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.)

Instructor(s)

MIT Course Number

18.969

As Taught In

Fall 2006

Level

Graduate

Cite This Course

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.

Other OCW Versions

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

Gualtieri, Marco. 18.969 Topics in Geometry: Dirac Geometry, Fall 2006. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-969-topics-in-geometry-dirac-geometry-fall-2006 (Accessed). License: Creative Commons BY-NC-SA


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