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Justin Hilburn, PMA 9.166: What is 3d Mirror Symmetry?
Tuesday, September 19, 2023, 02:00pm - 03:00pm
Relationships between quantum field theories, especially dualities, give rise to surprising connections between different areas of mathematics. Two celebrated examples are (2d) mirror symmetry, a duality of 2d QFTs, which unites algebraic geometry and symplectic topology and electric-magnetic duality, a duality of 4d QFTs, that underlies the geometric Langlands program. In this talk I will explain 3d mirror symmetry, a duality of 3d QFTs, and its relationship to its more established siblings. Just as in 2d, the QFTs in question admit two topological twists that are exchanged by mirror symmetry. The first, the 3d A-model, is constructed by counting solutions to the 3d Seiberg-Witten equations and the second, the 3d B-model or Rozansky-Witten, theory is constructed using algebraic geometry. We will see that the equivalence between these two TQFTs implies a set of well known conjectures due to Braden-Licata-Proudfoot-Webster.
Location: PMA 9.166

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