Tudor Dimofte - Tannaka/Koszul duality and line operators (part 1) скачать в хорошем качестве

Tudor Dimofte - Tannaka/Koszul duality and line operators (part 1)

Tudor Dimofte (University of Edinburgh); March 9, 2026 These seminars will focus on the representing line operators in topological and/or holomorphic QFT’s, from the perspective of categorical reconstruction theory. In particular, I’ll explain how fiber functors have several natural constructions in QFT, leading to field-theoretic incarnations of Tannaka and Koszul duality (following my own work but also many others, in particular work of Costello and collaborators). In the first talk, I’ll set up a general QFT framework for reconstruction theory, and discuss a basic application to constructing (generalized) quantum groups from 3d TQFT’s. In the second talk, I’ll consider 4d holomorphic-topological theories. I’ll review the work of Costello-Yamazaki-Witten on Yangians in 4d Chern-Simons theory, and explain how to generalize this to see structures such as Drinfeld coproducts. I’ll also generalize further to relate line operators in 4d Seiberg-Witten theories to CoHA’s of BPS states. In the final talk, I’ll consider 3d holomorphic-topological theories, and derive a new structure that I call a “dg-shifted” Yangian.