A generalized complex structure on the projective plane with type change along a cubic curve. (Image courtesy of Marco Gualtieri.)
Instructor(s)
Prof. Marco Gualtieri
MIT Course Number
18.969
As Taught In
Fall 2006
Level
Graduate
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.