18.969 Topics in Geometry

Fall 2006

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

Course Highlights

This course features an extensive set of assignments and lecture notes.

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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Prof. Marco Gualtieri

Course Meeting Times

Two sessions / week
1.5 hours / session