IMSc Webinar

From Finite Groups to Vertex Operator Algebras: A Gentle Tour of Tensor Categories

Harshit Yadav

University of Alberta

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zoom.us/j/91383430608

Meeting ID: 913 8343 0608
Passcode: moonshine

Tensor categories offer a common language for symmetry. I will begin with a foundational example, the category of representations Rep(G) of a finite group G, and discuss the Tannakian viewpoint (Milne–Deligne). From there, I will explain why non-semisimple tensor categories naturally arise in diverse contexts, such as in positive characteristic, at roots of unity, and in logarithmic CFT. Along the way, I will highlight connections to subfactors, algebraic geometry, number theory, and low-dimensional topology.

The final part will focus on understanding the representation categories of Vertex Operator Algebras (VOAs). A recursive approach is useful here: one can analyze a few key examples (due to seminal works of Feigin, Frenkel, Kazhdan, Lusztig, Arakawa etc.) and then relate many others via constructions like extensions, cosets, and orbifolds. I will concentrate on VOA extensions and the underlying categorical mechanism, which involves commutative algebra objects and their local modules. This provides a clean framework for transferring properties like rationality and rigidity from one VOA to another, which we will illustrate with concrete examples.