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BIMSA TQFT and Higher Symmetries Seminar
A target for ribbon 2-functors from higher derived Chern-Simons theory in 4d
A target for ribbon 2-functors from higher derived Chern-Simons theory in 4d
演讲者
时间
2025年04月08日 09:45 至 11:30
地点
A3-2-301
线上
Zoom 468 248 1222
(BIMSA)
摘要
Procedures for producing 3d topological invariants from the data of quantum group Hopf algebras are well-known. To lift these topological quantum field theories (TQFT) to higher-dimensions, we need to perform a categorification. However, many unknowns and difficulties still stand in our way. In this talk, I will propose a grounded approach to this problem, starting from a derived higher-homotopy generalization of the 3d Chern-Simons theory to 4-dimensions. By extracting the Hopf categorical quantum symmetries of the theory, I will show that the 2-category of its module categories is not only braided monoidal, but is in fact ribbon tensor. I will explain how the underlying Hopf category structure allows us to pinpoint when the 2-representation 2-category becomes sylleptic, and also to resolve a major problem plaguing pivotal 2-categories as described by Douglas-Reutter.
This is based on my recent works https://arxiv.org/abs/2501.06486 and https://arxiv.org/abs/2501.08041.
This is based on my recent works https://arxiv.org/abs/2501.06486 and https://arxiv.org/abs/2501.08041.