Resurgent Extrapolation and QFT: Mining Perturbation Theory for Non-perturbative Information

Resurgence implies that a wealth of non-perturbative information is generically encoded in perturbative data. It also motivates improved approaches to the problem of decoding this information. I describe some recent developments in the search for optimal methods of extrapolation and analytic continuation, based on ideas from the theory of resurgent asymptotics. I will illustrate some of the ideas with applications to examples in quantum field theory.