Generalized complex (GC) geometry is a relatively new field of study
that has its roots in Dirac geometry, and can be seen as generalizing
Poisson, complex, and symplectic geometry. Many concepts and methods
from symplectic geometry have been generalized and applied to GC
geometry. For instance, in 2006 Yi Lin and Susan Tolman developed a
notion of generalized Hamiltonian actions and generalized moment
maps. These maps have proven to have many properties analogous to
their symplectic counterparts.
In this talk, I will give an introduction to GC geometry and
generalized Hamiltonian actions, and discuss the reduction of a GC
manifold by a generalized Hamiltonian action.