Explore new perspectives on Borel summation in this 59-minute lecture by Aaron Fenyes at the Institut des Hautes Etudes Scientifiques (IHES). Focus on the Airy-Lucas functions introduced by Charbonnier et al., which generalize the Airy equation and can be expressed as thimble integrals. Examine why these solutions can be obtained through Borel summation from both linear ODE and integral perspectives. Delve into ongoing research on integral equations and their applications. Gain insights into the mathematical connections between Airy-Lucas functions, linear ODEs, and Borel summation techniques. Note important references to related research papers and corrections to mathematical notations presented during the lecture.