DisCoMath Seminar: Constructing Unitary Fusion Category Representations with the Jellyfish Algorithm

Event Image
discomath seminar quinn kolt

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


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

Brendan Rooney
Event Snapshot
When and Where
November 05, 2021
2:30 pm - 3:30 pm
Room/Location: 2305

This is an RIT Only Event

Interpreter Requested?


student experience