I discuss one and two-parameter solutions of sigma models on symmetric spaces contained in E11. Embedding one-parameter sigma model solutions in space-time give a metric which depends on harmonic functions typical in general relativity, supergravity and M-theory. Embedding two-parameter sigma model solutions in space-time give a metric which depends on general travelling wave functions in M* and M’-theory (theories which have space-time signatures with more than one time). Weyl reflection allows the latter solutions to be mapped to M-theory solutions where the wave functions depend explicitly on extra co-ordinates contained in the fundamental representation of E11. I will also give an example of two-time physics realisable in the laboratory

It will be shown how supersymmetry and superalgebras arise in lattice models both in one and higher dimensions. Examples using correlated fermions and bosons will be primarily used. Some of the examples will have associated superalgebras and others will have supersymmetry more commonly used in field theory. Some aspects of continuum limits will also be touched upon.