Caltech-Tsinghua Joint Colloquium

Braiding of Verma modules for the quantum group U_{q} (sl_{2}) leads to a TQFT that associates q-series invariants to 3-manifolds equipped with Spin-C structures. One of the main interests in these invariants is that they are expected to admit categorification, thus providing new insights into the mysterious world of smooth 4-maniolds. Building on recent works with M.Jagadale and P.Putrov, we describe what this homological lift looks like with mod 2 coefficients. We prove that the proposed categorification is invariant under Kirby moves for all weakly negative definite plumbed manifolds.