Resurgent large genus asymptotics of intersection numbers

Author:

Bertrand Eynard, Elba Garcia-Failde, Alessandro Giacchetto, Paolo Gregori, Danilo Lewański

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Mathematical Physics (math-ph), Geometric Topology (math.GT)

journal:

date:

2023-09-05 16:00:00

Abstract

In this paper, we present a novel approach for computing the large genus asymptotics of intersection numbers. Our strategy is based on a resurgent analysis of the $n$-point functions of such intersection numbers, which are computed via determinantal formulae, and relies on the presence of a quantum curve. With this approach, we are able to extend the recent results of Aggarwal for Witten-Kontsevich intersection numbers with the computation of all subleading corrections, proving a conjecture of Guo-Yang, and to obtain new results on $r$-spin and Theta-class intersection numbers.

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