On the Laplace Transform of the Monodromy as a Function of the Pertubation Parameter in WKB-Voros Resurgence We consider the Voros resurgence or WKB problem of monodromy for a family of connections of the form ∇+t.Φ, and look at the transport along a path as a function of t. Taking the Laplace transform, we discuss the analytic continuation properties leading to asymptotic estimates for the monodromy as t→∞. If time permits we'll discuss possible relations with spectral networks and harmonic mappings to buildings.