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Resurgent large genus asymptotics of intersection numbers

By Alessandro Giacchetto

Appears in collection : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens

In the past several decades, it has been established that numerous fundamental invariants in physics and geometry can be expressed in terms of the so-called Witten-Kontsevich intersection numbers. In this talk, I will present a novel approach for calculating their large genus asymptotics. Our technique is based on a resurgent analysis of the n-point functions of such intersection numbers, which are computed using determinantal formulae and depend significantly on the presence of an underlying ODE. I will show how, with this approach, we are able to extend the recent results of Aggarwal with the computation of all subleading corrections. If time permits, I will also explain how the same technique can be applied to address other enumerative problems. Based on a joint work with B. Eynard, E. Garcia-Failde, P. Gregori, D. Lewanski.

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Citation data

  • DOI 10.24350/CIRM.V.20098903
  • Cite this video Giacchetto, Alessandro (03/10/2023). Resurgent large genus asymptotics of intersection numbers. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20098903
  • URL https://dx.doi.org/10.24350/CIRM.V.20098903

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