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Young Seminar
Organizers: Douglas Lundholm (IHP/IHES) & Julien Sabin (Cergy)


Jakob Palmkvist (IHÉS): "Arithmetic quantum gravity and hyperbolic Weyl groups"
Wednesday 10 July 2013, 14:00 - 15:00
Amphithéâtre Darboux


Abstract: In many gravity theories, the dynamics of the metric exhibits a chaotic behavior in the limit near a spacelike singularity. It can be described by a billard motion, controlled by the Weyl group of a hyperbolic Kac-Moody algebra, which for pure four-dimensional gravity is an infinite-dimensional extension of the Lie algebra sl(2,R). This approximation provides an approach to quantum gravity where the solutions of the Wheeler–DeWitt equation are given by automorphic forms of the Weyl group, realized as the modular group PGL(2,Z). I will explain this modular realization of the hyperbolic Weyl group, and generalizations to other theories, in particular eleven-dimensional supergravity. The talk is based on the paper arXiv:1010.2212 with Axel Kleinschmidt and Hermann Nicolai.