Journal article

Topological recursion for irregular spectral curves

Norman Do, Paul Norbury

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | WILEY | Published : 2018

Abstract

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.

University of Melbourne Researchers

Grants

Awarded by Australian Research Council


Funding Acknowledgements

The authors were partially supported by the Australian Research Council grants DE130100650 (ND) and DP1094328 (PN).