Explore the intricacies of Lagrangian subvarieties within irreducible symplectic (or hyper-Kaehler) manifolds in this one-hour seminar talk. Delve into the properties of these mathematical structures, with a particular focus on their interaction with Lagrangian fibrations of the ambient hyper-Kähler. Examine the albanese dimension of Lagrangian surfaces and gain insights into the complex relationships between these geometric entities. Presented as part of the IMSA Seminar series, this advanced mathematical discussion offers a deep dive into the realm of differential geometry and symplectic topology.