Modularity and Resurgence of Topological 3-manifolds Invariants

par Ioana Coman (IPMU)

mercredi 18 déc. 2024, 12:00 → 13:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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.

This talk will be streamed from Amphithéâtre Léon Motchane. The zoom link is also available by subscribing to the mailing list: sympa@listes.math.cnrs.fr