I review the theory of non-linear realisations and Kac-Moody algebras, I explain how to construct the non-linear realisation based on the Kac-Moody algebra $E_{11}$ and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a spacetime with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of spacetime, lead to precisely the equations of motion of eleven dimensional supergravity theory. By taking different group decompositions of $E_{11}$ we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the non-linear realisation is a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the $E_{11}$ conjecture given many years ago.

It has been conjectured that the fundamental theory of strings and branes has an $E_{11}$ symmetry. I will explain how this conjecture leads to a generalized space-time, which is automatically equipped with its own geometry, as well as equations of motion for the fields that live on this generalized space-time.

We will review the conjecture that the Kac-Moody Symmetry E_11 is an underlying symmetry of strings and branes. We will show that it leads to a generalised geometry involving an extension of our usual formulation of space-time.