If you want to have the progressive idea of unifying the geometry of a Poisson Structure with a closed two-form, unifying generalized complex geometry with complex and symplectic geometry, Dirac geometry is a must which is facilitated for you in this [course_title]. This [course_title] will help you gleam in the field of Linear Algebra of a Split-Signature Real Bilinear Form, Hodge Decomposition Theorem, Hermitian Geometry, Equivalence Theorem etc.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer need to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: MIT
Course Curriculum
| Smooth manifolds, geometry of foliations, and symplectic structure. | 00:30:00 | ||
| Comments on previous lecture, symplectic manifolds, and Poisson geometry. | 00:45:00 | ||
| Almost complex structure, Hermitian structure, integrability of J, forms on a complex manifold, and Dolbeault cohomology. | 00:30:00 | ||
| Geometry of V+V*, linear Dirac structures, and generalized matrices. | 00:45:00 | ||
| Spinors, the spin group, a bilinear pairing on spinors, and pure spinors. | 00:45:00 | ||
| Generalized Hodge star, and spinors for TM+T*M and the Courant algebroid. | 00:45:00 | ||
| Exact Courant algebroids, and Severa’s classification of exact Courant algebroids. | 00:30:00 | ||
| Dirac structures, and geometry of Lie groups. | 00:45:00 | ||
| Bilinear forms on groups | 00:30:00 | ||
| Integrability, Dirac maps, and manifolds with Courant structure. | 00:45:00 | ||
| Integrability and spinors, and Lie bialgebroids and deformations | 00:30:00 | ||
| Generalized complex structures and topological obstructions, intermediate cases, spinorial description, and introduction to Hermitian geometry. | 01:00:00 | ||
| Generalized Kahler geometry. | 00:30:00 | ||
| Linear algebra, and T-duality. | 00:30:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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