What is the best way to extract information from a finite amount of perturbative information? This is a common problem in applications. We may only be able to compute a (small) finite number of coefficients of an expansion of a function about some special parameter point, and we wish to learn about the behaviour near another point (possibly very distant).
I will discuss some recent work with Ovidiu Costin using resurgence ideas to address the mathematical question of optimal and near-optimal methods of analytic continuation, and I will illustrate with several applications in quantum field theory.
