29
JournalJournal of the London Mathematical Society
Issue number3
Publication statusPublished - 1 Jun 2018


  • 05A15
  • 14N10
  • 32G15 (primary)

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