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Recent progress on the formal degree conjecture

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If you have a question about this talk, please contact Rong Zhou.

The local Langlands correspondence is more than a bijective correspondence: it promises an extensive dictionary between the representation theory of reductive p-adic groups and the arithmetic of their L-parameters. One entry in this dictionary is a conjectural formula of Hiraga, Ichino, and Ikeda for the size of a discrete series representation—its “formal degree”—in terms of a gamma factor of its L-parameter. In this talk, I’ll explain why the conjecture is true for almost all supercuspidal representations. Time permitting, I’ll also compute the sign of the gamma factor, verifying a conjecture of Gross and Reeder.

This talk is part of the Number Theory Seminar series.

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