Topics in Geometry: Dirac Geometry
A graduate-level MIT OpenCourseWare course on generalized geometry, centered on Dirac geometry as developed by Courant, Weinstein, and Severa, alongside generalized complex geometry as introduced by Hitchin. The course treats Dirac geometry as a way to unify Poisson structures with closed 2-forms, and shows how generalized complex geometry merges complex and symplectic geometry, tying it to mirror symmetry. Materials include lecture notes covering the theoretical development of these structures, aimed at first-year graduate students with a solid background in differential geometry. As with other MIT OCW offerings, the course is free to study, with no certificate attached, and is meant for self-directed learners working through the notes at their own pace rather than following video lectures.