211116 Gil Cavalcanti

Generalised complex structures are a simultaneous generalisation of complex and symplectic manifolds, but differently from those two cases, generalised complex structures are not homogeneous and have nontrivial local invariants. In fact, in a connected manifold the structure can be symplectic at some points and complex at other points, that is, its type can change. This type changing behaviour is a rich source of puzzles. I will review the basics of generalised complex geometry, including its applications, then explain the main results that allow us to deal with these type change points and possible consequences of these. This talk is based on joint work with Bailey and Leer-Duran.