Some Generalized Geometry and Its Relation to M-theory
Generalized geometry is a new language in which all the fields of M-theory can be combined into a geometric whole. The basic idea is to make U-duality an explicit symmetry of the theory. This can be done for limits of M-theory in which fields are explicitly dependent on 4,5,6,7 and 8 co-ordinates and there are indications of how to make this work even in 11-dimensional spacetime. One way of looking at things is to use the E11 algebra as a tool to make the construction explicit. I will discuss some of the mathematics of generalized geometry, its relation to windings of the M2 brane, how U-duality emerges. I will also briefly say some things about supersymmetry and F-theory.