In 2014 Gaiotto conjectured a Lagrangian correspondence between holomorphic Lagrangian of opers in the Dolbeault moduli space of Higgs bundles ​and the de Rham moduli space of holomorphic connections. ​The conjecture was solved in 2016 for holomorphic opers in paper with Fredrickson, Kydonakis, Mazzeo, Mulase and Neitzke. ​ By a similar analysis method, Collier and Wentworth, extended the correspondence for more general Lagrangians consisting of stable points. ​ In my talk, I will present an algebraic geometry description of the Lagrangian correspondence of Gaiotto, based on the work of Simpson.​