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Algebraic Geometry Student Research Seminar

Friday, October 6, 2023 - 10:00am

Victor Alekseev



University of Pennsylvania


Mirror symmetry is a conjectural duality between pairs of Calabi-Yau manifolds with additional structures. We explain two instances of mirror symmetry. First, the number of rational curves on a quintic 3-fold can be obtained from the complex periods on the mirror manifold. Second, coherent sheaves on an elliptic curve are closely related to closed geodesics on a torus. Based on these observations, we formulate homological mirror symmetry as an equivalence of categories.