Seminar 1: 14:00-15:00 March 4, 2025

Part I: Non-abelian flat connections

- It is expected that saddle points and associated perturbative series of the path integral of a quantum theory are related by their resurgent properties. This is exemplified in complex Chern-Simons theory. We discuss the construction of partition function of sl2C Chern-Simons theory on hyperbolic knot complements as state integrals, and study the resurgent properties of the perturbative series of the state integrals. The complete set of Stokes constants are calculated. We emphasize that this construction miss the trivial saddle point corresponding to the abelian flat connection on the three manifold.

Seminar 2: 10:00-11:00 March 6, 2025
Part II: BPS interpretation, abelian flat connections
- We explore the relation between sl2C Chern-Simons theory and 3d SCFT and discuss the interesting revelation that the Stokes constants in the former theory are BPS invariants in the latter theory. We also discuss how to extend the resurgent structure in sl2C Chern-Simons to include abelian flat connections and the associated perturbative series.