In this talk we will introduce fusion categories and discuss how they are classified. Starting from the definition of a category and focusing on examples arising from finite groups, we will introduce the necessary algebraic structures and properties, highlighting their description in terms of solutions to various sets of polynomial equations. If there's time we'll talk about techniques used for classification and the state of affairs for various notions of equivalence. The talk will be fairly elementary, requiring at most some group theory and linear algebra.
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