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Generalised Geometry for String and M-theory
The spacetimes that provide backgrounds for string and for M-theory have hidden symmetries when compactified on a d-dimensional at torus. These are variously the S,T or U-dualities and are controlled by Od;d for string theory and the exceptional groups Ed for M-theory in the cases
d = 4; 5; 6; 7 or 8. Generalised geometry is a description of the backgrounds if there are no compactification onto a torus. We will describe the generalised geometry for these simple cases and then move on to how one can see generalised geometry arises from the E11 construction. The construction shows how dualities can be made manifest as symmetries of the theory even in the absence of symmetries of the background or compactification. We will end with some observations about how one can construct gauged versions of the theory and on the quantised string and M2-branes.