Introduction to Resurgence in Asymptotic Expansions - Lecture

Explore the phenomenon of resurgence in mathematics through a lecture by Maxim Kontsevich at the Institut des Hautes Etudes Scientifiques (IHES). Delve into a novel example related to the Stirling formula and its generalization to quantum dilogarithm. Examine the definition of rational Stirling numbers and their role in the asymptotic expansion of the normalized factorial. Discover how the asymptotic behavior of Stirling numbers for large even k is controlled by numbers for small odd k, and vice versa. Learn about the deformation of Stirling numbers to Euler polynomials in the case of quantum dilogarithm. Cover topics including unique collections of functions, dramatic origins, elementary examples, generalizations, steel link series, and generalized series throughout this 50-minute presentation.