The Jacquet-Langlands correspondence of von Neumann dimensions over arithmetic groups

Abstract: We first show the local-global compatibility of Tamagawa measures and Plancherel measures under the local/global Jacquet-Langlands correspondence. We then prove that the global Jacquet-Langlands correspondence preserves von Neumann dimensions over arithmetic groups.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | video )

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Noncommutative geometry in NYC

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