For certain problems, taking the Borel sum of an intuitively chosen divergent series solution will often produce a holomorphic solution. When does this happen, and what is special about the holomorphic solutions obtained in this way? We will present work in progress on these questions, focusing on two kinds of problems: linear ODEs and integrals over Lefschetz thimbles. The first day’s lectures start with a presentation of our questions and an overview of our expected results.

Joint work with Aaron Fenyes.