Explore a comprehensive lecture on Floer theory and quantum groups presented by Sergei Gukov from CalTech. Delve into the long-anticipated connection between Vafa-Witten and Marcus-Kapustin-Witten theories and their relation to Floer homologies of 3-manifolds. Examine recent developments in direct computation of these invariants based on PDEs and moduli spaces. Investigate moduli spaces in 4D gauge theories and their computation for an infinite family of 3-manifolds relevant to various surgery operations, including the Gluck twist, knot surgeries, and log-transforms. Compare the results to skein modules of the same 3-manifolds and understand the importance of K-theoretic versions of these moduli spaces in relation to a three-dimensional Spin^c TQFT associated with quantum groups at generic values of the parameter q.