Conformal Geometric Algebra
This is an extension of geometric algebra that by working in a higher dimensional space one can represent both translations as well as rotations via rotors, in a unified way. This has been very important for my recent work and has led me to finding, like Prof. Almeida, that a 5d space with signature (+,-,-,-,-) is a key area for physics. The conformal geometric algebra is a key feature of setting this up, and has allowed me to get 'geometric' versions of electromagnetism and Dirac theory, in which translations can be done by rotors, and reduce down in a sensible way to an underlying 4d space. The latter, crucially, however, turns out to be de Sitter space, which now becomes the base space for EM and Dirac theory in 4d. I have also got quite a long way in setting up gravity this way, though that is not yet complete. I will go through the basics of the conformal geometric algebra, which is interesting in its own right just from the geometry point of view, and then tie this in with cosmology, gravity, EM theory and Dirac theory. It even feeds through to give an insight into the 'holography' that is very popular in string theory at the moment, and gives a concrete realisation of it.