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3-dimensional mirror symmetry
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This expository article discusses recent advances in understanding 3-dimensional mirror symmetry and the mathematical definitions of the Higgs and Coulomb branches. This is a slightly expanded version of an article appearing in the Notices of the AMS.
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Supersymmetry for brane diagrams and bow varieties
For affine type A bow diagrams, non-emptiness of the associated bow variety is equivalent to supersymmetry of the corresponding brane diagram, which can be checked by a finite set of inequalities.
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