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Explore recent advancements in link and 3-manifold invariants associated with Verma modules of U_q(sl_N) at generic q in this hour-long conference talk. Delve into the construction of these new invariants, which can be combined into a Spin^c-decorated TQFT and possess integer coefficients for links in general 3-manifolds. Learn about the potential for categorification of these invariants and the various components that may contribute to constructing 3-manifold homology. Examine a simpler set of homological invariants that categorifies the signed count of broken flows interpolating between different complex flat connections on a 3-manifold. Discover how this version of 3-manifold homology can be rigorously defined and proven to be invariant under Kirby-Neumann moves for plumbed 3-manifolds.
