Modularity and resurgence of topological 3-manifold invariants
byIoana Coman
Abstract:A type of BPS q-series, proposed recently as a topological invariant which provides a non-perturbative completion of complex Chern-Simons theory on closed 3-dimensional manifolds, has mathematical definitions based for example on 3D topology, quantum groups and resurgence, and key properties their integrality and behaviour under surgery formulae. These q-series invariants have displayed relations to vertex operator algebras, and structurally, they have intriguing modular properties. Their mathematical formulation is nevertheless quite constrained, relying heavily on certain negative-definite conditions, and much effort has been devoted to extending this definition. This operation is called “going to the other side”, with different interpretations from the physics, vertex algebra, and 3D topology perspectives. I will discuss different approaches to this challenge, in particular through modularity and resurgence, with implications for the related vertex operator algebras.
All talks Fall '24: New trends in QFT, modularity, resurgence