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Noncommutative Geometry Seminar - Cain Edie-Michell

Noncommutative Geometry Seminar
November 8, 2018
1:50PM - 2:45PM
Math Building 105

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Add to Calendar 2018-11-08 13:50:00 2018-11-08 14:45:00 Noncommutative Geometry Seminar - Cain Edie-Michell Title: Classifying fusion categories generated by an object of small dimension. Speaker: Cain Edie-Michell (Vanderbilt University) Abstract: One of the main goals in the study of fusion categories is to provide a complete classification result. However at the current time not even a conjectural description of all fusion categories has been given. Because a complete classification is completely out of reach with current techniques, current research on fusion categories focuses on classifying ``small” fusion categories, where small can have a variety of different meanings. For this talk, small will mean generated by an object of small Frobenius-Perron dimension. I will discuss a recent partial classification result of mine along these lines. I assume the generating object has dimension less than 2, along with a mild assumption on the commutativity of the generating object. This classification contains some very surprising categories, including some exceptional quantum subgroups. Math Building 105 Department of Mathematics math@osu.edu America/New_York public

Title: Classifying fusion categories generated by an object of small dimension.

Speaker: Cain Edie-Michell (Vanderbilt University)

Abstract: One of the main goals in the study of fusion categories is to provide a complete classification result. However at the current time not even a conjectural description of all fusion categories has been given. Because a complete classification is completely out of reach with current techniques, current research on fusion categories focuses on classifying ``small” fusion categories, where small can have a variety of different meanings. For this talk, small will mean generated by an object of small Frobenius-Perron dimension. I will discuss a recent partial classification result of mine along these lines. I assume the generating object has dimension less than 2, along with a mild assumption on the commutativity of the generating object. This classification contains some very surprising categories, including some exceptional quantum subgroups.

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