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On Fusion categories, gradings, and representations of Hopf algebras

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If you have a question about this talk, please contact Nathan Bowler.

Fusion categories arise in several areas of mathematics, for example in the representation theory of finite dimension Hopf algebras and in topological quantum field theories. My goal in this talk will be to give an exposition to the theory of fusion categories, and to explain why the categorical point of view is very fruitful in the study of finite dimensional semisimple Hopf algebras. I will explain some basic notions in the field, such as module categories, dual categories, categorical centers and gradings. I will also explain what examples we have for fusion categories, and their connection to finite groups and their cohomology.

This is joint work with Evgeny Musicantov.

This talk is part of the Category Theory Seminar series.

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