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Non-Abelian states in quantum Hall systems

Fractional quantum Hall systems are archetypes for topological order--systems which exhibit fractionalization and support anyonic statistics. In particular, some of these quantum Hall states are conjectured to possess non-Abelian anyons; emergent particles whose braiding can be used to perform quantum computations. In this talk, I will give an overview of non-Abelian topological order and their status pertaining to quantum Hall systems. I will then suggest possible avenues to realizing more exotic non-Abelian states.