Algebraic geometry | Conjectures

Mirror symmetry conjecture

In mathematics, mirror symmetry is a conjectural relationship between certain Calabi–Yau manifolds and a constructed "mirror manifold". The conjecture allows one to relate the number of rational curves on a Calabi-Yau manifold (encoded as Gromov–Witten invariants) to integrals from a family of varieties (encoded as period integrals on a variation of Hodge structures). In short, this means there is a relation between the number of genus algebraic curves of degree on a Calabi-Yau variety and integrals on a dual variety . These relations were original discovered by Candelas, De la Ossa, Green, and Parkes in a paper studying a generic quintic threefold in as the variety and a construction from the quintic Dwork family giving . Shortly after, Sheldon Katz wrote a summary paper outlining part of their construction and conjectures what the rigorous mathematical interpretation could be. (Wikipedia).

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Alessandro Chiodo - Towards a global mirror symmetry (Part 1)

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From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten

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From playlist Geometry

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Alessandro Chiodo - Towards a global mirror symmetry (Part 3)

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From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten

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Alessandro Chiodo - Towards a global mirror symmetry (Part 2)

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From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten

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From playlist Mathematics

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Tony Yue Yu - 1/4 The Frobenius Structure Conjecture for Log Calabi-Yau Varieties

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From playlist Mathematics

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Chiu-Chu Melissa Liu: On the remodeling conjecture for toric Calabi-Yau 3-orbifolds

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Open Gromov-Witten Invariants from the Fukaya Category - Kai Hugtenburg

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On the Gamma conjecture associated with toric flips - Hiroshi Iritani

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From playlist Mathematics

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From playlist Mathematics

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From playlist 23. The Big Bang, Inflation, and General Cosmology 2

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Mirror symmetry for chain type polynomials - Umut Varolgunes

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Related pages

Heterotic string theory | Kuranishi structure | Proj construction | Geometric invariant theory | Supersymmetry | String theory | Algebraic torus | Homogeneous polynomial | Deformation (mathematics) | Conformal equivalence | Generation (particle physics) | Hodge structure | Mirror symmetry (string theory) | Euler characteristic | Dwork family | Moduli of algebraic curves | Euler class | Lefschetz hyperplane theorem | Interior product | Quintic threefold | Gromov–Witten invariant | Homotopy associative algebra | Poincaré duality | Pseudoholomorphic curve | Canonical bundle | Cotangent complex | Symplectic geometry | Vector bundle | Kodaira–Spencer map | Blowing up | Hilbert space | Kähler manifold | Algebraic curve | Automorphism group | Period (algebraic geometry) | Line bundle | Chern class | Moduli space | Serre duality | Correlation function (quantum field theory) | Singularity (mathematics) | Virtual fundamental class | Calabi–Yau manifold | Crepant resolution