Session S16 - Quantum symmetries

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Knots and Links in Modular Tensor Categories

Sung Kim

University of Southern California, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Modular Tensor Categories (MTCs) are algebraic structures that are equivalent to $(2+1)$-topological quantum field theories. Knot theory has become a powerful practical tool to help us understand and distinguish MTCs. Since the advent of MTCs, it has been conjectured that these categories are classified just by their modular data $(S, T)$ where $S$ and $T$ are invariants derived from the Hopf link and once-twisted unknot respectively. However, Mignard and Schauenburg recently disproved this conjecture by studying a specific class of MTCs known as the twisted quantum double of finite groups. As a result, the study of other knot and link invariants beyond the modular data is important to advance in the classification of MTCs. In this poster, I will provide a basic introduction to MTCs and a new construction technique known as zesting. I will also discuss a particular link invariant, the $W$-matrix, that is derived from the Whitehead link and how zesting affects knot and link invariants.

Joint work with Julia Plavnik (Indiana University Bloomington) and Colleen Delaney (Indiana University Bloomington).

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