In generalized geometry, one studies geometric structures on Courant algebroids, a generalisation of the tangent bundle of a manifold. A fundamental example is the generalized tangent bundle TM+T^***M of a manifold. Generalized complex (GC) structures are geometric structures unifying and extending both complex and symplectic structures.
In this talk, I will give a gentle introduction to generalized (complex) geometry. I will then focus on the deformation theory of GC structures on the generalized tangent bundle, as developed by Marco Gualtieri in his PhD thesis. In particular, he proved a theorem on the existence of locally complete families of GC deformations, extending a proof of Kuranishi for the classical result on deformations of complex structures.
If time permits, I will also discuss an extension of this result to a broader class of Courant algebroids, highlighting certain analytical aspects of the classical arguments of Kuranishi and Gualtieri that must first be revisited.
*The location is MR14 and not the usual room.*