Geometry of Manifolds
A second-semester graduate course from MIT OpenCourseWare focused on symplectic manifolds, with extended digressions into complex geometry and the geometry of 4-manifolds, emphasizing topological considerations throughout. The course builds on a first course in differential geometry and works through symplectic linear algebra, symplectomorphisms, Lagrangian submanifolds, almost complex structures, and Kahler geometry, using 4-manifold examples to connect topology and geometry. Materials include detailed lecture notes covering each topic in sequence, assignments, and reference readings drawn from standard texts in symplectic and differential geometry. As with other MIT OpenCourseWare offerings, all materials are free to access and there is no certificate; the course is meant for self-study or supplementary use alongside a formal graduate program in mathematics.