

The model theory of Hardy fields and linear differential equations
By Matthias Aschenbrenner


Topological Recursion, Painlevé Equation, Exact WKB and Resurgence
By Kohei Iwaki
By Aaron Fenyes
Appears in collection : New perspectives on Borel summation
The second day’s lectures are dedicated to a family of examples: the Airy-Lucas functions introduced by Charbonnier et al. (arXiv:2203.16523). These functions satisfy linear ODEs that generalize the Airy equation. They can also, like the Airy function, be expressed as thimble integrals. We will explain, from both perspectives, why these solutions can be obtained by Borel summation. We first discuss the linear ODE perspective, with the help of our work in progress on integral equations (arXiv:2309.00603).
Joint work with Veronica Fantini.
References:
(3:59) https://arxiv.org/abs/2203.16523
(33:25) https://arxiv.org/abs/2309.00603
Corrections:
(3:59) Name should be spelled Charbonnier
(44:42) Parameters should be ₂F₁(1/2 − m/n, 1/2 + m/n, 1/2, ...)