"Three distinct geometries on S7 arise as solutions of the classical equations of motion in eleven dimensions. In addition to the conventional riemannian geometry, one can also obtain the two exceptional Cartan-Schouten compact flat geometries with torsion."

“The BEH mechanism operates within the context of gauge theories. Despite the fact that grand unification schemes reach scales comparable to the Planck scale, there was, a priori, no indication that Yang-Mills fields offer any insight into quantum gravity. The only approach to quantum gravity that had some success, in particular in the context of a quantum interpretation of the black hole entropies, are the superstring theory approaches and the possible merging of the five perturbative approaches into an elusive M-theory whose classical limit would be 11-dimensional supergravity.”

“What we hear about eternal inflation or the string landscape, seems somehow unavoidably to lead to some kind of multiverse. However, it seems to me there is a fundamental problem there. Once of course you have the multiverse, then you can start playing around and try to find probability or getting to the anthropic principle, or whatever. But the point is that the picture is essentially a classical one, and it is difficult to see that if you have many universes, coming essentially with an inflationary state, that there would not be plenty of horizons in this. Now the quantum mechanics of horizons is, I think, perfectly not understood. The simplest example is the black hole, where after all nobody knows really if the problem lies in the singularity or if it lies really already in the horizon.”