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Explore a one-hour lecture delving into a novel approach to mirror symmetry developed by Abouzaid, Groman, and Varolgunes, focusing on homological mirror symmetry (HMS) for symplectic Calabi-Yau manifolds. Learn how HMS provides access to derived Fukaya categories of compact symplectic CY manifolds through the derived category of coherent sheaves of mirror CYs. Examine the extensive literature on conjectural mirrors of complete intersection CYs in toric varieties based on combinatorial ansatz, and understand emerging HMS proofs, particularly Seidel's technique of proving HMS in large volume limits with deformation arguments. Discover intrinsic mirror construction methods like the Gross-Siebert program and Fukaya's Family Floer theory that directly incorporate quantum corrections, applicable to broader classes of symplectic CYs and offering deeper structural understanding of mirror symmetry.
