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, including their role as characters of logarithmic vertex algebras. Examine the integer coefficients of these q-series invariants as solutions to specific enumerative problems, and investigate their relationships to other 3-manifold invariants labeled by Spin and Spin-C structures when q approaches special values. Follow the lecture's progression through introductory concepts, key developments, definitions, graph theory, adjacency matrices, integrals, examples, and discussions on invariance and the Rokhlin variant.