Topics in Geometry: Dirac Geometry

A mathematical diagram.

A generalized complex structure on the projective plane with type change along a cubic curve. (Image courtesy of Marco Gualtieri.)


MIT Course Number


As Taught In

Fall 2006



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Course Description

Course Features

Course Description

This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry.

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This is a graduate-level course in Geometry. The content varies year to year, according to the interests of the instructor and the students.

Related Content

Marco Gualtieri. 18.969 Topics in Geometry: Dirac Geometry. Fall 2006. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

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