In this talk, I will introduced the deformed Hermitian Yang-Mills equation. Specifically, I will start from a local model of a section type special Lagrangian submanifold in a complex manifold with semi-flat Calabi-Yau metric. The sympletic structure of the special Lagrangian submanifold will give one some tips how to construct a complex submanifold in the mirror Calabi-Yau manifold. Moreover, this construction is deeply related to the deformed Hermitian Yang-Mills equation.
- Background knowledge: some basic complex geometry
- Naichung Conan Leung, Shing-Tung Yau, & Eric Zaslow. From Special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai Transform. Adv. Theor. Math. Phys. 4 (2000), no.6, 1319-1341.
- Adam Jacob, & Shing-Tung Yau. A special Lagrange type equation for holomorphic line bundles. arXiv:1411.7457.