November 7, 2019
1:50 pm
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3:00 pm
Cockins Hall 240
Title: Quadratic d-numbers and categorical dimensions
Speaker: Andrew Schopieray - MSRI
Abstract: In the context of conformal field theory, Moore and Seiberg claimed the study of modular tensor categories "should be viewed as a generalization of group theory". In this analogy the order of the group is the category's dimension, now taking values outside the natural numbers, which begs the question: what is the set of possible dimensions? This question is almost entirely open, but we provide a partial solution in the case the dimension lies in a quadratic extension of the rational numbers. Despite being a major source of open research questions, this material will be approachable to anyone with modest knowledge of undergraduate algebra.
