Resurgence Theory - Generalised Borel-Laplace Summation, "Alien Calculus" by David Sauzin

Delve into the second lecture of an introductory mini-course on Resurgence Theory, focusing on generalised Borel-Laplace summation and "alien calculus." Explore the refinement of Borel-Laplace summation methods designed to encompass transseries arising in various mathematical and physical contexts. Learn about resurgent series, their divergent power series nature, and their role as common asymptotic expansions for multiple analytic functions. Discover Jean ÉCALLE's "alien derivations" and their application in measuring exponentially small discrepancies and describing moduli spaces in local analytic dynamical systems. Gain insights into André VOROS's approach to WKB series of 1D Schrödinger operators and its connection to resurgence in \hbar. Benefit from the expertise of David Sauzin from the Institute of Celestial Mechanics and Computation of the Ephemerides in Paris as he presents this advanced mathematical topic with applications ranging from wall-crossing phenomena and exact WKB method to deformation quantisation and TQFT.