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Dave Penneys : Planar algebras and evaluation algorithms

Jones' planar algebras are a useful tool for studying and constructing fusion categories, which generalize the representation categories of (quantum) groups. Thus we think of fusion categories and planar algebras as encoding quantum symmetries. I will give an overview of Jones' planar algebras with attention to specific examples. Along the way, we will discuss several evaluation algorithms which give quantum invariants, including the Jones polynomial.

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