Abstract:

One of the most interesting open conjectures in geometry is the SYZ conjecture. It roughly states that (complex) 3D Calabi Yau manifold should admit a fibration over a (real) 3D base such that the smooth fibres are special Lagrangian tori. Gukov, Yau, and Zaslow speculated further on the existence of similar fibrations for G2 manifolds. In this talk we will give a brief introduction to G2-manifolds, their calibrated submanifolds and a discussion of how such fibrations with K3 fibres could look like.