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Hyperbolic billiard motion is the canonical example of classical and quantum chaos. However, if the billiard domain has certain arithmetic properties, the resulting quantum chaos is quite different and exhibits features that are more typical of integrable systems. I will review some of these features, which have connections to deep concepts from number theory. I will then explain how such arithmetic quantum chaotic systems arise naturally inside black holes, as the interior singularity is approached.

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Sean Hartnoll, Cambridge University
Seminar Room 0.03, ETP
Contact: Alexander Altland