Abstract

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.