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Posted April 16, 2025

Algebra and Number Theory Seminar Questions or comments?

Andrew Riesen, MIT
Orbifolds of Pointed Vertex Algebras

We will discuss the interplay of tensor categories $C$ with some group action $G$ and orbifolds $V^G$ of vertex operator algebras (VOAs for short). More specifically, we will show how the categorical structure of $\mathrm{TwMod}_G V$ allows one to not only simplify previous results done purely through VOA techniques but vastly extend them. One such example is the Dijkgraaf-Witten conjecture, now a theorem, which describes how the category of modules of a holomorphic orbifold should look like. Additionally, our techniques also allow us to expand the modular fusion categories known to arise from VOAs, we show that every group-theoretical fusion category comes from a VOA orbifold. This talk is based on joint work with Terry Gannon.