In this talk, I will present a new approach to the computation of the large genus asymptotics of Witten–Kontsevich intersection numbers. Our technique is based on a resurgent analysis of the n-point function of such intersection numbers, which are computed via determinantal formulae, and relies heavily on the presence of an underlying first order differential system. With this approach, we are able to extend the recent results of Aggarwal with the computation of subleading corrections, and to obtain completely new results on r-spin and Theta-class intersection numbers. Based on the joint work with B. Eynard, E. Garcia-Failde, P. Gregori, D. Lewański.