Introduction to 1-Summability and Resurgence Theory -

Introduction to 1-Summability and Resurgence Theory

Time: 2024-05-23 Published By: Ruixin Li

Speaker(s): David Sauzin(Capital Normal University, Beijing on leave from CNRS - IMCCE, Paris)

Time: April 23 - May 21, 2024

Venue: Room 29, Quan Zhai, BICMR

Abstract:

Resurgence Theory, born within the mathematical theory of nonlinear dynamical systems in the late 1970s, has become more and more used in the mathematics/physics research literature, especially since the 2010s, with a burst of activity in applications ranging from quantum mechanics, wall-crossing phenomena, field theory and gauge theory to string theory. This talk will be a light mathematical introduction to what the resurgent toolbox concretely consists of, beginning with the more classical topic of Borel-Laplace summability. Typically, a resurgent series is a divergent power series in one indeterminate that appears as the common asymptotic expansion to several analytic functions; these functions are obtained by Borel-Laplace summation in different directions and differ by exponentially small quantities. More than 40 years ago, Jean Ecalle invented the so-called "alien derivations" to handle these exponentially small discrepancies at the level of the formal series themselves. One gets a subalgebra of the commutative algebra of formal series in one indeterminate, endowed with infinitely many independent derivations. Various applications will be outlined.

Lecture 1:

Time: April 23, 4:00-6:00 pm