January 12, 2021
TITLE: From resurgence to topological strings
ABSTRACT:
The theory of resurgence suggests that the perturbative series that we often calculate
in physics and mathematics are the tip of the iceberg in an extended structure, involving generalized formal power series (also called trans-series), and relations between them, encoded in Stokes constants. In topological field and strings theories, these additional sectors potentially provide new topological invariants for geometric objects. In this talk, after introducing some basic tools of the theory of resurgence, I will discuss the example of complex Chern-Simons theory, where Stokes constants provide an infinite number of integer invariants of hyperbolic knots.
I will also discuss what is known in the case of topological strings and enumerative invariants of Calabi-Yau threefolds, and present some open problems.
