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Thirty years ago, work of Witten and Reshetikhin-Turaev activated the study of quantum invariants of links and three-manifolds. A cornerstone of subsequent developments was a three-pronged approach involving 1) quantum field theory (Chern-Simons); 2) rational VOA's (WZW); and 3) semisimple representation theory of quantum groups. The second and third perspectives have since been extended, to logarithmic VOA's and related non-semisimple quantum-group categories. I will propose a family of 3d quantum field theories that similarly extend the first perspective to a non-semisimple (and more so, derived) regime. The 3d QFT's combine Chern-Simons theory with a topologically twisted supersymmetric theory. They support boundary VOA's whose module categories are dual to modules for Feigin-Tipunin algebras and (correspondingly) to modules for small quantum groups at even roots of unity. The QFT is also compatible with deformations by flat connections, related to the center of quantum groups at roots of unity.

This is joint work with T. Creutzig, N. Garner, and N. Geer.

This Zoom talk for the audience in MSB 1147 will be followed by meet-and-greet with interested graduate students on MSB patio. RSVP by Wednesday 9/29, 2pm to gradadvisor@math.ucdavis.edu if you would like lunch.