Hermann Nicolai (AEI, Potsdam)

Abstract: As shown a long time ago by Belinskii, Khalatnikov and
Lifshitz (BKL) the generic solutions of the vacuum Einstein equations
exhibit chaotic oscillations in the vicinity of a spacelike (cosmological)
singularity. In this talk it will be shown that the presence or absence
of chaos in Einstein's theory and its generalizations is rooted in the
structure of the fundamental Weyl chamber of some underlying indefinite
Kac Moody algebra. A novel proposal is made for an effective description
of this system in terms of a sigma-model over a coset space G/H in one
(time) dimension, where G is the "group" associated with the indefinite
Kac Moody algebra, and H is its "maximal compact subgroup". For D=11
supergravity (and thus M theory), the relevant algebra is the maximally
extended hyperbolic Kac Moody algebra E10.