New Perspectives on Borel Summation - Lecture 1

Explore new perspectives on Borel summation in this comprehensive lecture, the first of a four-part series. Delve into the intriguing phenomenon where taking the Borel sum of carefully chosen divergent series solutions often yields holomorphic solutions for certain problems. Investigate the conditions under which this occurs and examine the unique properties of these holomorphic solutions. Focus on two key problem areas: linear ODEs and integrals over Lefschetz thimbles. Gain insights into ongoing research, including an overview of expected results and the central questions driving this investigation. This lecture, presented by Veronica Fantini from the Institut des Hautes Etudes Scientifiques (IHES), is based on joint work with Aaron Fenyes and serves as an excellent introduction to the series, setting the stage for a deep exploration of Borel summation techniques and their applications in mathematical analysis.