DisCoMath Seminar: Constructing Unitary Fusion Category Representations with the Jellyfish Algorithm
Discrete & Computational Math Seminar (DisCoMath)
Constructing Unitary Fusion Category Representations with the Jellyfish Algorithm
Quinn Kolt
Applied Mathematics & Computer Science Student
School of Mathematical Sciences, RIT
Abstract:
The graphical calculus is a modern technique for classifying and constructing “unitary fusion” categories, categories which model elementary particles that merge and split. In particular, if one can obtain enough diagrammatic relations to evaluate all “closed” diagrams, this graphical calculus uniquely describes the category. However, in order to prove existence, one must also find a representation of the category. Cuntz algebras, a type of C*-algebra, are a natural home for the representations of many fusion categories. The Jellyfish algorithm allows us to use diagrams to find what these Cuntz algebra representations should be in an intuitive way. Using this computation, we can then prove existence by showing that this construction is indeed a well-defined representation in the associated Cuntz algebra. In this talk, I will apply this process on the unitary fusion category with Fibonacci fusion rules.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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