Number of irreducible representations in the cuspidal automorphic spectrum

Abstract: Let \(G\) be a reductive group defined and split over a global function field. We are interested in the sum of multiplicities of irreducible representations containing a regular depth zero representation of \(G(O)\), where \(O\) is the ring of integral adeles, in the automorphic cuspidal spectrum. The sum is expressed in terms of the number of \(\mathbb{F}_q\)-points of Hitchin moduli spaces of groups associated to \(G\). When \( G=GL(n) \), it implies some cases of Deligne's conjecture by Langlands correspondence.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom info: TBA

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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