Introduction to Resurgence via Wall-crossing Structures - Lecture 1

Explore an alternative approach to the classical Borel-Écalle resummation method for factorially divergent series in this lecture. Delve into the concept of analytic wall-crossing structures, introduced by Yan Soibelman and the speaker in arXiv: 2005.10651. Learn how to define a holomorphic bundle over a small disc directly in the original coordinate, using gauge transformations with convergent series in exponentially small terms to glue trivialized bundles on overlapping sectors. Examine the resulting global geometric object: a bundle over a neighborhood of a wheel of 1-dimensional torus orbits in a higher-dimensional toric variety. Gain insights through various examples, including exponential integrals, a generalization to closed 1-forms (encompassing the Stirling formula), and the quantum dilogarithm. This 1-hour and 15-minute talk by Maxim Kontsevich from the Institut des Hautes Etudes Scientifiques (IHES) offers a comprehensive introduction to resurgence via wall-crossing structures.