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A natural problem in the study ofÌýlocalÌýsystemsÌýon complex varieties is to characterize those that arise in a family of varieties. We refer to suchÌýlocalÌýsystemsÌýas motivic. Simpson conjectured that for a reductive group G,ÌýrigidÌýG-localÌýsystemsÌýwith suitable conditions at infinity are motivic. This was proven for curves when G = GL_n by Katz who classified suchÌýrigidÌýlocalÌýsystems. In this talk, we prove Simpson's conjecture for curves for an arbitrary reductive group G. Our proof goes through the (tamely ramified)Ìý geometric Langlands program in characteristic zero. If time permits, we state a generalization of Simpson's conjecture to an arbitrary smooth projective variety.