The SYZ conjecture for singular moduli spaces of sheaves on K3 surfaces

I will report about my recent joint work with Angel Rios Ortiz on the SYZ conjecture for a special class of singular symplectic varieties. The SYZ conjecture predicts that nef and isotropic line bundles are associated to lagrangian fibrations. After having recalled some generalities about symplectic varieties and the SYZ conjecture, I will state the main result and explain the main ideas behind its proof.