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SUMMARY:DisCoMath Seminar: Constructing Unitary Fusion Category Representations with the Jellyfish Algorithm
DTSTART:20211105T183000Z
DTEND:20211105T193000Z
UID:EVENT-180066@www.rit.edu/events
LOCATION:Thomas Gosnell Hall - 2305
DESCRIPTION: Discrete & Computational Math Seminar (DisCoMath)Constructing Unitary Fusion Category Representations with the Jellyfish Algorithm
Quinn KoltApplied Mathematics & Computer Science StudentSchool 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.
Speaker Webpage.
Intended Audience:Undergraduates, graduates, and experts. Those with interest in the topic.
Keep up with DisCoMath Seminars on the DisCoMathS webpage.To request an interpreter, please visit myaccess.rit.edu
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