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This will be an introductory talk to the speaker's later talk in the Geometry/topology Seminar: In this talk I will define a complex version of the special Lagrangian graph equation with potential introduced by Harvey-Lawson. I will discuss existence of solutions on a compact Kahler manifold under certain analytic assumptions. I will also talk about a conjecture relating existence in general to an algebro-geometric notion of stability (analogous to slope stability for holomorphic vector bundles), and provide motivation from mirror symmetry. This is joint work with Tristan C. Collins and S.-T. Yau.