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There are two ways to systematically characterize topological orders: one is based on ground states via mapping group representations (such as modular data S,T matrix in 2+1D), which works in any dimensions; the other is based topological excitations via modular tensor category in 2+1D, or higher categories in higher dimensions. The first approach do not need to know excitations.
Amir Khodaeian Karim
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Arkya Chatterjee (he/him)
No audio though, looks like she's muted
she is muted
my mic does not work
may be later