Abstract:

Generalized geometry is a recent approach to geometric structures encompassing symplectic and complex geometry. At its heart lies a Clifford module, which is essentially a global version of the spin representation of the Clifford algebra.

In this talk I will give an introduction to generalized geometry from the Clifford algebra viewpoint, survey the main achievements of the theory and mention some recent results (joint with Joan Porti) concerning 3-manifolds.