From Turaev to Rokhlin via VOA Characters and Curve Counting

Explore a comprehensive lecture on new q-series invariants of 3-manifolds labeled by Spin-C structures, delivered by Sergei Gukov from the California Institute of Technology. Delve into the topological origins of these invariants and discover their unexpected properties and connections to other mathematical areas, such as characters of logarithmic vertex algebras. Examine the interpretation of integer coefficients in these q-series invariants as solutions to specific enumerative problems. Investigate the relationships between these invariants and other 3-manifold invariants labeled by Spin and Spin-C structures when q approaches special values. Cover topics including motivation, properties, early papers, logarithmic VOA, examples, Dramafitpt homology, Fagin, and branches throughout this in-depth exploration of advanced mathematical concepts.