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Mathematics Colloquium

Nick Gurski
Case Western Reserve University

Title: More multiplications please! Higher Tannaka reconstruction and trialgebras
Date: Friday, February 5, 2021
Place and Time: Zoom, 3:05-3:55 pm

Abstract. A topological quantum field theory (TQFT) is a gadget for turning manifolds into algebra. You can construct these directly in low dimensions, and a now-classic theorem of Abrams characterizes 2-dimensional TQFTs as being equivalent to commutative Frobenius algebras. This classification shows how an algebraic description of a TQFT usually involves something more complicated than just a ring. You can try to understand this extra structure on a ring using Tannaka reconstruction, a theory that identifies features of a ring with features of its category of modules. I will try to explain some of the relationship between TQFTs and Tannaka reconstruction, and then describe a joint project with David Yetter in which we work on extending these relationships to a 2-categorical context in order to construct the trialgebras of Crane-Frenkel and apply them to the study of 4-dimensional TQFTs.