Appears in collection : New perspectives on Borel summation

We review the Laplace and Borel transforms from a new perspective that highlights the geometric structure of the Borel plane. This geometric structure is relevant to both of the kinds of problems we study. For linear ODEs, the solutions that can be obtained by Borel summation are indexed by singular points on the Borel plane. Similarly, integrals over Lefschetz thimbles can be recast as Laplace integrals along rays departing from singular points.

Joint work with Veronica Fantini.

Correction: (49:55) Formula should be Ai(y) = const. * y^(1/2) * K(...)