The effectiveness of Borel–Laplace summability for Lefschetz thimble integrals

Abstract: Borel--Laplace summation is a classical summability method that associates an analytic function to a divergent power series. Divergent power series often appear in mathematics and physics: solving ODEs with irregular singularities, computing asymptotics, computing perturbative expansions in QFT, in complex Chern--Simons, etc. One special feature of the Borel--Laplace sum is that it works well for integrals over Lefschetz thimbles (thimble integrals). Indeed, the Borel--Laplace sum of the asymptotics of a thimble integral is the thimble integral itself. This is part of a joint project with A. Fenyes.